arXiv subjects

Elias Bareinboim

Publications and source records attributed to Elias Bareinboim.

53 records · Page 3Linked to original sources

arXiv2022

The Causal-Neural Connection: Expressiveness, Learnability, and Inference

One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mechanisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An important property of many kinds of neural networks is universal approximability: the ability to approximate any function to arbitrary precision. Given this property, one may be tempted to surmise that a collection of neural nets is capable of learning any SCM by training on data generated by that SCM. In this paper, we show this is not the case by disentangling the notions of expressivity and learnability. Specifically, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits of what can be learned from data, still holds for neural models. For instance, an arbitrarily complex and expressive neural net is unable to predict the effects of interventions given observational data alone. Given this result, we introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences. Building on this new class of models, we focus on solving two canonical tasks found in the literature known as causal identification and estimation. Leveraging the neural toolbox, we develop an algorithm that is both sufficient and necessary to determine whether a causal effect can be learned from data (i.e., causal identifiability); it then estimates the effect whenever identifiability holds (causal estimation). Simulations corroborate the proposed approach.

cs.LG↗

arXiv2022

Neural Causal Models for Counterfactual Identification and Estimation

Evaluating hypothetical statements about how the world would be had a different course of action been taken is arguably one key capability expected from modern AI systems. Counterfactual reasoning underpins discussions in fairness, the determination of blame and responsibility, credit assignment, and regret. In this paper, we study the evaluation of counterfactual statements through neural models. Specifically, we tackle two causal problems required to make such evaluations, i.e., counterfactual identification and estimation from an arbitrary combination of observational and experimental data. First, we show that neural causal models (NCMs) are expressive enough and encode the structural constraints necessary for performing counterfactual reasoning. Second, we develop an algorithm for simultaneously identifying and estimating counterfactual distributions. We show that this algorithm is sound and complete for deciding counterfactual identification in general settings. Third, considering the practical implications of these results, we introduce a new strategy for modeling NCMs using generative adversarial networks. Simulations corroborate with the proposed methodology.

cs.LG↗

arXiv2022

Causal Imitation Learning with Unobserved Confounders

One of the common ways children learn is by mimicking adults. Imitation learning focuses on learning policies with suitable performance from demonstrations generated by an expert, with an unspecified performance measure, and unobserved reward signal. Popular methods for imitation learning start by either directly mimicking the behavior policy of an expert (behavior cloning) or by learning a reward function that prioritizes observed expert trajectories (inverse reinforcement learning). However, these methods rely on the assumption that covariates used by the expert to determine her/his actions are fully observed. In this paper, we relax this assumption and study imitation learning when sensory inputs of the learner and the expert differ. First, we provide a non-parametric, graphical criterion that is complete (both necessary and sufficient) for determining the feasibility of imitation from the combinations of demonstration data and qualitative assumptions about the underlying environment, represented in the form of a causal model. We then show that when such a criterion does not hold, imitation could still be feasible by exploiting quantitative knowledge of the expert trajectories. Finally, we develop an efficient procedure for learning the imitating policy from experts' trajectories.

cs.LG↗

arXiv2022

Sequential Causal Imitation Learning with Unobserved Confounders

"Monkey see monkey do" is an age-old adage, referring to naïve imitation without a deep understanding of a system's underlying mechanics. Indeed, if a demonstrator has access to information unavailable to the imitator (monkey), such as a different set of sensors, then no matter how perfectly the imitator models its perceived environment (See), attempting to reproduce the demonstrator's behavior (Do) can lead to poor outcomes. Imitation learning in the presence of a mismatch between demonstrator and imitator has been studied in the literature under the rubric of causal imitation learning (Zhang et al., 2020), but existing solutions are limited to single-stage decision-making. This paper investigates the problem of causal imitation learning in sequential settings, where the imitator must make multiple decisions per episode. We develop a graphical criterion that is necessary and sufficient for determining the feasibility of causal imitation, providing conditions when an imitator can match a demonstrator's performance despite differing capabilities. Finally, we provide an efficient algorithm for determining imitability and corroborate our theory with simulations.

