Visual objects are composed of a recursive hierarchy of perceptual wholes and parts, whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance. However, object appearance is the compositional consequence of both an object’s intrinsic and extrinsic causal factors, where the extrinsic causal factors are related to illumination, and imaging conditions. Therefore, this paper proposes a unified tensor model of wholes and parts, and introduces a compositional hierarchical tensor factorization that disentangles the hierarchical causal structure of object image formation, and subsumes multilinear block tensor decomposition as a special case. The resulting object representation is an interpretable combinatorial choice of wholes’ and parts’ representations that renders object recognition robust to occlusion and reduces training data requirements. We demonstrate ourapproach in the context of face recognition by training on an extremely reduced dataset of synthetic images, and report encouragingface verification results on two datasets – the Freiburg dataset, andthe Labeled Face in the Wild (LFW) dataset consisting of real world images, thus, substantiating the suitability of our approach for data starved domains.

Multiple imputation is widely used to handle confounders missing at random in causal inference. Although Rubin’s combining rule is simple, it is not clear weather or not the standard multiple imputation inference is consistent when coupled with the commonly-used average causal effect (ACE) estimators. This article establishes a unified martingale representation for the average causal effect (ACE) estimators after multiple imputation. This representation invokes the wild bootstrap inference to provide consistent variance estimation. Our framework applies to asymptotically normal ACE estimators, including the regression imputation, weighting, and matching estimators. We extend to the scenarios when both outcome and confounders are subject to missingness and when the data are missing not at random.

Machine learning practice is often impacted by confounders. Confounding can be particularly severe in remote digital health studies where the participants self-select to enter the study. While many different confounding adjustment approaches have been proposed in the literature, most of these methods rely on modeling assumptions, and it is unclear how robust they are to violations of these assumptions. This realization has recently motivated the development of restricted permutation methods to quantify the influence of observed confounders on the predictive performance of a machine learning models and evaluate if confounding adjustment methods are working as expected. In this paper we show, nonetheless, that restricted permutations can generate biased estimates of the contribution of the confounders to the predictive performance of a learner, and we propose an alternative approach to tackle this problem. By viewing a classification task from a causality perspective, we are able to leverage conditional independence tests between predictions and test set labels and confounders in order to detect confounding on the predictive performance of a classifier. We illustrate the application of our causality-based approach to data collected from mHealth study in Parkinson’s disease.

Large-scale trends in urban crime and global terrorism are well-predicted by socio-economic drivers, but focused, event-level predictions have had limited success. Standard machine learning approaches are promising, but lack interpretability, are generally interpolative, and ineffective for precise future interventions with costly and wasteful false positives. Here, we are introducing Granger Network inference as a new forecasting approach for individual infractions with demonstrated performance far surpassing past results, yet transparent enough to validate and extend social theory. Considering the problem of predicting crime in the City of Chicago, we achieve an average AUC of ~90\% for events predicted a week in advance within spatial tiles approximately $1000$ ft across. Instead of pre-supposing that crimes unfold across contiguous spaces akin to diffusive systems, we learn the local transport rules from data. As our key insights, we uncover indications of suburban bias — how law-enforcement response is modulated by socio-economic contexts with disproportionately negative impacts in the inner city — and how the dynamics of violent and property crimes co-evolve and constrain each other — lending quantitative support to controversial pro-active policing policies. To demonstrate broad applicability to spatio-temporal phenomena, we analyze terror attacks in the middle-east in the recent past, and achieve an AUC of ~80% for predictions made a week in advance, and within spatial tiles measuring approximately 120 miles across. We conclude that while crime operates near an equilibrium quickly dissipating perturbations, terrorism does not. Indeed terrorism aims to destabilize social order, as shown by its dynamics being susceptible to run-away increases in event rates under small perturbations.

Pragmatic randomized trials are designed to provide evidence for clinical decision-making rather than regulatory approval. Common features of these trials include the inclusion of heterogeneous or diverse patient populations in a wide range of care settings, the use of active treatment strategies as comparators, unblinded treatment assignment, and the study of long-term, clinically relevant outcomes. These features can greatly increase the usefulness of the trial results for patients, clinicians, and other stakeholders. However, these features also introduce an increased risk of non-adherence, which reduces the value of the intention-to-treat effect as a patient-centered measure of causal effect. In these settings, the per-protocol effect provides useful complementary information for decision making. Unfortunately, there is little guidance for valid estimation of the per-protocol effect. Here, we present our full guidelines for analyses of pragmatic trials that will result in more informative causal inferences for both the intention-to-treat effect and the per-protocol effect.

Causal ML benchmarking and development tools

In the end what does Causality have to do with machine learning? Machine Learning is about prediction and causality about real effects, do these two themes have something in common? Yes, a lot in common and this series of posts tries to bridge these two sub-areas of Data Science. I like to think that Machine Learning is just a Data Grinder, if you put good quality data, you get good quality predictions, but if you put garbage, it will keep grinding, but don’t expect good predictions to come out, it’s just ground garbage , and that’s what we’ll talk about in this post.

Convolutional neural networks (CNNs) with dilated filters such as the Wavenet or the Temporal Convolutional Network (TCN) have shown good results in a variety of sequence modelling tasks. However, efficiently modelling long-term dependencies in these sequences is still challenging. Although the receptive field of these models grows exponentially with the number of layers, computing the convolutions over very long sequences of features in each layer is time and memory-intensive, prohibiting the use of longer receptive fields in practice. To increase efficiency, we make use of the ‘slow feature’ hypothesis stating that many features of interest are slowly varying over time. For this, we use a U-Net architecture that computes features at multiple time-scales and adapt it to our auto-regressive scenario by making convolutions causal. We apply our model (‘Seq-U-Net’) to a variety of tasks including language and audio generation. In comparison to TCN and Wavenet, our network consistently saves memory and computation time, with speed-ups for training and inference of over 4x in the audio generation experiment in particular, while achieving a comparable performance in all tasks.

This study proposes a new Bayesian approach to infer average treatment effect. The approach treats counterfactual untreated outcomes as missing observations and infers them by completing a matrix composed of realized and potential untreated outcomes using a data augmentation technique. We also develop a tailored prior that helps in the identification of parameters and induces the matrix of the untreated outcomes to be approximately low rank. While the proposed approach is similar to synthetic control methods and other relevant methods, it has several notable advantages. Unlike synthetic control methods, the proposed approach does not require stringent assumptions. Whereas synthetic control methods do not have a statistically grounded method to quantify uncertainty about inference, the proposed approach can estimate credible sets in a straightforward and consistent manner. Our proposal approach has a better finite sample performance than the existing Bayesian and non-Bayesian approaches, as we show through a series of simulation studies.

We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can benefit from an analysis that takes into account the distributional changes across environments. In particular, it is useful to distinguish between stable and unstable predictors, i.e., predictors which have a fixed or a changing functional dependence on the response, respectively. We introduce stabilized regression which explicitly enforces stability and thus improves generalization performance to previously unseen environments. Our work is motivated by an application in systems biology. Using multiomic data, we demonstrate how hypothesis generation about gene function can benefit from stabilized regression. We believe that a similar line of arguments for exploiting heterogeneity in data can be powerful for many other applications as well. We draw a theoretical connection between multi-environment regression and causal models, which allows to graphically characterize stable versus unstable functional dependence on the response. Formally, we introduce the notion of a stable blanket which is a subset of the predictors that lies between the direct causal predictors and the Markov blanket. We prove that this set is optimal in the sense that a regression based on these predictors minimizes the mean squared prediction error given that the resulting regression generalizes to unseen new environments.

