Variance Minimization in the Wasserstein Space for Invariant Causal Prediction

• URL: http://arxiv.org/abs/2110.07064v1
• Date: Wed, 13 Oct 2021 22:30:47 GMT
• Title: Variance Minimization in the Wasserstein Space for Invariant Causal Prediction
• Authors: Guillaume Martinet, Alexander Strzalkowski, Barbara E. Engelhardt
• Abstract summary: 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.
• Score: 72.13445677280792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal inference problem leverages the invariance property of a causal mechanism across differing experimental environments (Peters et al., 2016; Heinze-Deml et al., 2018). This method, invariant causal prediction (ICP), has a substantial computational defect -- the runtime scales exponentially with the number of possible causal variables. 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 -- the Wasserstein variance -- that is derived from tools in optimal transport theory and is used to quantify distributional variability across environments. 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.

Related papers

• Local Prediction-Powered Inference [7.174572371800217]
  This paper introduces a specific algorithm for local multivariable regression using PPI. The confidence intervals, bias correction, and coverage probabilities are analyzed and proved the correctness and superiority of our algorithm.
  arXiv  Detail & Related papers  (2024-09-26T22:15:53Z)
• Invariant Causal Prediction with Local Models [52.161513027831646]
  We consider the task of identifying the causal parents of a target variable among a set of candidates from observational data. We introduce a practical method called L-ICP ($textbfL$ocalized $textbfI$nvariant $textbfCa$usal $textbfP$rediction), which is based on a hypothesis test for parent identification using a ratio of minimum and maximum statistics.
  arXiv  Detail & Related papers  (2024-01-10T15:34:42Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Invariant Probabilistic Prediction [45.90606906307022]
  We show that arbitrary distribution shifts do not, in general, admit invariant and robust probabilistic predictions. We propose a method to yield invariant probabilistic predictions, called IPP, and study the consistency of the underlying parameters.
  arXiv  Detail & Related papers  (2023-09-18T18:50:24Z)
• Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression [14.493176427999028]
  We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE) with linear regression models. We show that the T-learner fails to achieve the consistency except the random assignment, while the IPW-learner converges the risk to zero if the propensity score is known.
  arXiv  Detail & Related papers  (2022-02-10T18:51:52Z)
• Invariant Ancestry Search [6.583725235299022]
  We introduce the concept of minimal invariance and propose invariant ancestry search (IAS) In its population version, IAS outputs a set which contains only ancestors of the response and is the output of ICP. We develop scalable algorithms and perform experiments on simulated and real data.
  arXiv  Detail & Related papers  (2022-02-02T08:28:00Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• Latent Causal Invariant Model [128.7508609492542]
  Current supervised learning can learn spurious correlation during the data-fitting process. We propose a Latent Causal Invariance Model (LaCIM) which pursues causal prediction.
  arXiv  Detail & Related papers  (2020-11-04T10:00:27Z)
• Stable Prediction via Leveraging Seed Variable [73.9770220107874]
  Previous machine learning methods might exploit subtly spurious correlations in training data induced by non-causal variables for prediction. We propose a conditional independence test based algorithm to separate causal variables with a seed variable as priori, and adopt them for stable prediction. Our algorithm outperforms state-of-the-art methods for stable prediction.
  arXiv  Detail & Related papers  (2020-06-09T06:56:31Z)

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.