**Paper**: **Effects of interventions and optimal strategies in the stochastic system approach to causality**

We consider the problem of defining the effect of an intervention on a time-varying risk factor or treatment for a disease or a physiological marker; we develop here the latter case. So, the system considered is $(Y,A,C)$, where $Y=(Y_t)$, is the marker process of interest, $A=A_t$ the treatment. A realistic case is that the treatment can be changed only at discrete times. In an observational study the treatment attribution law is unknown; however, the physical law can be estimated without knowing the treatment attribution law, provided a well-specified model is available. An intervention is specified by the treatment attribution law, which is thus known. Simple interventions will simply randomize the attribution of the treatment; interventions that take into account the past history will be called ‘strategies’. The effect of interventions can be defined by a risk function $R^{\intr}=\Ee_{\intr}[L(\bar Y_{t_J}, \bar A_{t_{J}},C)]$, where $L(\bar Y_{t_J}, \bar A_{t_{J}},C)$ is a loss function, and contrasts between risk functions for different strategies can be formed. Once we can compute effects for any strategy, we can search for optimal or sub-optimal strategies; in particular we can find optimal parametric strategies. We present several ways for designing strategies. As an illustration, we consider the choice of a strategy for containing the HIV load below a certain level while limiting the treatment burden. A simulation study demonstrates the possibility of finding optimal parametric strategies.

**Paper**: **Visual Entropy and the Visualization of Uncertainty**

Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 >0.97, p<0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.

**Paper**: **Network Dependence and Confounding by Network Structure Lead to Invalid Inference**

Researchers across the health and social sciences generally assume that observations are independent, even while relying on convenience samples that draw subjects from one or a small number of communities, schools, hospitals, etc. A paradigmatic example of this is the Framingham Heart Study (FHS). Many of the limitations of such samples are well-known, but the issue of statistical dependence due to social network ties has not previously been addressed. We show that, along with anticonservative variance estimation, this network dependence can result in confounding by network structure that biases associations away from the null. Using a statistical test that we adapted from one developed for spatial autocorrelation, we test for network dependence and for possible confounding by network structure in several of the thousands of influential papers published using FHS data. Results suggest that some of the many decades of research on coronary heart disease, other health outcomes, and peer influence using FHS data may be biased and anticonservative due to unacknowledged network dependence. We conclude that these issues are not unique to the FHS; as researchers in psychology, medicine, and beyond grapple with replication failures, this unacknowledged source of invalid statistical inference should be part of the conversation.

**Paper**: **Incremental causal effects**

This is a draft. The ignorability assumption is a key assumption in causal inference. It is commonly made, but often violated in observational studies. In this paper, we investigate a local version of this assumption for continuous treatments, where potential outcomes are independent of the treatment assignment only in a neighborhood of the current treatment assignment. Similarly, we introduce a local version of the overlap condition, where the positivity assumption only holds in a neighborhood of observations. Under these local assumptions, we show that the effect of shifting a continuous treatment variable by a small amount across the whole population (termed incremental treatment effect) is still identifiable, and that the incremental treatment effect is equal to the average derivative or average partial effect. Moreover, we prove that in certain regression settings, estimating the incremental effect is easier than estimating the average treatment effect in terms of asymptotic variance and more robust to additive confounding. For high-dimensional settings, we develop a simple feature transformation that allows for doubly-robust estimation and doubly-robust inference of incremental causal effects. Finally, we compare the behaviour of estimators of the incremental treatment effect and average treatment effect on simulated data.

**Paper**: **Multi-cause causal inference with unmeasured confounding and binary outcome**

Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that if additional data such as negative controls are available, then the causal effects are indeed identifiable. In this paper, we show that these additional data are not necessary for causal identification, provided that the treatments and outcome follow Gaussian and logistic structural equation models, respectively. Our novel identification strategy is based on the symmetry and tail properties of the observed data distribution. We further develop two-step likelihood-based estimation procedures. We illustrate our method through simulations and a real data application studying the causal relationship between the volume of various brain regions and cognitive scores.

**Paper**: **On Mutual Information Maximization for Representation Learning**

Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate problems: For example, MI is notoriously hard to estimate, and using it as an objective for representation learning may lead to highly entangled representations due to its invariance under arbitrary invertible transformations. Nevertheless, these methods have been repeatedly shown to excel in practice. In this paper we argue, and provide empirical evidence, that the success of these methods might be only loosely attributed to the properties of MI, and that they strongly depend on the inductive bias in both the choice of feature extractor architectures and the parametrization of the employed MI estimators. Finally, we establish a connection to deep metric learning and argue that this interpretation may be a plausible explanation for the success of the recently introduced methods.