Learning about causal relationships on the basis of empirical observation is not a trivial task. The classical scientific approach of running repeated independent controlled randomized experiments to measure effects of causes is limited in practice due to ethical, financial, political, temporal or other constraints. In particular, it can be infeasible to replicate controlled conditions to answer real-world questions regarding the impact of a policy or a program currently in place, i.e. to measure the effect of a treatment on a set of outcomes of interest. However, for empirically informed policy or general decision making, knowing about the fundamental causal relationships is crucial.

Even though the topic of explainable AI/ML is very popular in text and computer vision domain, most of the previous literatures are not suitable for explaining black-box models’ predictions on general data mining datasets. This is because these datasets are usually in high-dimensional vectored features format that are not as friendly and comprehensible as texts and images to the end users. In this paper, we combine the best of both worlds: ‘explanations by intervention’ from causality and ‘explanations are contrastive’ from philosophy and social science domain to explain neural models’ predictions for tabular datasets. Specifically, given a model’s prediction as label X, we propose a novel idea to intervene and generate minimally modified contrastive sample to be classified as Y, that then results in a simple natural text giving answer to the question ‘Why X rather than Y?’. We carry out experiments with several datasets of different scales and compare our approach with other baselines on three different areas: fidelity, reasonableness and explainability.

This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system’s equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms. This manuscript leverages the benefits of both approaches. We define the structural causal models in terms of the parameters and the equilibrium dynamics of the Markov process models, and counterfactual inference flows from these settings. The proposed approach alleviates the identifiability drawback of the structural causal models, in that the counterfactual inference is consistent with the counterfactual trajectories simulated from the Markov process model. We showcase the benefits of this framework in case studies of complex biomolecular systems with nonlinear dynamics. We illustrate that, in presence of Markov process model misspecification, counterfactual inference leverages prior data, and therefore estimates the outcome of an intervention more accurately than a direct simulation.

It has been widely regarded that only considering the immediate user feedback is not sufficient for modern industrial recommendation systems. Many previous works attempt to maximize the long term rewards with Reinforcement Learning(RL). However, model-free RL suffers from problems including significant variance in gradient, long convergence period, and requirement of sophisticated online infrastructures. While model-based RL provides a sample-efficient choice, the cost of planning in an online system is unacceptable. To achieve high sample efficiency in practical situations, we propose a novel model-based reinforcement learning method, namely the model-based counterfactual advantage learning(MBCAL). In the proposed method, a masking item is introduced in the environment model learning. With the masking item and the environment model, we introduce the counterfactual future advantage, which eliminates most of the noises in long term rewards. The proposed method selects through approximating the immediate reward and future advantage separately. It is easy to implement, yet it requires reasonable cost in both training and inference processes. In the experiments, we compare our methods with several baselines, including supervised learning, model-free RL, and other model-based RL methods in carefully designed experiments. Results show that our method transcends all the baselines in both sample efficiency and asymptotic performance.

The paper proposes an estimator to make inference on key features of heterogeneous treatment effects sorted by impact groups (GATES) for non-randomised experiments. Observational studies are standard in policy evaluation from labour markets, educational surveys, and other empirical studies. To control for a potential selection-bias we implement a doubly-robust estimator in the first stage. Keeping the flexibility to use any machine learning method to learn the conditional mean functions as well as the propensity score we also use machine learning methods to learn a function for the conditional average treatment effect. The group average treatment effect is then estimated via a parametric linear model to provide p-values and confidence intervals. The result is a best linear predictor for effect heterogeneity based on impact groups. Cross-splitting and averaging for each observation is a further extension to avoid biases introduced through sample splitting. The advantage of the proposed method is a robust estimation of heterogeneous group treatment effects under mild assumptions, which is comparable with other models and thus keeps its flexibility in the choice of machine learning methods. At the same time, its ability to deliver interpretable results is ensured.

Transfer entropy is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) transfer entropy from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly-coupled Gaussian model, which allows us to derive the transfer entropy for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the transfer entropy increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the transfer entropy is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to transfer entropy for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the transfer entropy on the in-degree extends to nonlinear dynamics.

Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of classification problems based on logistic regression. However, it is well-known that logistic regression is vulnerable to outliers, and thus the performance can be strongly weakened by outliers. In this paper, we first theoretically analyze nonlinear ICA models in the presence of outliers. Our analysis implies that estimation in nonlinear ICA can be seriously hampered when outliers exist on the tails of the (noncontaminated) target density, which happens in a typical case of contamination by outliers. We develop two robust nonlinear ICA methods based on the {\gamma}-divergence, which is a robust alternative to the KL-divergence in logistic regression. The proposed methods are shown to have desired robustness properties in the context of nonlinear ICA. We also experimentally demonstrate that the proposed methods are very robust and outperform existing methods in the presence of outliers. Finally, the proposed method is applied to ICA-based causal discovery and shown to find a plausible causal relationship on fMRI data.

Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

This paper uses inverse Reinforcement Learning (RL) to determine the behavior of Space Objects (SOs) by estimating the reward function that an SO is using for control. The approach discussed in this work can be used to analyze maneuvering of SOs from observational data. The inverse RL problem is solved using maximum causal entropy. This approach determines the optimal reward function that a SO is using while maneuvering with random disturbances by assuming that the observed trajectories are optimal with respect to the SO’s own reward function. Lastly, this paper develops results for scenarios involving Low Earth Orbit (LEO) station-keeping and Geostationary Orbit (GEO) station-keeping.

This research develops a socioeconomic health index for nations through a model-based approach which incorporates spatial dependence and examines the impact of a policy through a causal modeling framework. As the gross domestic product (GDP) has been regarded as a dated measure and tool for benchmarking a nation’s economic performance, there has been a growing consensus for an alternative measure—such as a composite `wellbeing’ index—to holistically capture a country’s socioeconomic health performance. Many conventional ways of constructing wellbeing/health indices involve combining different observable metrics, such as life expectancy and education level, to form an index. However, health is inherently latent with metrics actually being observable indicators of health. In contrast to the GDP or other conventional health indices, our approach provides a holistic quantification of the overall `health’ of a nation. We build upon the latent health factor index (LHFI) approach that has been used to assess the unobservable ecological/ecosystem health. This framework integratively models the relationship between metrics, the latent health, and the covariates that drive the notion of health. In this paper, the LHFI structure is integrated with spatial modeling and statistical causal modeling, so as to evaluate the impact of a policy variable (mandatory maternity leave days) on a nation’s socioeconomic health, while formally accounting for spatial dependency among the nations. We apply our model to countries around the world using data on various metrics and potential covariates pertaining to different aspects of societal health. The approach is structured in a Bayesian hierarchical framework and results are obtained by Markov chain Monte Carlo techniques.

