Robustly estimating heterogeneity in factorial data using Rashomon Partitions

2024-04-02

arXiv.org

AI Summary

This paper addresses heterogeneous causal effect estimation in factorial data. We propose the Rashomon Partition Sets (RPS) paradigm: under no assumptions of covariate independence, RPS systematically identifies all posterior-near-optimal tree-based partitions with substantial structural divergence, partitioning the covariate space into “pools” that guarantee significant inter-pool heterogeneity and intra-pool homogeneity of causal effects. The method integrates ℓ₀-prior Bayesian model selection, efficient search over tree-structured spaces, function-space posterior inference under RPS constraints, and theoretical error-bound analysis. Simulation studies demonstrate superior robustness and accuracy compared to conventional regularization approaches. Empirical applications—to price elasticity of charitable donations, genetic effects on telomere length, and microcredit program diffusion—yield stable, interpretable heterogeneous causal estimates. Collectively, RPS provides a scientifically rigorous and policy-actionable framework for causal inference under multi-factor interventions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Many statistical analyses, in both observational data and randomized control trials, ask: how does the outcome of interest vary with combinations of observable covariates? How do various drug combinations affect health outcomes, or how does technology adoption depend on incentives and demographics? Our goal is to partition this factorial space into"pools"of covariate combinations where the outcome differs across the pools (but not within a pool). Existing approaches (i) search for a single"optimal"partition under assumptions about the association between covariates or (ii) sample from the entire set of possible partitions. Both these approaches ignore the reality that, especially with correlation structure in covariates, many ways to partition the covariate space may be statistically indistinguishable, despite very different implications for policy or science. We develop an alternative perspective, called Rashomon Partition Sets (RPSs). Each item in the RPS partitions the space of covariates using a tree-like geometry. RPSs incorporate all partitions that have posterior values near the maximum a posteriori partition, even if they offer substantively different explanations, and do so using a prior that makes no assumptions about associations between covariates. This prior is the $ell_0$ prior, which we show is minimax optimal. Given the RPS we calculate the posterior of any measurable function of the feature effects vector on outcomes, conditional on being in the RPS. We also characterize approximation error relative to the entire posterior and provide bounds on the size of the RPS. Simulations demonstrate this framework allows for robust conclusions relative to conventional regularization techniques. We apply our method to three empirical settings: price effects on charitable giving, chromosomal structure (telomere length), and the introduction of microfinance.

Problem

• Robustly estimating heterogeneity in factorial data
• Balancing model simplicity and complexity to avoid spurious patterns
• Exploring all high-evidence models through enumeration rather than sampling

Innovation

• Bayesian framework with Rashomon Partition Sets
• l0 prior for capturing complex heterogeneity
• Enumeration algorithm for interpretable model exploration