Recursive Causal Discovery

Causal discovery, i.e., learning the causal graph from data, is often the first step toward the identification and estimation of causal effects, a key requirement in numerous scientific domains. Causal discovery is hampered by two main challenges: limited data results in errors in statistical testing and the computational complexity of the learning task is daunting. This paper builds upon and extends four of our prior publications (Mokhtarian et al., 2021; Akbari et al., 2021; Mokhtarian et al., 2022, 2023a). These works introduced the concept of removable variables, which are the only variables that can be removed recursively for the purpose of causal discovery. Presence and identification of removable variables allow recursive approaches for causal discovery, a promising solution that helps to address the aforementioned challenges by reducing the problem size successively. This reduction not only minimizes conditioning sets in each conditional independence (CI) test, leading to fewer errors but also significantly decreases the number of required CI tests. The worst-case performances of these methods nearly match the lower bound. In this paper, we present a unified framework for the proposed algorithms, refined with additional details and enhancements for a coherent presentation. A comprehensive literature review is also included, comparing the computational complexity of our methods with existing approaches, showcasing their state-of-the-art efficiency. Another contribution of this paper is the release of RCD, a Python package that efficiently implements these algorithms. This package is designed for practitioners and researchers interested in applying these methods in practical scenarios. The package is available at github.com/ban-epfl/rcd, with comprehensive documentation provided at rcdpackage.com.

Confounded Budgeted Causal Bandits

We study the problem of learning 'good' interventions in a stochastic environment modeled by its underlying causal graph. Good interventions refer to interventions that maximize rewards. Specifically, we consider the setting of a pre-specified budget constraint, where interventions can have non-uniform costs. We show that this problem can be formulated as maximizing the expected reward for a stochastic multi-armed bandit with side information. We propose an algorithm to minimize the cumulative regret in general causal graphs. This algorithm trades off observations and interventions based on their costs to achieve the optimal reward. This algorithm generalizes the state-of-the-art methods by allowing non-uniform costs and hidden confounders in the causal graph. Furthermore, we develop an algorithm to minimize the simple regret in the budgeted setting with non-uniform costs and also general causal graphs. We provide theoretical guarantees, including both upper and lower bounds, as well as empirical evaluations of our algorithms. Our empirical results showcase that our algorithms outperform the state of the art.

Modeling Systemic Risk: A Time-Varying Nonparametric Causal Inference Framework

We propose a nonparametric and time-varying directed information graph (TV-DIG) framework to estimate the evolving causal structure in time series networks, thereby addressing the limitations of traditional econometric models in capturing high-dimensional, nonlinear, and time-varying interconnections among series. This framework employs an information-theoretic measure rooted in a generalized version of Granger-causality, which is applicable to both linear and nonlinear dynamics. Our framework offers advancements in measuring systemic risk and establishes meaningful connections with established econometric models, including vector autoregression and switching models. We evaluate the efficacy of our proposed model through simulation experiments and empirical analysis, reporting promising results in recovering simulated time-varying networks with nonlinear and multivariate structures. We apply this framework to identify and monitor the evolution of interconnectedness and systemic risk among major assets and industrial sectors within the financial network. We focus on cryptocurrencies' potential systemic risks to financial stability, including spillover effects on other sectors during crises like the COVID-19 pandemic and the Federal Reserve's 2020 emergency response. Our findings reveals significant, previously underrecognized pre-2020 influences of cryptocurrencies on certain financial sectors, highlighting their potential systemic risks and offering a systematic approach in tracking evolving cross-sector interactions within financial networks.

Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data

We study the problem of identifying the unknown intervention targets in structural causal models where we have access to heterogeneous data collected from multiple environments. The unknown intervention targets are the set of endogenous variables whose corresponding exogenous noises change across the environments. We propose a two-phase approach which in the first phase recovers the exogenous noises corresponding to unknown intervention targets whose distributions have changed across environments. In the second phase, the recovered noises are matched with the corresponding endogenous variables. For the recovery phase, we provide sufficient conditions for learning these exogenous noises up to some component-wise invertible transformation. For the matching phase, under the causal sufficiency assumption, we show that the proposed method uniquely identifies the intervention targets. In the presence of latent confounders, the intervention targets among the observed variables cannot be determined uniquely. We provide a candidate intervention target set which is a superset of the true intervention targets. Our approach improves upon the state of the art as the returned candidate set is always a subset of the target set returned by previous work. Moreover, we do not require restrictive assumptions such as linearity of the causal model or performing invariance tests to learn whether a distribution is changing across environments which could be highly sample inefficient. Our experimental results show the effectiveness of our proposed algorithm in practice.