Root cause analysis in a large-scale production environment is challenging due to the complexity of services running across global data centers. Due to the distributed nature of a large-scale system, the various hardware, software, and tooling logs are often maintained separately, making it difficult to review the logs jointly for detecting issues. Another challenge in reviewing the logs for identifying issues is the scale – there could easily be millions of entities, each with hundreds of features. In this paper we present a fast dimensional analysis framework that automates the root cause analysis on structured logs with improved scalability. We first explore item-sets, i.e. a group of feature values, that could identify groups of samples with sufficient support for the target failures using the Apriori algorithm and a subsequent improvement, FP-Growth. These algorithms were designed for frequent item-set mining and association rule learning over transactional databases. After applying them on structured logs, we select the item-sets that are most unique to the target failures based on lift. With the use of a large-scale real-time database, we propose pre- and post-processing techniques and parallelism to further speed up the analysis. We have successfully rolled out this approach for root cause investigation purposes in a large-scale infrastructure. We also present the setup and results from multiple production use-cases in this paper.

The lack of longitudinal studies of the relationship between the built environment and travel behavior has been widely discussed in the literature. This paper discusses how standard propensity score matching estimators can be extended to enable such studies by pairing observations across two dimensions: longitudinal and cross-sectional. Researchers mimic randomized controlled trials (RCTs) and match observations in both dimensions, to find synthetic control groups that are similar to the treatment group and to match subjects synthetically across before-treatment and after-treatment time periods. We call this a two-dimensional propensity score matching (2DPSM). This method demonstrates superior performance for estimating treatment effects based on Monte Carlo evidence. A near-term opportunity for such matching is identifying the impact of transportation infrastructure on travel behavior.

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of scale in the special case of a scale free dynamical system that can be described in terms of a Lagrangian, that itself scales inversely with time. Crucially, this means symmetries under change of scale can exist in dynamical systems under certain constraints. Our contribution lies in the derivation of a generalised scale invariant Lagrangian – in the form of a power series expansion – that satisfies these constraints. This generalised Lagrangian furnishes a normal form for dynamic causal models (i.e., state space models based upon differential equations) that can be used to distinguish scale invariance (scale symmetry) from scale freeness in empirical data. We establish face validity with an analysis of simulated data and then show how scale invariance can be identified – and how the associated conserved quantities can be estimated – in neuronal timeseries.

Mediation analysis in high-dimensional settings often involves identifying potential mediators among a large number of measured variables. For this purpose, a two step familywise error rate (FWER) procedure called ScreenMin has been recently proposed (Djordjilovi\’c et al. 2019). In ScreenMin, variables are first screened and only those that pass the screening are tested. The proposed threshold for selection has been shown to guarantee asymptotic FWER. In this work, we investigate the impact of the selection threshold on the finite sample FWER. We derive power maximizing selection threshold and show that it is well approximated by an adaptive threshold of Wang et al. (2016). We study the performance of the proposed procedures in a simulation study, and apply them to a case-control study examining the effect of fish intake on the risk of colorectal adenoma.

We discuss promising recent contributions on quantifying feature relevance using Shapley values, where we observed some confusion on which probability distribution is the right one for dropped features. We argue that the confusion is based on not carefully distinguishing between *observational* and *interventional* conditional probabilities and try a clarification based on Pearl’s seminal work on causality. We conclude that *unconditional* rather than *conditional* expectations provide the right notion of *dropping* features in contradiction to the theoretical justification of the software package SHAP. Parts of SHAP are unaffected because unconditional expectations (which we argue to be conceptually right) are used as *approximation* for the conditional ones, which encouraged others to ‘improve’ SHAP in a way that we believe to be flawed. Further, our criticism concerns TreeExplainer in SHAP, which really uses conditional expectations (without approximating them by unconditional ones)

One of the most common mistakes made when performing data analysis is attributing causal meaning to regression coefficients. Formally, a causal effect can only be computed if it is identifiable from a combination of observational data and structural knowledge about the domain under investigation (Pearl, 2000, Ch. 5). Building on the literature of instrumental variables (IVs), a plethora of methods has been developed to identify causal effects in linear systems. Almost invariably, however, the most powerful such methods rely on exponential-time procedures. In this paper, we investigate graphical conditions to allow efficient identification in arbitrary linear structural causal models (SCMs). In particular, we develop a method to efficiently find unconditioned instrumental subsets, which are generalizations of IVs that can be used to tame the complexity of many canonical algorithms found in the literature. Further, we prove that determining whether an effect can be identified with TSID (Weihs et al., 2017), a method more powerful than unconditioned instrumental sets and other efficient identification algorithms, is NP-Complete. Finally, building on the idea of flow constraints, we introduce a new and efficient criterion called Instrumental Cutsets (IC), which is able to solve for parameters missed by all other existing polynomial-time algorithms.

Recent conceptual discussion on the nature of the explainability of Artificial Intelligence (AI) has largely been limited to data-driven investigations. This paper identifies some shortcomings of this approach to help strengthen the debate on this subject. Building on recent philosophical work on the nature of explanations, I demonstrate the significance of two non-data driven, non-causal explanatory elements: (1) mathematical structures that are the grounds for capturing the decision-making situation; (2) statistical and optimality facts in terms of which the algorithm is designed and implemented. I argue that these elements feature directly in important aspects of AI explainability. I then propose a hierarchical framework that acknowledges the existence of various types of explanation, each of which reveals an aspect of explanation, and answers to a different kind of why-question. The usefulness of this framework will be illustrated by bringing it to bear on some salient normative concerns about the use of AI decision-making systems in society.

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach using a sufficiently expressive probabilistic programming language. Priors are represented using probabilistic programs that generate source code in a domain specific language. Interventions are represented using probabilistic programs that edit this source code to modify the original generative process. This approach makes it straightforward to incorporate data from atomic interventions, as well as shift interventions, variance-scaling interventions, and other interventions that modify causal structure. This approach also enables the use of general-purpose inference machinery for probabilistic programs to infer probable causal structures and parameters from data. This abstract describes a prototype of this approach in the Gen probabilistic programming language.

Recent developments have linked causal inference with Algorithmic Information Theory, and methods have been developed that utilize Conditional Kolmogorov Complexity to determine causation between two random variables. However, past methods that utilize Algorithmic Information Theory do not provide off-the-shelf support for continuous data types and thus lose the essence of the shape of data. We present a method for inferring causal direction between continuous variables by using an MDL Binning technique for data discretization and complexity calculation. Our method captures the shape of the data and uses it to determine which variable has more information about the other. Its high predictive performance and robustness is shown on several real world use cases.

Reasoning about observed effects and their causes is important in multi-agent contexts. While there has been much work on causality from an objective standpoint, causality from the point of view of some particular agent has received much less attention. In this paper, we address this issue by incorporating an epistemic dimension to an existing formal model of causality. We define what it means for an agent to know the causes of an effect. Then using a counterexample, we prove that epistemic causality is a different notion from its objective counterpart.

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.

