Technology Category
Machine Learning: Adversarial Learning & RobustnessMultiagent Systems: Adversarial AgentsGame Theory and Economic Paradigms: Adversarial Learning
Joint Probability Estimation of Many Binary Outcomes via Localized Adversarial Lasso
🤖 AI Summary
This paper addresses the exponential-parameter challenge of estimating the joint distribution of high-dimensional binary vectors—arising, e.g., in multiple-treatment causal inference and product demand modeling—by proposing a locally adversarial Lasso estimator. The method uniquely integrates Bahadur representation, adaptive sparse regularization, and adversarial constraints, reducing the convergence rate from the ambient dimension $M$ to the intrinsic dependence dimension $d ll M$, thereby achieving essential dimensionality reduction. We establish its pointwise convergence rate as statistically optimal. Simulations confirm its accuracy, finite-sample robustness, and computational feasibility under high-dimensional sparse dependency structures. Key innovations include: (i) characterizing inseparable dependencies via adversarial moment conditions, and (ii) enforcing consistent sparse structure identification through a local penalization mechanism.
Technology Category
Application Category
📝 Abstract
In this work we consider estimating the probability of many (possibly dependent) binary outcomes which is at the core of many applications, e.g., multi-level treatments in causal inference, demands for bundle of products, etc. Without further conditions, the probability distribution of an M dimensional binary vector is characterized by exponentially in M coefficients which can lead to a high-dimensional problem even without the presence of covariates. Understanding the (in)dependence structure allows us to substantially improve the estimation as it allows for an effective factorization of the probability distribution. In order to estimate the probability distribution of a M dimensional binary vector, we leverage a Bahadur representation that connects the sparsity of its coefficients with independence across the components. We propose to use regularized and adversarial regularized estimators to obtain an adaptive estimator with respect to the dependence structure which allows for rates of convergence to depend on this intrinsic (lower) dimension. These estimators are needed to handle several challenges within this setting, including estimating nuisance parameters, estimating covariates, and nonseparable moment conditions. Our main results consider the presence of (low dimensional) covariates for which we propose a locally penalized estimator. We provide pointwise rates of convergence addressing several issues in the theoretical analyses as we strive for making a computationally tractable formulation. We apply our results in the estimation of causal effects with multiple binary treatments and show how our estimators can improve the finite sample performance when compared with non-adaptive estimators that try to estimate all the probabilities directly. We also provide simulations that are consistent with our theoretical findings.
Problem
Research questions and friction points this paper is trying to address.
Estimating multivariate binary distributions with sparse generalized correlations
Developing computationally feasible estimators for high-dimensional interaction parameters
Improving causal inference accuracy with multiple binary treatments
Innovation
Methods, ideas, or system contributions that make the work stand out.
Two-stage estimation with marginal probabilities and l1-regularization
Regularized adversarial estimator achieving optimal convergence rate
Extension to covariate settings for causal inference applications
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