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Jose M. Peña

Publications and source records attributed to Jose M. Peña.

At least 19 recordsLinked to original sources
arXiv2026

Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables

To reach human level intelligence, learning algorithms need to incorporate causal reasoning. But identifying causality, and particularly counterfactual reasoning, remains elusive. In this paper, we make progress on counterfactual inference in nonseparable outcome models by utilizing instrumental variables (IVs). IVs are a classic tool for mitigating bias from unobserved confounders when estimating causal effects. While IV methods for effect estimation have been extended to nonseparable outcome models under different assumptions, existing IV approaches to counterfactual prediction typically assume one-dimensional outcomes and additive noise. In this paper, we show that under standard IV assumptions, along with the assumption that the outcome function is invertible and has a triangular structure, then the treatment-outcome relationship becomes identifiable from observed data. We furthermore propose a method to learn the outcome function utilizing normalizing flows. This outcome function estimator can then be used to perform counterfactual inference. We refer to the method as Flow IV.

stat.ML↗
arXiv2025

Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows

We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, accounting for various confounding strengths. The output of the $ρ$-GNF is what we term the $ρ_{curve}$, which provides the bounds for the ACE given an interval of assumed $ρ$ values. The $ρ_{curve}$ also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter $ρ$ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method.

stat.ME↗
arXiv2024

$ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows

We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $ρ$-GNF ($ρ$-graphical normalizing flow), where $ρ{\in}[-1,+1]$ is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, while accounting for various assumed strengths of the unobserved confounding. The output of the $ρ$-GNF is what we denote as the $ρ_{curve}$ that provides the bounds for the ACE given an interval of assumed $ρ$ values. In particular, the $ρ_{curve}$ enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of $ρ$-GNF. One benefit is that the $ρ$-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.

stat.ME↗
arXiv2024

Deep Learning With DAGs

Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in practice. As non-parametric causal models, DAGs require no assumptions about the functional form of the hypothesized relationships. Nevertheless, to simplify the task of empirical evaluation, researchers tend to invoke such assumptions anyway, even though they are typically arbitrary and do not reflect any theoretical content or prior knowledge. Moreover, functional form assumptions can engender bias, whenever they fail to accurately capture the complexity of the causal system under investigation. In this article, we introduce causal-graphical normalizing flows (cGNFs), a novel approach to causal inference that leverages deep neural networks to empirically evaluate theories represented as DAGs. Unlike conventional approaches, cGNFs model the full joint distribution of the data according to a DAG supplied by the analyst, without relying on stringent assumptions about functional form. In this way, the method allows for flexible, semi-parametric estimation of any causal estimand that can be identified from the DAG, including total effects, conditional effects, direct and indirect effects, and path-specific effects. We illustrate the method with a reanalysis of Blau and Duncan's (1967) model of status attainment and Zhou's (2019) model of conditional versus controlled mobility. To facilitate adoption, we provide open-source software together with a series of online tutorials for implementing cGNFs. The article concludes with a discussion of current limitations and directions for future development.

stat.ML↗
arXiv2023

Alternative Measures of Direct and Indirect Effects

There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also show that the new measures can partially handle unmeasured treatment-outcome confounding, and bound long-term effects by combining experimental and observational data.

stat.ME↗
arXiv2023

On the Probability of Immunity

This work is devoted to the study of the probability of immunity, i.e. the effect occurs whether exposed or not. We derive necessary and sufficient conditions for non-immunity and $ε$-bounded immunity, i.e. the probability of immunity is zero and $ε$-bounded, respectively. The former allows us to estimate the probability of benefit (i.e., the effect occurs if and only if exposed) from a randomized controlled trial, and the latter allows us to produce bounds of the probability of benefit that are tighter than the existing ones. We also introduce the concept of indirect immunity (i.e., through a mediator) and repeat our previous analysis for it. Finally, we propose a method for sensitivity analysis of the probability of immunity under unmeasured confounding.

stat.ME↗
arXiv2023

Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxies

We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters which, then, can be presented to the analyst as a 2-D plot to assist her in decision making. The second method assumes the existence of a measured nondifferential proxy (i.e., direct effect) of the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

stat.ME↗
arXiv2022

Factorization of the Partial Covariance in Singly-Connected Path Diagrams

We extend path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to determine the contribution of each node and edge to the partial covariance. It also allows us to show that Simpson's paradox cannot occur in singly-connected path diagrams.