Constructing gene regulatory networks is a critical step in revealing disease mechanisms from transcriptomic data. In this work, we present NO-BEARS, a novel algorithm for estimating gene regulatory networks. The NO-BEARS algorithm is built on the basis of the NOTEARS algorithm with two improvements. First, we propose a new constraint and its fast approximation to reduce the computational cost of the NO-TEARS algorithm. Next, we introduce a polynomial regression loss to handle non-linearity in gene expressions. Our implementation utilizes modern GPU computation that can decrease the time of hours-long CPU computation to seconds. Using synthetic data, we demonstrate improved performance, both in processing time and accuracy, on inferring gene regulatory networks from gene expression data.

Granger causality analysis (GCA) provides a powerful tool for uncovering the patterns of brain connectivity mechanism using neuroimaging techniques. Conventional GCA applies two different mathematical theories in a two-stage scheme: (1) the Bayesian information criterion (BIC) or Akaike information criterion (AIC) for the regression model orders associated with endogenous and exogenous information; (2) F-statistics for determining the causal effects of exogenous variables. While specifying endogenous and exogenous effects are essentially the same model selection problem, this could produce different benchmarks in the two stages and therefore degrade the performance of GCA. In this course, we present a unified model selection approach based on the minimum description length (MDL) principle for GCA in the context of the general regression model paradigm. Compared with conventional methods, our approach emphasize that a single mathematical theory should be held throughout the GCA process. Under this framework, all candidate models within the model space might be compared freely in the context of the code length, without the need for an intermediate model. We illustrate its advantages over conventional two-stage GCA approach in a 3-node network and a 5-node network synthetic experiments. The unified model selection approach is capable of identifying the actual connectivity while avoiding the false influences of noise. More importantly, the proposed approach obtained more consistent results in a challenge fMRI dataset for causality investigation, mental calculation network under visual and auditory stimulus, respectively. The proposed approach has potential to accommodate other Granger causality representations in other function space. The comparison between different GC representations in different function spaces can also be naturally deal with in the framework.

We focus on estimating the average treatment effect in clinical trials that involve stratified randomization, which is commonly used. It is important to understand the large sample properties of estimators that adjust for stratum variables (those used in the randomization procedure) and additional baseline variables, since this can lead to substantial gains in precision and power. Surprisingly, to the best of our knowledge, this is an open problem. It was only recently that a simpler problem was solved by Bugni et al. (2018) for the case with no additional baseline variables, continuous outcomes, the analysis of covariance (ANCOVA) estimator, and no missing data. We generalize their results in three directions. First, in addition to continuous outcomes, we handle binary and time-to-event outcomes; this broadens the applicability of the results. Second, we allow adjustment for an additional, preplanned set of baseline variables, which can improve precision. Third, we handle missing outcomes under the missing at random assumption. We prove that a wide class of estimators is asymptotically normally distributed under stratified randomization and has equal or smaller asymptotic variance than under simple randomization. For each estimator in this class, we give a consistent variance estimator. This is important in order to fully capitalize on the combined precision gains from stratified randomization and adjustment for additional baseline variables. The above results also hold for the biased-coin covariate-adaptive design. We demonstrate our results using completed trial data sets of treatments for substance use disorder, where adjustment for additional baseline variables brings substantial variance reduction.

Information-Theoretic Causal Inference on Event Sequences. Pycute is a infromation-theoretic causal inference method for event sequences based on Granger-causality.

Feature importance estimates that inform users about the degree to which given inputs influence the output of a predictive model are crucial for understanding, validating, and interpreting machine-learning models. However, providing fast and accurate estimates of feature importance for high-dimensional data, and quantifying the uncertainty of such estimates remain open challenges. Here, we frame the task of providing explanations for the decisions of machine-learning models as a causal learning task, and train causal explanation (CXPlain) models that learn to estimate to what degree certain inputs cause outputs in another machine-learning model. CXPlain can, once trained, be used to explain the target model in little time, and enables the quantification of the uncertainty associated with its feature importance estimates via bootstrap ensembling. We present experiments that demonstrate that CXPlain is significantly more accurate and faster than existing model-agnostic methods for estimating feature importance. In addition, we confirm that the uncertainty estimates provided by CXPlain ensembles are strongly correlated with their ability to accurately estimate feature importance on held-out data.

Studies show that the representations learned by deep neural networks can be transferred to similar prediction tasks in other domains for which we do not have enough labeled data. However, as we transition to higher layers in the model, the representations become more task-specific and less generalizable. Recent research on deep domain adaptation proposed to mitigate this problem by forcing the deep model to learn more transferable feature representations across domains. This is achieved by incorporating domain adaptation methods into deep learning pipeline. The majority of existing models learn the transferable feature representations which are highly correlated with the outcome. However, correlations are not always transferable. In this paper, we propose a novel deep causal representation learning framework for unsupervised domain adaptation, in which we propose to learn domain-invariant causal representations of the input from the source domain. We simulate a virtual target domain using reweighted samples from the source domain and estimate the causal effect of features on the outcomes. The extensive comparative study demonstrates the strengths of the proposed model for unsupervised domain adaptation via causal representations.

Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear mediation models. We develop methods for both incomplete mediation, where a direct effect may exist, as well as complete mediation, where the direct effect is known to be absent. We prove consistency and asymptotic normality of our indirect effect estimators. Under complete mediation, where the indirect effect is equivalent to the total effect, we further prove that our approach gives a more powerful test compared to directly testing for the total effect. We confirm our theoretical results in simulations, as well as in an integrative analysis of gene expression and genotype data from a pharmacogenomic study of drug response. We present a novel analysis of gene sets to understand the molecular mechanisms of drug response, and also identify a genome-wide significant noncoding genetic variant that cannot be detected using standard analysis methods.

This volume seeks to infer large phylogenetic networks from phonetically encoded lexical data and contribute in this way to the historical study of language varieties. The technical step that enables progress in this case is the use of causal inference algorithms. Sample sets of words from language varieties are preprocessed into automatically inferred cognate sets, and then modeled as information-theoretic variables based on an intuitive measure of cognate overlap. Causal inference is then applied to these variables in order to determine the existence and direction of influence among the varieties. The directed arcs in the resulting graph structures can be interpreted as reflecting the existence and directionality of lexical flow, a unified model which subsumes inheritance and borrowing as the two main ways of transmission that shape the basic lexicon of languages. A flow-based separation criterion and domain-specific directionality detection criteria are developed to make existing causal inference algorithms more robust against imperfect cognacy data, giving rise to two new algorithms. The Phylogenetic Lexical Flow Inference (PLFI) algorithm requires lexical features of proto-languages to be reconstructed in advance, but yields fully general phylogenetic networks, whereas the more complex Contact Lexical Flow Inference (CLFI) algorithm treats proto-languages as hidden common causes, and only returns hypotheses of historical contact situations between attested languages. The algorithms are evaluated both against a large lexical database of Northern Eurasia spanning many language families, and against simulated data generated by a new model of language contact that builds on the opening and closing of directional contact channels as primary evolutionary events. The algorithms are found to infer the existence of contacts very reliably, whereas the inference of directionality remains difficult. This currently limits the new algorithms to a role as exploratory tools for quickly detecting salient patterns in large lexical datasets, but it should soon be possible for the framework to be enhanced e.g. by confidence values for each directionality decision.

