Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore not well suited to many questions from applications, for example in Bayesian filtering and reliability estimation. This work introduces a parametric polynomial kernel method that can be used for inferring the future behaviour of Ordinary Differential Equation models, including chaotic dynamical systems, from observations. Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent. The polynomial technique presented here is based on a nonparametric method, kernel ridge regression. However, the time complexity of nonparametric kernel ridge regression scales cubically with the number of training data points. Our parametric polynomial method avoids this manifestation of the curse of dimensionality, which becomes particularly relevant when working with large time series data sets. Two numerical demonstrations are presented. First, a simple regression test case is used to illustrate the method and to compare the performance with standard Artificial Neural Network techniques. Second, a more substantial test case is the inference of a chaotic spatio-temporal dynamical system, the Lorenz–Emanuel system, from observations. Our method was able to successfully track the future behaviour of the system over time periods much larger than the training data sampling rate. Finally, some limitations of the method are presented, as well as proposed directions for future work to mitigate these limitations.
Evaluating novel contextual bandit policies using logged data is crucial in applications where exploration is costly, such as medicine. But it usually relies on the assumption of no unobserved confounders, which is bound to fail in practice. We study the question of policy evaluation when we instead have proxies for the latent confounders and develop an importance weighting method that avoids fitting a latent outcome regression model. We show that unlike the unconfounded case no single set of weights can give unbiased evaluation for all outcome models, yet we propose a new algorithm that can still provably guarantee consistency by instead minimizing an adversarial balance objective. We further develop tractable algorithms for optimizing this objective and demonstrate empirically the power of our method when confounders are latent.
Article: Causal inference with DAGs in R
Directed acyclic graphs (DAGs) are a powerful tool to understand and deal with causal inference. The book ‘Causal inference in statistics: a primer’ is a useful reference to start. A DAG is a visual encoding of a joint distribution of a set of variables. In a DAG all the variables are depicted as vertices and connected by arrows or directed paths, sequences of arrows in which every arrow points to some direction. DAGs are acyclic because no directed path can form a closed loop. The dagitty package is an effective tool for drawing and analyzing DAGs. Available functions include identification of minimal sufficient adjustment sets for estimating causal effects. Let’s now focus on the following example. We are interesting in draw causal inference of the treatment (T) effect on a certain outcome (Y). The analysis can be biased due to the presence of several confounders (X1, X2, X3).
Behavioral software models play a key role in many software engineering tasks; unfortunately, these models either are not available during software development or, if available, they quickly become outdated as the implementations evolve. Model inference techniques have been proposed as a viable solution to extract finite-state models from execution logs. However, existing techniques do not scale well when processing very large logs, such as system-level logs obtained by combining component-level logs. Furthermore, in the case of component-based systems, existing techniques assume to know the definitions of communication channels between components. However, this information is usually not available in the case of systems integrating 3rd-party components with limited documentation. In this paper, we address the scalability problem of inferring the model of a component-based system from the individual component-level logs, when the only available information about the system are high-level architecture dependencies among components and a (possibly incomplete) list of log message templates denoting communication events between components. Our model inference technique, called SCALER, follows a divide and conquer approach. The idea is to first infer a model of each system component from the corresponding logs; then, the individual component models are merged together taking into account the dependencies among components, as reflected in the logs. We evaluated SCALER in terms of scalability and accuracy, using a dataset of logs from an industrial system; the results show that SCALER can process much larger logs than a state-of-the-art tool, while yielding more accurate models.
Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. This is a key feature since identification is generally more credible if the full vector of conditioning variables, including possible transformations, is high-dimensional. The second stage consists of a low-dimensional kernel regression, reducing CATE to a function of the covariate(s) of interest. We consider two variants of the estimator depending on whether the nuisance functions are estimated over the full sample or over a hold-out sample. Building on Belloni at al. (2017) and Chernozhukov et al. (2018), we derive functional limit theory for the estimators and provide an easy-to-implement procedure for uniform inference based on the multiplier bootstrap. The empirical application revisits the effect of maternal smoking on a baby’s birth weight as a function of the mother’s age.