stat.ME↗
arXiv2022

Counterfactual Analysis of the Impact of the IMF Program on Child Poverty in the Global-South Region using Causal-Graphical Normalizing Flows

This work demonstrates the application of a particular branch of causal inference and deep learning models: \emph{causal-Graphical Normalizing Flows (c-GNFs)}. In a recent contribution, scholars showed that normalizing flows carry certain properties, making them particularly suitable for causal and counterfactual analysis. However, c-GNFs have only been tested in a simulated data setting and no contribution to date have evaluated the application of c-GNFs on large-scale real-world data. Focusing on the \emph{AI for social good}, our study provides a counterfactual analysis of the impact of the International Monetary Fund (IMF) program on child poverty using c-GNFs. The analysis relies on a large-scale real-world observational data: 1,941,734 children under the age of 18, cared for by 567,344 families residing in the 67 countries from the Global-South. While the primary objective of the IMF is to support governments in achieving economic stability, our results find that an IMF program reduces child poverty as a positive side-effect by about 1.2$\pm$0.24 degree (`0' equals no poverty and `7' is maximum poverty). Thus, our article shows how c-GNFs further the use of deep learning and causal inference in AI for social good. It shows how learning algorithms can be used for addressing the untapped potential for a significant social impact through counterfactual inference at population level (ACE), sub-population level (CACE), and individual level (ICE). In contrast to most works that model ACE or CACE but not ICE, c-GNFs enable personalization using \emph{`The First Law of Causal Inference'}.

cs.AI↗
arXiv2022

Simple yet Sharp Sensitivity Analysis for Unmeasured Confounding

We present a method for assessing the sensitivity of the true causal effect to unmeasured confounding. The method requires the analyst to set two intuitive parameters. Otherwise, the method is assumption-free. The method returns an interval that contains the true causal effect, and whose bounds are arbitrarily sharp, i.e. practically attainable. We show experimentally that our bounds can be tighter than those obtained by the method of Ding and VanderWeele (2016a) which, moreover, requires to set one more parameter than our method. Finally, we extend our method to bound the natural direct and indirect effects when there are measured mediators and unmeasured exposure-outcome confounding.

stat.ME↗
arXiv2021

On the Non-Monotonicity of a Non-Differentially Mismeasured Binary Confounder

Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a non-differential binary proxy of it is observed. We identify conditions under which adjusting for the proxy comes closer to the incomputable true average causal effect than not adjusting at all. Unlike other works, we do not assume that the average causal effect of the confounder on the outcome is in the same direction among treated and untreated.

stat.ME↗
arXiv2020

Towards Conditional Path Analysis

We extend path analysis by giving sufficient conditions for computing the partial covariance of two random variables from their covariance. This is specifically done by correcting the covariance with the product of some partial variance ratios. As a result, the partial covariance retains the covariance's salient feature of factorizing over the edges in the paths between the two variables of interest.

math.ST↗
arXiv2020

On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder

Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a nondifferential proxy of it is observed. We show that, under certain monotonicity assumption that is empirically verifiable, adjusting for the proxy produces a measure of the effect that is between the unadjusted and the true measures.

stat.ME↗
arXiv2019

Unifying Gaussian LWF and AMP Chain Graphs to Model Interference

An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions. Specifically, we define the new class of models, introduce global and local and pairwise Markov properties for them, and prove their equivalence. We also propose an algorithm for maximum likelihood parameter estimation for the new models, and report experimental results. Finally, we show how to compute the effects of interventions in the new models.

stat.ML↗
arXiv2018

Identifiability of Gaussian Structural Equation Models with Dependent Errors Having Equal Variances

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman chain graphs (Andersson et al., 2001). These chain graphs were originally developed to represent independence models. However, they are also suitable for representing causal models with additive noise (Peña, 2016. Our result implies then that these causal models can be identified from observational data alone. Our result generalizes the result by Peters and Bühlmann (2014), who considered independent errors having equal variances. The suitability of the equal error variances assumption should be assessed on a per domain basis.

stat.ML↗
arXiv2018

Identification of Strong Edges in AMP Chain Graphs

The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the equivalence class. Likewise for the undirected edges. In this paper, we develop a procedure for identifying which edges in an essential graph are strong. We also show how this makes it possible to bound some causal effects when the true chain graph is unknown.

math.CO↗