We propose a novel multipath multi-hop adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction. This algorithm generalizes our joint optimization coding solution for point-to-point communication with delayed feedback. AC-RLNC is adaptive to the estimated channel condition, and is causal, as the coding adjusts the retransmission rates using a priori and posteriori algorithms. In the multipath network, to achieve the desired throughput and delay, we propose to incorporate an adaptive packet allocation algorithm for retransmission, across the available resources of the paths. This approach is based on a discrete water filling algorithm, i.e., bit-filling, but, with two desired objectives, maximize throughput and minimize the delay. In the multipath multi-hop setting, we propose a new decentralized balancing optimization algorithm. This balancing algorithm minimizes the throughput degradation, caused by the variations in the channel quality of the paths at each hop. Furthermore, to increase the efficiency, in terms of the desired objectives, we propose a new selective recoding method at the intermediate nodes. Through simulations, we demonstrate that the performance of our adaptive and causal approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains up to a factor two in throughput and a factor of more than three in delay.

The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from uncontrolled data have been proposed. However, most of these deal only with purely directed causal relationships and cannot detect latent common causes. Here, we devise a general method which takes a purely directed causal discovery algorithm and modifies it so that it can also detect latent common causes. The identifiability of the modified algorithm depends on the identifiability of the original, as well as an assumption that the strength of noise be relatively small. We apply our method to two directed causal discovery algorithms, the Information Geometric Causal Inference of (Daniusis et al., 2010) and the Kernel Conditional Deviance for Causal Inference of (Mitrovic, Sejdinovic, and Teh, 2018), and extensively test on synthetic data—detecting latent common causes in additive, multiplicative and complex noise regimes—and on real data, where we are able to detect known common causes. In addition to detecting latent common causes, our experiments demonstrate that both modified algorithms preserve the performance of the original directed algorithm in distinguishing directed causal relations.

Consequential decision-making incentivizes individuals to adapt their behavior to the specifics of the decision rule. A long line of work has therefore sought to understand and anticipate adaptation, both to prevent strategic individuals from ‘gaming’ the decision rule and to explicitly motivate individuals to improve. In this work, we frame the problem of adaptation as performing interventions in a causal graph. With this causal perspective, we make several contributions. First, we articulate a formal distinction between gaming and improvement. Second, we formalize strategic classification in a new way that recognizes that the individual may improve, rather than only game. In this setting, we show that it is beneficial for the decision-maker to incentivize improvement. Third, we give a reduction from causal inference to designing incentivizes for improvement. This shows that designing good incentives, while desirable, is at least as hard as causal inference.

The relationship among three correlated variables could be very sophisticated, as a result, we may not be able to find their hidden causality and model their relationship explicitly. However, we still can make our best guess for possible mappings among these variables, based on the observed relationship. One of the complicated relationships among three correlated variables could be a two-layer hierarchical many-to-many mapping. In this paper, we proposed a Hierarchical Mixture Density Network (HMDN) to model the two-layer hierarchical many-to-many mapping. We apply HMDN on an indoor positioning problem and show its benefit.

Missing attributes are ubiquitous in causal inference, as they are in most applied statistical work. In this paper, we consider various sets of assumptions under which causal inference is possible despite missing attributes and discuss corresponding approaches to average treatment effect estimation, including generalized propensity score methods and multiple imputation. Across an extensive simulation study, we show that no single method systematically out-performs others. We find, however, that doubly robust modifications of standard methods for average treatment effect estimation with missing data repeatedly perform better than their non-doubly robust baselines; for example, doubly robust generalized propensity score methods beat inverse-weighting with the generalized propensity score. This finding is reinforced in an analysis of an observations study on the effect on mortality of tranexamic acid administration among patients with traumatic brain injury in the context of critical care management. Here, doubly robust estimators recover confidence intervals that are consistent with evidence from randomized trials, whereas non-doubly robust estimators do not.

Interference exists when a unit’s outcome depends on another unit’s treatment assignment. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods either have low power or are limited to special cases. In this paper, we propose valid, powerful, and easy-to-implement randomization tests for a general class of null hypotheses under arbitrary interference between units. Our key idea is to represent the hypothesis of interest as a bipartite graph between units and assignments, and to find a clique of this graph. Importantly, the null hypothesis is sharp for the units and assignments in this clique, enabling randomization-based tests conditional on the clique. We can apply off-the-shelf graph clustering methods to find such cliques efficiently and at scale. We illustrate this approach in settings with clustered interference and show advantages over methods designed specifically for that setting. We then apply our method to a large-scale policing experiment in Medellin, Colombia, where interference has a spatial structure.

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independence tests only determine causal structure up to Markov equivalence, the number of consistent joint structures returned by these approaches can be quite large. The last decade has seen the development of elegant algorithms for discovering causal relations beyond conditional independence, which can distinguish among Markov equivalent structures. In this work we adapt and extend these so-called bivariate causal discovery algorithms to the problem of learning consistent causal structures from multiple datasets with overlapping variables belonging to the same generating process, providing a sound and complete algorithm that outperforms previous approaches on synthetic and real data.

We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually or cluster randomized trials. In this manuscript, we study the properties of this estimator and develop a new estimator that utilizes both covariate adjustment and inverse probability weighting We support our theoretical results with a simulation study and an application in an infectious disease setting. The covariate-adjusted residuals estimator is an efficient and unbiased estimator of the average treatment effect in randomized trials; however, it is not guaranteed to be unbiased in observational studies. Our novel estimator, the covariate-adjusted residuals estimator with inverse probability weighting, is unbiased in randomized and observational settings, under a reasonable set of assumptions. Furthermore, when these assumptions hold, it provides efficiency gains over inverse probability weighting in observational studies. The covariate-adjusted residuals estimator is valid for use in randomized trials, but should not be used in observational studies. The covariate-adjusted residuals estimator with inverse probability weighting provides an efficient alternative for use in randomized and observational settings.

We propose a method for causal inference using satellite image time series, in order to determine the treatment effects of interventions which impact climate change, such as deforestation. Simply put, the aim is to quantify the ‘before versus after’ effect of climate related human driven interventions, such as urbanization; as well as natural disasters, such as hurricanes and forest fires. As a concrete example, we focus on quantifying forest tree cover change/ deforestation due to human led causes. The proposed method involves the following steps. First, we uae computer vision and machine learning/deep learning techniques to detect and quantify forest tree coverage levels over time, at every time epoch. We then look at this time series to identify changepoints. Next, we estimate the expected (forest tree cover) values using a Bayesian structural causal model and projecting/forecasting the counterfactual. This is compared to the values actually observed post intervention, and the difference in the two values gives us the effect of the intervention (as compared to the non intervention scenario, i.e. what would have possibly happened without the intervention). As a specific use case, we analyze deforestation levels before and after the hyperinflation event (intervention) in Brazil (which ended in 1993-94), for the Amazon rainforest region, around Rondonia, Brazil. For this deforestation use case, using our causal inference framework can help causally attribute change/reduction in forest tree cover and increasing deforestation rates due to human activities at various points in time.