Efficiently Escaping Saddle Points for Non-Convex Policy Optimization

Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate first-order stationary point (FOSP) with the sample complexity of $O(\epsilon^{-3})$. However, FOSPs could be bad local optima or saddle points. Moreover, these algorithms often use importance sampling (IS) weights which could impair the statistical effectiveness of variance reduction. In this paper, we propose a variance-reduced second-order method that uses second-order information in the form of Hessian vector products (HVP) and converges to an approximate second-order stationary point (SOSP) with sample complexity of $\tilde{O}(\epsilon^{-3})$. This rate improves the best-known sample complexity for achieving approximate SOSPs by a factor of $O(\epsilon^{-0.5})$. Moreover, the proposed variance reduction technique bypasses IS weights by using HVP terms. Our experimental results show that the proposed algorithm outperforms the state of the art and is more robust to changes in random seeds.

CausalCite: A Causal Formulation of Paper Citations

Evaluating the significance of a paper is pivotal yet challenging for the scientific community. While the citation count is the most commonly used proxy for this purpose, they are widely criticized for failing to accurately reflect a paper's true impact. In this work, we propose a causal inference method, TextMatch, which adapts the traditional matching framework to high-dimensional text embeddings. Specifically, we encode each paper using the text embeddings by large language models (LLMs), extract similar samples by cosine similarity, and synthesize a counterfactual sample by the weighted average of similar papers according to their similarity values. We apply the resulting metric, called CausalCite, as a causal formulation of paper citations. We show its effectiveness on various criteria, such as high correlation with paper impact as reported by scientific experts on a previous dataset of 1K papers, (test-of-time) awards for past papers, and its stability across various sub-fields of AI. We also provide a set of findings that can serve as suggested ways for future researchers to use our metric for a better understanding of a paper's quality. Our code and data are at https://github.com/causalNLP/causal-cite.

On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery

Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density estimator. We establish an exponential concentration inequality for this estimator. We design a test for conditional independence (CI) based on our estimator, called VM-CI, which achieves optimal parametric rates under smoothness assumptions. Leveraging the exponential concentration, we prove a tight upper bound for the overall error of VM-CI. This, in turn, allows us to characterize the sample complexity of any constraint-based causal discovery algorithm that uses VM-CI for CI tests. To the best of our knowledge, this is the first sample complexity guarantee for causal discovery for continuous variables. Furthermore, we empirically show that VM-CI outperforms other popular CI tests in terms of either time or sample complexity (or both), which translates to a better performance in structure learning as well.

s-ID: Causal Effect Identification in a Sub-Population

Causal inference in a sub-population involves identifying the causal effect of an intervention on a specific subgroup within a larger population. However, ignoring the subtleties introduced by sub-populations can either lead to erroneous inference or limit the applicability of existing methods. We introduce and advocate for a causal inference problem in sub-populations (henceforth called s-ID), in which we merely have access to observational data of the targeted sub-population (as opposed to the entire population). Existing inference problems in sub-populations operate on the premise that the given data distributions originate from the entire population, thus, cannot tackle the s-ID problem. To address this gap, we provide necessary and sufficient conditions that must hold in the causal graph for a causal effect in a sub-population to be identifiable from the observational distribution of that sub-population. Given these conditions, we present a sound and complete algorithm for the s-ID problem.

Gaussian Database Alignment and Gaussian Planted Matching

Database alignment is a variant of the graph alignment problem: Given a pair of anonymized databases containing separate yet correlated features for a set of users, the problem is to identify the correspondence between the features and align the anonymized user sets based on correlation alone. This closely relates to planted matching, where given a bigraph with random weights, the goal is to identify the underlying matching that generated the given weights. We study an instance of the database alignment problem with multivariate Gaussian features and derive results that apply both for database alignment and for planted matching, demonstrating the connection between them. The performance thresholds for database alignment converge to that for planted matching when the dimensionality of the database features is \(\omega(\log n)\), where \(n\) is the size of the alignment, and no individual feature is too strong. The maximum likelihood algorithms for both planted matching and database alignment take the form of a linear program and we study relaxations to better understand the significance of various constraints under various conditions and present achievability and converse bounds. Our results show that the almost-exact alignment threshold for the relaxed algorithms coincide with that of maximum likelihood, while there is a gap between the exact alignment thresholds. Our analysis and results extend to the unbalanced case where one user set is not fully covered by the alignment.

On Identifiability of Conditional Causal Effects

We address the problem of identifiability of an arbitrary conditional causal effect given both the causal graph and a set of any observational and/or interventional distributions of the form $Q[S]:=P(S|do(V\setminus S))$, where $V$ denotes the set of all observed variables and $S\subseteq V$. We call this problem conditional generalized identifiability (c-gID in short) and prove the completeness of Pearl's $do$-calculus for the c-gID problem by providing sound and complete algorithm for the c-gID problem. This work revisited the c-gID problem in Lee et al. [2020], Correa et al. [2021] by adding explicitly the positivity assumption which is crucial for identifiability. It extends the results of [Lee et al., 2019, Kivva et al., 2022] on general identifiability (gID) which studied the problem for unconditional causal effects and Shpitser and Pearl [2006b] on identifiability of conditional causal effects given merely the observational distribution $P(\mathbf{V})$ as our algorithm generalizes the algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].