cs.LG↗

arXiv2022

Causal Fairness Analysis

Decision-making systems based on AI and machine learning have been used throughout a wide range of real-world scenarios, including healthcare, law enforcement, education, and finance. It is no longer far-fetched to envision a future where autonomous systems will be driving entire business decisions and, more broadly, supporting large-scale decision-making infrastructure to solve society's most challenging problems. Issues of unfairness and discrimination are pervasive when decisions are being made by humans, and remain (or are potentially amplified) when decisions are made using machines with little transparency, accountability, and fairness. In this paper, we introduce a framework for \textit{causal fairness analysis} with the intent of filling in this gap, i.e., understanding, modeling, and possibly solving issues of fairness in decision-making settings. The main insight of our approach will be to link the quantification of the disparities present on the observed data with the underlying, and often unobserved, collection of causal mechanisms that generate the disparity in the first place, challenge we call the Fundamental Problem of Causal Fairness Analysis (FPCFA). In order to solve the FPCFA, we study the problem of decomposing variations and empirical measures of fairness that attribute such variations to structural mechanisms and different units of the population. Our effort culminates in the Fairness Map, which is the first systematic attempt to organize and explain the relationship between different criteria found in the literature. Finally, we study which causal assumptions are minimally needed for performing causal fairness analysis and propose a Fairness Cookbook, which allows data scientists to assess the existence of disparate impact and disparate treatment.

cs.AI↗

arXiv2022

Causal Transportability for Visual Recognition

Visual representations underlie object recognition tasks, but they often contain both robust and non-robust features. Our main observation is that image classifiers may perform poorly on out-of-distribution samples because spurious correlations between non-robust features and labels can be changed in a new environment. By analyzing procedures for out-of-distribution generalization with a causal graph, we show that standard classifiers fail because the association between images and labels is not transportable across settings. However, we then show that the causal effect, which severs all sources of confounding, remains invariant across domains. This motivates us to develop an algorithm to estimate the causal effect for image classification, which is transportable (i.e., invariant) across source and target environments. Without observing additional variables, we show that we can derive an estimand for the causal effect under empirical assumptions using representations in deep models as proxies. Theoretical analysis, empirical results, and visualizations show that our approach captures causal invariances and improves overall generalization.

cs.CV↗

arXiv2021

Partial Counterfactual Identification from Observational and Experimental Data

This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) could be generated by a canonical family of SCMs with the same causal diagram where unobserved (exogenous) variables are discrete with a finite domain. Utilizing the canonical SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query. Solving such polynomial programs is in general computationally expensive. We therefore develop effective Monte Carlo algorithms to approximate the optimal bounds from an arbitrary combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.

cs.AI↗

arXiv2021

Nested Counterfactual Identification from Arbitrary Surrogate Experiments

The Ladder of Causation describes three qualitatively different types of activities an agent may be interested in engaging in, namely, seeing (observational), doing (interventional), and imagining (counterfactual) (Pearl and Mackenzie, 2018). The inferential challenge imposed by the causal hierarchy is that data is collected by an agent observing or intervening in a system (layers 1 and 2), while its goal may be to understand what would have happened had it taken a different course of action, contrary to what factually ended up happening (layer 3). While there exists a solid understanding of the conditions under which cross-layer inferences are allowed from observations to interventions, the results are somewhat scarcer when targeting counterfactual quantities. In this paper, we study the identification of nested counterfactuals from an arbitrary combination of observations and experiments. Specifically, building on a more explicit definition of nested counterfactuals, we prove the counterfactual unnesting theorem (CUT), which allows one to map arbitrary nested counterfactuals to unnested ones. For instance, applications in mediation and fairness analysis usually evoke notions of direct, indirect, and spurious effects, which naturally require nesting. Second, we introduce a sufficient and necessary graphical condition for counterfactual identification from an arbitrary combination of observational and experimental distributions. Lastly, we develop an efficient and complete algorithm for identifying nested counterfactuals; failure of the algorithm returning an expression for a query implies it is not identifiable.

cs.AI↗

arXiv2019

Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets

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.

cs.AI↗

arXiv2019

Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables

We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification problem is concerned with the conditions under which causal parameters can be uniquely estimated from an observational, non-causal covariance matrix. In this paper, we provide an algorithm for the identification of causal parameters in linear structural models that subsumes previous state-of-the-art methods. In other words, our algorithm identifies strictly more coefficients and models than methods previously known in the literature. Our algorithm builds on a graph-theoretic characterization of conditional independence relations between auxiliary and model variables, which is developed in this paper. Further, we leverage this new characterization for allowing identification when limited experimental data or new substantive knowledge about the domain is available. Lastly, we develop a new procedure for model testing using AVs.