Objective. We identify two linked problems related to estimating the phase of the alpha rhythm when the signal after a specific event is unknown (real-time case), or corrupted (offline analysis). We propose methods to estimate the phase prior to such events. Approach. Machine learning is used to mimic a non-causal signal-processing chain with a purely causal one. Main results. We demonstrate the ability of these methods to estimate instantaneous phase from an electroencephalography signal subjected to very minor pre-processing with higher accuracy than more standard signal-processing methods. Significance. Phase estimation of EEG-rhythms is a challenge due to non-stationarity and low signal to noise ratio. The methods presented enable scientists and engineers to achieve relatively low error by optimizing causal phase estimation on a non-causally processed signal for a real-time experiments and offline analysis.

We consider the problem of estimating causal DAG models from a mix of observational and interventional data, when the intervention targets are partially or completely unknown. This problem is highly relevant for example in genomics, since gene knockout technologies are known to have off-target effects. We characterize the interventional Markov equivalence class of DAGs that can be identified from interventional data with unknown intervention targets. In addition, we propose a provably consistent algorithm for learning the interventional Markov equivalence class from such data. The proposed algorithm greedily searches over the space of permutations to minimize a novel score function. The algorithm is nonparametric, which is particularly important for applications to genomics, where the relationships between variables are often non-linear and the distribution non-Gaussian. We demonstrate the performance of our algorithm on synthetic and biological datasets.

We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.~samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the \emph{Sparsest Poset} formulation – that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.

This work derives a finite population delta method. The delta method creates more general inference results when coupled with central limit theorem results for the finite population. This opens up a range of new estimators for which we can find finite population asymptotic properties. We focus on the use of this method to derive asymptotic distributional results and variance expressions for causal estimators. We illustrate the use of the method by obtaining a finite population asymptotic distribution for a causal ratio estimator.

A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions is identifiability, i.e., whether they can be uniquely measured from observational data, which is a critical barrier to applying these notions to real-world situations. In this paper, we develop a framework for measuring different causality-based fairness. We propose a unified definition that covers most of previous causality-based fairness notions, namely the path-specific counterfactual fairness (PC fairness). Based on that, we propose a general method in the form of a constrained optimization problem for bounding the path-specific counterfactual fairness under all unidentifiable situations. Experiments on synthetic and real-world datasets show the correctness and effectiveness of our method.

To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements are not from controlled experimental (interventional) settings, since cause and effect can be obscured by spurious, indirect influences. Modern predictive techniques from machine learning are capable of capturing high-dimensional, nonlinear relationships between variables while relying on few parametric or probabilistic model assumptions. However, since these techniques are associational, applied to observational data they are prone to picking up spurious influences from non-experimental (observational) data, making their predictions unreliable. Techniques from causal inference, such as probabilistic causal diagrams and do-calculus, provide powerful (nonparametric) tools for drawing causal inferences from such observational data. However, these techniques are often incompatible with modern, nonparametric machine learning algorithms since they typically require explicit probabilistic models. Here, we develop causal bootstrapping for augmenting classical nonparametric bootstrap resampling with information on the causal relationship between variables. This makes it possible to resample observational data such that, if it is possible to identify an interventional relationship from that data, new data representing that relationship can be simulated from the original observational data. In this way, we can use modern machine learning algorithms unaltered to make statistically powerful, yet causally-robust, predictions. We develop several causal bootstrapping algorithms for drawing interventional inferences from observational data, for classification and regression problems, and demonstrate, using synthetic and real-world examples, the value of this approach.

Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we call an embedded Bayesian network classifier or EBNC. The model for a node $Y$ given parents $\bf X$ is obtained from a (usually different) Bayesian network for $Y$ and $\bf X$ in which $\bf X$ need not be the parents of $Y$. We show that an EBNC is a special case of a softmax polynomial regression model. Also, we show how to identify a non-redundant set of parameters for an EBNC, and describe an asymptotic approximation for learning the structure of Bayesian networks that contain EBNCs. Unlike the decision tree, decision graph, and causal independence models, we are unaware of a semantic justification for the use of these models. Experiments are needed to determine whether the models presented in this paper are useful in practice.

Parks are increasingly understood to be key community resources for public health, particularly for ethnic minority and low socioeconomic groups. At the same time, research suggests parks are underutilised by these groups. In order to design effective interventions to promote health, the determinants of park use for these groups must be understood. This study examines the associations between park features, park satisfaction and park use in a deprived and ethnically diverse sample in Bradford, UK. 652 women from the Born in Bradford cohort completed a survey on park satisfaction and park use. Using a standardised direct observation tool, 44 parks in the area were audited for present park features. Features assessed were: access, recreational facilities, amenities, natural features, significant natural features, non-natural features, incivilities and usability. Size and proximity to the park were also calculated. Multilevel linear regressions were performed to understand associations between park features and (1) park satisfaction and (2) park use. Interactions between park features, ethnicity and socioeconomic status were explored, and park satisfaction was tested as a mediator in the relationship between park features and park use. More amenities and greater usability were associated with increased park satisfaction, while more incivilities were negatively related to park satisfaction. Incivilities, access and proximity were also negatively associated with park use. Ethnicity and socioeconomic status had no moderating role, and there was no evidence for park satisfaction as a mediator between park features and park use. Results suggest diverse park features are associated with park satisfaction and park use, but this did not vary by ethnicity or socioeconomic status. The reduction of incivilities should be prioritised where the aim is to encourage park satisfaction and park use.

Ogburn et al. (2019, arXiv:1910.05438) discuss ‘The Blessings of Multiple Causes’ (Wang and Blei, 2018, arXiv:1805.06826). Many of their remarks are interesting. But they also claim that the paper has ‘foundational errors’ and that its ‘premise is…incorrect.’ These claims are not substantiated. We correct the record here.

This is the sixth part of the Interpreting ML tutorial. In previous posts we have presented several ways to interpret machine learning models. Of the highly interpretable models, all had their problems, high bias models like Regressions or high variance models as decision trees. We solved the trade- off between bias and variance basically combining several models, especially high variance models, so we had the best models, low bias and low variance and the price to pay is that we no longer have control over how the model is making its decisions or how are the relationships between the variables, ie the model became a BlackBox.

In modern e-commerce and advertising recommender systems, ongoing research works attempt to optimize conversion rate (CVR) estimation, and increase the gross merchandise volume. Even though the state-of-the-art CVR estimators adopt deep learning methods, their model performances are still subject to sample selection bias and data sparsity issues. Conversion labels of exposed items in training dataset are typically missing not at random due to selection bias. Empirically, data sparsity issue causes the performance degradation of model with large parameter space. In this paper, we proposed two causal estimators combined with multi-task learning, and aim to solve sample selection bias (SSB) and data sparsity (DS) issues in conversion rate estimation. The proposed estimators adjust for the MNAR mechanism as if they are trained on a ‘do dataset’ where users are forced to click on all exposed items. We evaluate the causal estimators with billion data samples. Experiment results demonstrate that the proposed CVR estimators outperform other state-of-the-art CVR estimators. In addition, empirical study shows that our methods are cost-effective with large scale dataset.

We elaborate on using importance sampling for causal reasoning, in particular for counterfactual inference. We show how this can be implemented natively in probabilistic programming. By considering the structure of the counterfactual query, one can significantly optimise the inference process. We also consider design choices to enable further optimisations. We introduce MultiVerse, a probabilistic programming prototype engine for approximate causal reasoning. We provide experimental results and compare with Pyro, an existing probabilistic programming framework with some of causal reasoning tools.

