We study the differences arising from merging predictors in the causal and anticausal directions using the same data. In particular we study the asymmetries that arise in a simple model where we merge the predictors using one binary variable as target and two continuous variables as predictors. We use Causal Maximum Entropy (CMAXENT) as inductive bias to merge the predictors, however, we expect similar differences to hold also when we use other merging methods that take into account asymmetries between cause and effect. We show that if we observe all bivariate distributions, the CMAXENT solution reduces to a logistic regression in the causal direction and Linear Discriminant Analysis (LDA) in the anticausal direction. Furthermore, we study how the decision boundaries of these two solutions differ whenever we observe only some of the bivariate distributions implications for Out-Of-Variable (OOV) generalisation.

We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a pair of variables that has been dropped when learning the causal model. To this end, we use the "Leave-One-Variable-Out (LOVO)" prediction where $Y$ is inferred from $X$ without any joint observations of $X$ and $Y$, given only training data from $X,Z_1,\dots,Z_k$ and from $Z_1,\dots,Z_k,Y$. We demonstrate that causal models on the two subsets, in the form of Acyclic Directed Mixed Graphs (ADMGs), often entail conclusions on the dependencies between $X$ and $Y$, enabling this type of prediction. The prediction error can then be estimated since the joint distribution $P(X, Y)$ is assumed to be available, and $X$ and $Y$ have only been omitted for the purpose of falsification. After presenting this graphical method, which is applicable to general causal discovery algorithms, we illustrate how to construct a LOVO predictor tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness.

The framework comes with three practical challenges: (1) it requires the causal directed acyclic graph (DAG), together with an SCM, (2) it is statistically ill-posed since it probes regression models in regions of low probability density, (3) it relies on Shapley values which are computationally expensive to find. In this paper, we propose simplified, efficient methods of root cause analysis when the task is to identify a unique root cause instead of quantitative contribution analysis. Our proposed methods run in linear order of SCM nodes and they require only the causal DAG without counterfactuals. Furthermore, for those use cases where the causal DAG is unknown, we justify the heuristic of identifying root causes as the variables with the highest anomaly score.

Which set of features was responsible for a certain output of a machine learning model? Which components caused the failure of a cloud computing application? These are just two examples of questions we are addressing in this work by Identifying Coalition-based Explanations for Common and Rare Events in Any Model (ICECREAM). Specifically, we propose an information-theoretic quantitative measure for the influence of a coalition of variables on the distribution of a target variable. This allows us to identify which set of factors is essential to obtain a certain outcome, as opposed to well-established explainability and causal contribution analysis methods which can assign contributions only to individual factors and rank them by their importance. In experiments with synthetic and real-world data, we show that ICECREAM outperforms state-of-the-art methods for explainability and root cause analysis, and achieves impressive accuracy in both tasks.

Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) stop earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. Classical batch tests are not tailored for streaming data: valid inference after data peeking requires correcting for multiple testing which results in low power. Following the principle of testing by betting, we design sequential kernelized independence tests that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g., the Hilbert-Schmidt independence criterion. Our test is also valid under non-i.i.d., time-varying settings. We demonstrate the power of our approaches on both simulated and real data.

We consider the problem of answering observational, interventional, and counterfactual queries in a causally sufficient setting where only observational data and the causal graph are available. Utilizing the recent developments in diffusion models, we introduce diffusion-based causal models (DCM) to learn causal mechanisms, that generate unique latent encodings. These encodings enable us to directly sample under interventions and perform abduction for counterfactuals. Diffusion models are a natural fit here, since they can encode each node to a latent representation that acts as a proxy for exogenous noise. Our empirical evaluations demonstrate significant improvements over existing state-of-the-art methods for answering causal queries. Furthermore, we provide theoretical results that offer a methodology for analyzing counterfactual estimation in general encoder-decoder models, which could be useful in settings beyond our proposed approach.

Understanding the causal relationships among the variables of a system is paramount to explain and control its behaviour. Inferring the causal graph from observational data without interventions, however, requires a lot of strong assumptions that are not always realistic. Even for domain experts it can be challenging to express the causal graph. Therefore, metrics that quantitatively assess the goodness of a causal graph provide helpful checks before using it in downstream tasks. Existing metrics provide an absolute number of inconsistencies between the graph and the observed data, and without a baseline, practitioners are left to answer the hard question of how many such inconsistencies are acceptable or expected. Here, we propose a novel consistency metric by constructing a surrogate baseline through node permutations. By comparing the number of inconsistencies with those on the surrogate baseline, we derive an interpretable metric that captures whether the DAG fits significantly better than random. Evaluating on both simulated and real data sets from various domains, including biology and cloud monitoring, we demonstrate that the true DAG is not falsified by our metric, whereas the wrong graphs given by a hypothetical user are likely to be falsified.

Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently, explanations obtained are sensitive to model behaviour outside the data distribution, which may be irrelevant for all practical purposes. While on-manifold methods have been proposed which do not suffer from this problem, we show that such methods are overly dependent on the input data distribution, and therefore result in unintuitive and misleading explanations. To circumvent these problems, we propose ManifoldShap, which respects the model's domain of validity by restricting model evaluations to the data manifold. We show, theoretically and empirically, that ManifoldShap is robust to off-manifold perturbations of the model and leads to more accurate and intuitive explanations than existing state-of-the-art Shapley methods.

In this work, we initiate the idea of using denoising diffusion models to learn priors for online decision making problems. Our special focus is on the meta-learning for bandit framework, with the goal of learning a strategy that performs well across bandit tasks of a same class. To this end, we train a diffusion model that learns the underlying task distribution and combine Thompson sampling with the learned prior to deal with new tasks at test time. Our posterior sampling algorithm is designed to carefully balance between the learned prior and the noisy observations that come from the learner's interaction with the environment. To capture realistic bandit scenarios, we also propose a novel diffusion model training procedure that trains even from incomplete and/or noisy data, which could be of independent interest. Finally, our extensive experimental evaluations clearly demonstrate the potential of the proposed approach.

We introduce DoWhy-GCM, an extension of the DoWhy Python library, that leverages graphical causal models. Unlike existing causality libraries, which mainly focus on effect estimation questions, with DoWhy-GCM, users can ask a wide range of additional causal questions, such as identifying the root causes of outliers and distributional changes, causal structure learning, attributing causal influences, and diagnosis of causal structures. To this end, DoWhy-GCM users first model cause-effect relations between variables in a system under study through a graphical causal model, fit the causal mechanisms of variables next, and then ask the causal question. All these steps take only a few lines of code in DoWhy-GCM. The library is available at https://github.com/py-why/dowhy.