stat.ME↗

arXiv2018

Causal Identification under Markov Equivalence

Assessing the magnitude of cause-and-effect relations is one of the central challenges found throughout the empirical sciences. The problem of identification of causal effects is concerned with determining whether a causal effect can be computed from a combination of observational data and substantive knowledge about the domain under investigation, which is formally expressed in the form of a causal graph. In many practical settings, however, the knowledge available for the researcher is not strong enough so as to specify a unique causal graph. Another line of investigation attempts to use observational data to learn a qualitative description of the domain called a Markov equivalence class, which is the collection of causal graphs that share the same set of observed features. In this paper, we marry both approaches and study the problem of causal identification from an equivalence class, represented by a partial ancestral graph (PAG). We start by deriving a set of graphical properties of PAGs that are carried over to its induced subgraphs. We then develop an algorithm to compute the effect of an arbitrary set of variables on an arbitrary outcome set. We show that the algorithm is strictly more powerful than the current state of the art found in the literature.

cs.AI↗

arXiv2018

Budgeted Experiment Design for Causal Structure Learning

We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resolved. We prove that the corresponding objective function is submodular and a greedy algorithm suffices to achieve $(1-\frac{1}{e})$-approximation of the optimal value. We further present an accelerated variant of the greedy algorithm, which can lead to orders of magnitude performance speedup. We validate our proposed approach on synthetic and real graphs. The results show that compared to the purely observational setting, our algorithm orients the majority of the edges through a considerably small number of interventions.

cs.LG↗

arXiv2016

Incorporating Knowledge into Structural Equation Models using Auxiliary Variables

In this paper, we extend graph-based identification methods by allowing background knowledge in the form of non-zero parameter values. Such information could be obtained, for example, from a previously conducted randomized experiment, from substantive understanding of the domain, or even an identification technique. To incorporate such information systematically, we propose the addition of auxiliary variables to the model, which are constructed so that certain paths will be conveniently cancelled. This cancellation allows the auxiliary variables to help conventional methods of identification (e.g., single-door criterion, instrumental variables, half-trek criterion), as well as model testing (e.g., d-separation, over-identification). Moreover, by iteratively alternating steps of identification and adding auxiliary variables, we can improve the power of existing identification methods via a bootstrapping approach that does not require external knowledge. We operationalize this method for simple instrumental sets (a generalization of instrumental variables) and show that the resulting method is able to identify at least as many models as the most general identification method for linear systems known to date. We further discuss the application of auxiliary variables to the tasks of model testing and z-identification.

stat.ME↗

arXiv2015

External Validity: From Do-Calculus to Transportability Across Populations

The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called "transportability," defined as a license to transfer causal effects learned in experimental studies to a new population, in which only observational studies can be conducted. We introduce a formal representation called "selection diagrams" for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we reduce questions of transportability to symbolic derivations in the do-calculus. This reduction yields graph-based procedures for deciding, prior to observing any data, whether causal effects in the target population can be inferred from experimental findings in the study population. When the answer is affirmative, the procedures identify what experimental and observational findings need be obtained from the two populations, and how they can be combined to ensure bias-free transport.

stat.ME↗

arXiv2013

A General Algorithm for Deciding Transportability of Experimental Results

Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim (2011) derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize bias-free estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.

cs.AI↗

arXiv2012

Causal Inference by Surrogate Experiments: z-Identifiability

We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call z-identifiability, reduces to ordinary identifiability when Z = empty and, like the latter, can be given syntactic characterization using the do-calculus [Pearl, 1995; 2000]. We provide a graphical necessary and sufficient condition for z-identifiability for arbitrary sets X,Z, and Y (the outcomes). We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of do-calculus relative to z-identifiability, a result that does not follow from completeness relative to ordinary identifiability.

cs.AI↗

arXiv2007

Descents and nodal load in scale-free networks

The load of a node in a network is the total traffic going through it when every node pair sustains a uniform bidirectional traffic between them on shortest paths. We show that nodal load can be expressed in terms of the more elementary notion of a node's descents in breadth-first-search (BFS or shortest-path) trees, and study both the descent and nodal-load distributions in the case of scale-free networks. Our treatment is both semi-analytical (combining a generating-function formalism with simulation-derived BFS branching probabilities) and computational for the descent distribution; it is exclusively computational in the case of the load distribution. Our main result is that the load distribution, even though it can be disguised as a power-law through subtle (but inappropriate) binning of the raw data, is in fact a succession of sharply delineated probability peaks, each of which can be clearly interpreted as a function of the underlying BFS descents. This find is in stark contrast with previously held belief, based on which a power law of exponent -2.2 was conjectured to be valid regardless of the exponent of the power-law distribution of node degrees.

cond-mat.stat-mech↗