We consider the problem of predicting a response $Y$ from a set of covariates $X$ when test and training distributions differ. Since such differences may have causal explanations, we consider test distributions that emerge from interventions in a structural causal model, and focus on minimizing the worst-case risk. Causal regression models, which regress the response on its direct causes, remain unchanged under arbitrary interventions on the covariates, but they are not always optimal in the above sense. For example, for linear models and bounded interventions, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct interventions on $X$ and interventions that occur indirectly via exogenous variables $A$. It takes into account that, in practice, minimax solutions need to be identified from data. Our framework allows us to characterize under which class of interventions the causal function is minimax optimal. We prove sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, NILE, that achieves distribution generalization in a nonlinear IV setting with linear extrapolation. We prove consistency and present empirical results.
A vast amount of expert and domain knowledge is captured by causal structural priors, yet there has been little research on testing such priors for generalization and data synthesis purposes. We propose a novel model architecture, Causal Structural Hypothesis Testing, that can use nonparametric, structural causal knowledge and approximate a causal model's functional relationships using deep neural networks. We use these architectures for comparing structural priors, akin to hypothesis testing, using a deliberate (non-random) split of training and testing data. Extensive simulations demonstrate…
We introduce profile matching, a multivariate matching method for randomized experiments and observational studies that finds the largest possible unweighted samples across multiple treatment groups that are balanced relative to a covariate profile. This covariate profile can represent a specific population or a target individual, facilitating the generalization and personalization of causal inferences. For generalization, because the profile often amounts to summary statistics for a target population, profile matching does not always require accessing individual-level data, which may be unava…
In this paper, we focus on estimating the average treatment effect (ATE) of a target population when individual-level data from a source population and summary-level data (e.g., first or second moments of certain covariates) from the target population are available. In the presence of heterogeneous treatment effect, the ATE of the target population can be different from that of the source population when distributions of treatment effect modifiers are dissimilar in these two populations, a phenomenon also known as covariate shift. Many methods have been developed to adjust for covariate shift,…
Randomized experiments are an excellent tool for estimating internally valid causal effects with the sample at hand, but their external validity is frequently debated. While classical results on the estimation of Population Average Treatment Effects (PATE) implicitly assume random selection into experiments, this is typically far from true in many medical, social-scientific, and industry experiments. When the experimental sample is different from the target sample along observable or unobservable dimensions, experimental estimates may be of limited use for policy decisions. We begin by decompo…
Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space $\mathbb{R}^p$. However, it is increasingly common that complex datasets are best summarized as data points in non-linear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is non-linear. We develop doubly robust estimators and associated asymptotic theory …
Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated a…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
The predominant method for evaluating the quality of causal models is to measure the graphical accuracy of the learned model structure. We present an alternative method for evaluating causal models that directly measures the accuracy of estimated interventional distributions. We contrast such distributional measures with structural measures, such as structural Hamming distance and structural intervention distance, showing that structural measures often correspond poorly to the accuracy of estimated interventional distributions. We use a number of real and synthetic datasets to illustrate vario…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$, computes a causal query, $Q$, as a function of known population probabilities, $I$, in every model entailed by a set of model assumptions, $M$. Many problems in causal inference can be viewed as the problem of enumerating instances of the relation that satisfy given criteria. This unifies a number of previously studied problems, including causal effect identificat…
ETH Zürich（苏黎世联邦理工学院）；MPI Tübingen（蒂宾根马克斯·普朗克研究所）；University of Copenhagen（哥本哈根大学）
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits …
In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also kn…
University of Maryland, College Park（马里兰大学帕克分校）；Department of Computer Science（计算机科学系）
This paper introduces Whittemore, a language for causal programming. Causal programming is based on the theory of structural causal models and consists of two primary operations: identification, which finds formulas that compute causal queries, and estimation, which applies formulas to transform probability distributions to other probability distribution. Causal programming provides abstractions to declare models, queries, and distributions with syntax similar to standard mathematical notation, and conducts rigorous causal inference, without requiring detailed knowledge of the underlying algor…