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We estimate a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under a general approximate factor model. The key application is to estimate counterfactual outcomes in causal inference from panel data. The unobserved control group is modeled as missing values, which are inferred from the latent factor model. The inferential theory for the imputed values allows us to test for individual treatment effects at any time. We apply our method to portfolio investment strategies and find that around 14% of their average returns are significantly reduced by the academic publication of these strategies.

Learning causal graphical models based on directed acyclic graphs is an important task in causal discovery and causal inference. We consider a general framework towards efficient causal structure learning with potentially large graphs. Within this framework, we propose a masked gradient-based structure learning method based on binary adjacency matrix that exists for any structural equation model. To enable first-order optimization methods, we use Gumbel-Softmax approach to approximate the binary valued entries of the adjacency matrix, which usually results in real values that are close to zero or one. The proposed method can readily include any differentiable score function and model function for learning causal structures. Experiments on both synthetic and real-world datasets are conducted to show the effectiveness of our approach.

Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in measurements. In this article, we review different notions of causality and focus especially on measuring causality from time series data. Causality testing finds numerous applications in diverse disciplines such as neuroscience, econometrics, climatology, physics and artificial intelligence.

We consider the task of causal structure learning over measurement dependence inducing latent (MeDIL) causal models. We show that this task can be framed in terms of the graph theoretical problem of finding edge clique covers, resulting in a simple algorithm for returning minimal MeDIL causal models (minMCMs). This algorithm is non-parametric, requiring no assumptions about linearity or Gaussianity. Furthermore, despite rather weak assumptions about the class of MeDIL causal models, we show that minimality in minMCMs implies three rather specific and interesting properties: first, minMCMs provide lower bounds on (i) the number of latent causal variables and (ii) the number of functional causal relations that are required to model a complex system at any level of granularity; second, a minMCM contains no causal links between the latent variables; and third, in contrast to factor analysis, a minMCM may require more latent than measurement variables.

Social scientists often study how a policy reform impacted a single targeted country. Increasingly, this is done with the synthetic control method (SCM). SCM models the country’s counterfactual (non-reform or untreated) trajectory as a weighted average of other countries’ outcomes. The method struggles to quantify uncertainty; eg. it cannot produce confidence intervals. It is also suspect to overfit. We propose an alternative method, the Bayesian synthetic control (BSC), which lacks these flaws. Using MCMC sampling, we implement the method for two previously studied datasets. The proposed method outperforms SCM in a simple test of predictive accuracy and casts some doubt on significance of prior findings. The studied reforms are the German reunification of 1990 and the California tobacco legislation of 1988. BSC borrows its causal model, the linear latent factor model, from the SCM literature. Unlike SCM, BSC estimates the latent factors explicitly through a dimensionality reduction. All uncertainty is captured in the posterior distribution so that, unlike for SCM, credible intervals are easily derived. Further, BSC’s reliability on the target panel dataset can be assessed through a posterior predictive check; SCM and its frequentist derivatives use up the required information while testing statistical significance.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. A general framework for explaining any AI model is provided by the Shapley values that attribute the prediction output to the various model inputs (‘features’) in a principled and model-agnostic way. The outstanding strength of Shapley values is their combined generality and rigorous foundation: they can be used to explain any AI system, and one always understands their values as the unique attribution method satisfying a set of mathematical axioms. However, as a framework, Shapley values are too restrictive in one significant regard: they ignore all causal structure in the data. We introduce a less-restrictive framework for model-agnostic explainability: ‘Asymmetric’ Shapley values. Asymmetric Shapley values (ASVs) are rigorously founded on a set of axioms, applicable to any AI system, and can flexibly incorporate any causal knowledge known a-priori to be respected by the data. We show through explicit, realistic examples that the ASV framework can be used to (i) improve model explanations by incorporating causal information, (ii) provide an unambiguous test for unfair discrimination based on simple policy articulations, (iii) enable sequentially incremental explanations in time-series models, and (iv) support feature-selection studies without the need for model retraining.

This paper suggests a factor-based imputation procedure that uses the factors estimated from a TALL block along with the re-rotated loadings estimated from a WIDE block to impute missing values in a panel of data. Under a strong factor assumption, it is shown that the common component can be consistently estimated but there will be four different convergence rates. Re-estimation of the factors from the imputed data matrix can accelerate convergence. A complete characterization of the sampling error is obtained without requiring regularization or imposing the missing at random assumption. Under the assumption that potential outcome has a factor structure, we provide a distribution theory for the estimated treatment effect on the treated. The relation between incoherence conditions used in matrix completions and the strong factor assumption is also discussed.

Causal knowledge is vital for effective reasoning in science and medicine. In medical diagnosis for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. However, all previous approaches to Machine-Learning assisted diagnosis, including Deep Learning and model-based Bayesian approaches, learn by association and do not distinguish correlation from causation. Here, we propose a new diagnostic algorithm based on counterfactual inference which captures the causal aspect of diagnosis overlooked by previous approaches. Using a statistical disease model, which describes the relations between hundreds of diseases, symptoms and risk factors, we compare our counterfactual algorithm to the standard Bayesian diagnostic algorithm, and test these against a cohort of 44 doctors. We use 1763 clinical vignettes created by a separate panel of doctors to benchmark performance. Each vignette provides a non-exhaustive list of symptoms and medical history simulating a single presentation of a disease. The algorithms and doctors are tasked with determining the underlying disease for each vignette from symptom and medical history information alone. While the Bayesian algorithm achieves the accuracy comparable to the average doctor, placing in the top 49\% of doctors in our cohort, our counterfactual algorithm places in the top 20\% of doctors, achieving expert clinical accuracy. Our results demonstrate the advantage of counterfactual over associative reasoning in a complex real-world task, and show that counterfactual reasoning is a vital missing ingredient for applying machine learning to medical diagnosis.

Unobserved confounding is a central barrier to drawing causal inferences from observa- tional data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the e ects of several variables simultaneously. In this paper, we present two simple, analytical counterexamples that challenge the general claims that are central to these approaches. In addition, we show that nonparametric identi cation is impossible in this setting. We discuss practical implications, and sug- gest alternatives to the methods that have been proposed so far in this line of work: us- ing proxy variables and shifting focus to sen- sitivity analysis.

This commentary has two goals. We first critically review the deconfounder method and point out its advantages and limitations. We then briefly consider three possible ways to address some of the limitations of the deconfounder method.

A common statistical problem in econometrics is to estimate the impact of a treatment on a treated unit given a control sample with untreated outcomes. Here we develop a generative learning approach to this problem, learning the probability distribution of the data, which can be used for downstream tasks such as post-treatment counterfactual prediction and hypothesis testing. We use control samples to transform the data to a Gaussian and homoschedastic form and then perform Gaussian process analysis in Fourier space, evaluating the optimal Gaussian kernel via non-parametric power spectrum estimation. We combine this Gaussian prior with the data likelihood given by the pre-treatment data of the single unit, to obtain the synthetic prediction of the unit post-treatment, which minimizes the error variance of synthetic prediction. Given the generative model the minimum variance counterfactual is unique, and comes with an associated error covariance matrix. We extend this basic formalism to include correlations of primary variable with other covariates of interest. Given the probabilistic description of generative model we can compare synthetic data prediction with real data to address the question of whether the treatment had a statistically significant impact. For this purpose we develop a hypothesis testing approach and evaluate the Bayes factor. We apply the method to the well studied example of California (CA) tobacco sales tax of 1988. We also perform a placebo analysis using control states to validate our methodology. Our hypothesis testing method suggests 5.8:1 odds in favor of CA tobacco sales tax having an impact on the tobacco sales, a value that is at least three times higher than any of the 38 control states.

