Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects

• URL: http://arxiv.org/abs/2212.04922v2
• Date: Tue, 7 Nov 2023 14:06:32 GMT
• Title: Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects
• Authors: Jake Fawkes, Robert Hu, Robin J. Evans, Dino Sejdinovic
• Abstract summary: We build upon a previously introduced framework, Counterfactual Mean Embeddings, for representing causal distributions within Reproducing Kernel Hilbert Spaces (RKHS) These improved estimators are inspired by doubly robust estimators of the causal mean, using a similar form within the kernel space. This leads to new permutation based tests for distributional causal effects, using the estimators we propose as tests statistics.
• Score: 18.791409397894835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for \emph{distributional} causal effects, where the treatment affects not just the mean, but also higher order moments of the distribution, as well as multidimensional or structured outcomes. We build upon a previously introduced framework, Counterfactual Mean Embeddings, for representing causal distributions within Reproducing Kernel Hilbert Spaces (RKHS) by proposing new, improved, estimators for the distributional embeddings. These improved estimators are inspired by doubly robust estimators of the causal mean, using a similar form within the kernel space. We analyse these estimators, proving they retain the doubly robust property and have improved convergence rates compared to the original estimators. This leads to new permutation based tests for distributional causal effects, using the estimators we propose as tests statistics. We experimentally and theoretically demonstrate the validity of our tests.

Related papers

• Doubly Robust Inference in Causal Latent Factor Models [12.116813197164047]
  This article introduces a new estimator of average treatment effects under unobserved confounding in modern data-rich environments featuring large numbers of units and outcomes. We derive finite-sample weighting and guarantees, and show that the error of the new estimator converges to a mean-zero Gaussian distribution at a parametric rate.
  arXiv  Detail & Related papers  (2024-02-18T17:13:46Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Testing Causality for High Dimensional Data [15.818502261466403]
  We revisit the emphlinear trace method to infer the causal direction between two random variables of high dimensions. We extend the results to nonlinear trace functionals with sharper confidence bounds under certain distributional assumptions. We support our theoretical results with encouraging experiments on synthetic datasets.
  arXiv  Detail & Related papers  (2023-03-14T10:25:56Z)
• Confidence and Dispersity Speak: Characterising Prediction Matrix for Unsupervised Accuracy Estimation [51.809741427975105]
  This work aims to assess how well a model performs under distribution shifts without using labels. We use the nuclear norm that has been shown to be effective in characterizing both properties. We show that the nuclear norm is more accurate and robust in accuracy than existing methods.
  arXiv  Detail & Related papers  (2023-02-02T13:30:48Z)
• A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond [0.9172870611255595]
  Cross-fit inverse probability weighting (AIPW) with cross-fitting is a popular choice in practice. We study this cross-fit AIPW estimator under well-specified outcome regression and propensity score models in a high-dimensional regime. Our work utilizes a novel interplay between three distinct tools--approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach.
  arXiv  Detail & Related papers  (2022-05-20T14:17:53Z)
• Variance Minimization in the Wasserstein Space for Invariant Causal Prediction [72.13445677280792]
  In this work, we show that the approach taken in ICP may be reformulated as a series of nonparametric tests that scales linearly in the number of predictors. Each of these tests relies on the minimization of a novel loss function that is derived from tools in optimal transport theory. We prove under mild assumptions that our method is able to recover the set of identifiable direct causes, and we demonstrate in our experiments that it is competitive with other benchmark causal discovery algorithms.
  arXiv  Detail & Related papers  (2021-10-13T22:30:47Z)
• Causality and Generalizability: Identifiability and Learning Methods [0.0]
  This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. We propose a general framework for distributional robustness with respect to intervention-induced distributions.
  arXiv  Detail & Related papers  (2021-10-04T13:12:11Z)
• Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap [140.98628848491146]
  We introduce deconfounding scores, which induce better overlap without biasing the target of estimation. We show that deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data. In particular, we show that this technique could be an attractive alternative to standard regularizations.
  arXiv  Detail & Related papers  (2021-04-12T18:50:11Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)
• Balance-Subsampled Stable Prediction [55.13512328954456]
  We propose a novel balance-subsampled stable prediction (BSSP) algorithm based on the theory of fractional factorial design. A design-theoretic analysis shows that the proposed method can reduce the confounding effects among predictors induced by the distribution shift. Numerical experiments on both synthetic and real-world data sets demonstrate that our BSSP algorithm significantly outperforms the baseline methods for stable prediction across unknown test data.
  arXiv  Detail & Related papers  (2020-06-08T07:01:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.