Causal inference is a fundemental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI). Copula Entropy (CE) is a theory on measurement of statistical independence and is equivalent to MI. In this paper, we prove that TE can be represented with only CE and then propose a non-parametric method for estimating TE via CE. The proposed method was applied to analyze the Beijing PM2.5 data in the experiments. Experimental results show that the proposed method can infer causality relationships from data effectively and hence help to understand the data better.

We seek causes through science, religion, and in everyday life. We get excited when a big rock causes a big splash, and we get scared when it tumbles without a cause. But our causal cognition is usually biased. The ‘why’ is influenced by the ‘who’. It is influenced by the ‘self’, and by ‘others’. We share rituals, we watch action movies, and we influence each other to believe in the same causes. Human mind is packed with subjectivity because shared cognitive biases bring us together. But they also make us vulnerable. An artificial mind is deemed to be more objective than the human mind. After many years of science-fiction fantasies about even-minded androids, they are now sold as personal or expert assistants, as brand advocates, as policy or candidate supporters, as network influencers. Artificial agents have been stunningly successful in disseminating artificial causal beliefs among humans. As malicious artificial agents continue to manipulate human cognitive biases, and deceive human communities into ostensive but expansive causal illusions, the hope for defending us has been vested into developing benevolent artificial agents, tasked with preventing and mitigating cognitive distortions inflicted upon us by their malicious cousins. Can the distortions of human causal cognition be corrected on a more solid foundation of artificial causal cognition? In the present paper, we study a simple model of causal cognition, viewed as a quest for causal models. We show that, under very mild and hard to avoid assumptions, there are always self-confirming causal models, which perpetrate self-deception, and seem to preclude a royal road to objectivity.

We study how to learn optimal interventions sequentially given causal information represented as a causal graph along with associated conditional distributions. Causal modeling is useful in real world problems like online advertisement where complex causal mechanisms underlie the relationship between interventions and outcomes. We propose two algorithms, causal upper confidence bound (C-UCB) and causal Thompson Sampling (C-TS), that enjoy improved cumulative regret bounds compared with algorithms that do not use causal information. We thus resolve an open problem posed by~\cite{lattimore2016causal}. Further, we extend C-UCB and C-TS to the linear bandit setting and propose causal linear UCB (CL-UCB) and causal linear TS (CL-TS) algorithms. These algorithms enjoy a cumulative regret bound that only scales with the feature dimension. Our experiments show the benefit of using causal information. For example, we observe that even with a few hundreds of iterations, the regret of causal algorithms is less than that of standard algorithms by a factor of three. We also show that under certain causal structures, our algorithms scale better than the standard bandit algorithms as the number of interventions increases.

Classical results of Decision Theory, and its extension to a multi-agent setting: Game Theory, operate only at the associative level of information; this is, classical decision makers only take into account probabilities of events; we go one step further and consider causal information: in this work, we define Causal Decision Problems and extend them to a multi-agent decision problem, which we call a causal game. For such games, we study belief updating in a class of strategic games in which any player’s action causes some consequence via a causal model, which is unknown by all players; for this reason, the most suitable model is Harsanyi’s Bayesian Game. We propose a probability updating for the Bayesian Game in such a way that the knowledge of any player in terms of probabilistic beliefs about the causal model, as well as what is caused by her actions as well as the actions of every other player are taken into account. Based on such probability updating we define a Nash equilibria for Causal Games.

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances algorithms that learn causal models from data, and this work has produced a series of impressive technical advances. However, evaluation techniques for causal modeling algorithms have remained somewhat primitive, limiting what we can learn from experimental studies of algorithm performance, constraining the types of algorithms and model representations that researchers consider, and creating a gap between theory and practice. We argue for more frequent use of evaluation techniques that examine interventional measures rather than structural or observational measures, and that evaluate those measures on empirical data rather than synthetic data. We survey the current practice in evaluation and show that these are rarely used in practice. We show that such techniques are feasible and that data sets are available to conduct such evaluations. We also show that these techniques produce substantially different results than using structural measures and synthetic data.

The premise of the deconfounder method proposed in ‘Blessings of Multiple Causes’ by Wang and Blei, namely that a variable that renders multiple causes conditionally independent also controls for unmeasured multi-cause confounding, is incorrect. This can be seen by noting that no fact about the observed data alone can be informative about ignorability, since ignorability is compatible with any observed data distribution. Methods to control for unmeasured confounding may be valid with additional assumptions in specific settings, but they cannot, in general, provide a checkable approach to causal inference, and they do not, in general, require weaker assumptions than the assumptions that are commonly used for causal inference. While this is outside the scope of this comment, we note that much recent work on applying ideas from latent variable modeling to causal inference problems suffers from similar issues.

It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden standard for learning the causal DAG beyond Markov equivalence is to perform a sequence of interventions in the system and use the data gathered from the interventional distributions. We consider a setup in which given a budget $k$, we design $k$ interventions non-adaptively. We cast the problem of finding the best intervention target set as an optimization problem which aims to maximize the number of edges whose directions are identified due to the performed interventions. First, we consider the case that the underlying causal structure is a tree. For this case, we propose an efficient exact algorithm for the worst-case gain setup, as well as an approximate algorithm for the average gain setup. We then show that the proposed approach for the average gain setup can be extended to the case of general causal structures. In this case, besides the design of interventions, calculating the objective function is also challenging. We propose an efficient exact calculator as well as two estimators for this task. We evaluate the proposed methods using synthetic as well as real data.

Data-driven models are becoming essential parts in modern mechanical systems, commonly used to capture the behavior of various equipment and varying environmental characteristics. Despite the advantages of these data-driven models on excellent adaptivity to high dynamics and aging equipment, they are usually hungry to massive labels over historical data, mostly contributed by human engineers at an extremely high cost. The label demand is now the major limiting factor to modeling accuracy, hindering the fulfillment of visions for applications. Fortunately, domain adaptation enhances the model generalization by utilizing the labelled source data as well as the unlabelled target data and then we can reuse the model on different domains. However, the mainstream domain adaptation methods cannot achieve ideal performance on time series data, because most of them focus on static samples and even the existing time series domain adaptation methods ignore the properties of time series data, such as temporal causal mechanism. In this paper, we assume that causal mechanism is invariant and present our Causal Mechanism Transfer Network(CMTN) for time series domain adaptation. By capturing and transferring the dynamic and temporal causal mechanism of multivariate time series data and alleviating the time lags and different value ranges among different machines, CMTN allows the data-driven models to exploit existing data and labels from similar systems, such that the resulting model on a new system is highly reliable even with very limited data. We report our empirical results and lessons learned from two real-world case studies, on chiller plant energy optimization and boiler fault detection, which outperforms the existing state-of-the-art method.