Causal Invariance Learning via Efficient Optimization of a Nonconvex Objective

• URL: http://arxiv.org/abs/2412.11850v2
• Date: Tue, 17 Dec 2024 15:44:30 GMT
• Title: Causal Invariance Learning via Efficient Optimization of a Nonconvex Objective
• Authors: Zhenyu Wang, Yifan Hu, Peter Bühlmann, Zijian Guo,
• Abstract summary: We propose a novel method for finding causal relationships among variables. We show that our method converges to a standard gradient method. Our algorithm avoids exhaustive searches, making it especially when the number of covariants is large.
• Score: 12.423111378195667
• License:
• Abstract: Data from multiple environments offer valuable opportunities to uncover causal relationships among variables. Leveraging the assumption that the causal outcome model remains invariant across heterogeneous environments, state-of-the-art methods attempt to identify causal outcome models by learning invariant prediction models and rely on exhaustive searches over all (exponentially many) covariate subsets. These approaches present two major challenges: 1) determining the conditions under which the invariant prediction model aligns with the causal outcome model, and 2) devising computationally efficient causal discovery algorithms that scale polynomially, instead of exponentially, with the number of covariates. To address both challenges, we focus on the additive intervention regime and propose nearly necessary and sufficient conditions for ensuring that the invariant prediction model matches the causal outcome model. Exploiting the essentially necessary identifiability conditions, we introduce Negative Weight Distributionally Robust Optimization (NegDRO), a nonconvex continuous minimax optimization whose global optimizer recovers the causal outcome model. Unlike standard group DRO problems that maximize over the simplex, NegDRO allows negative weights on environment losses, which break the convexity. Despite its nonconvexity, we demonstrate that a standard gradient method converges to the causal outcome model, and we establish the convergence rate with respect to the sample size and the number of iterations. Our algorithm avoids exhaustive search, making it scalable especially when the number of covariates is large. The numerical results further validate the efficiency of the proposed method.

Related papers

• Heteroscedastic Double Bayesian Elastic Net [1.1240642213359266]
  We propose the Heteroscedastic Double Bayesian Elastic Net (HDBEN), a novel framework that jointly models the mean and log- variance. Our approach simultaneously induces sparsity and grouping in the regression coefficients and variance parameters, capturing complex variance structures in the data.
  arXiv  Detail & Related papers  (2025-02-04T05:44:19Z)
• Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization [11.940138507727577]
  Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way. Existing methods that can attain sample-efficient estimation are based on exponential time algorithms. This paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions.
  arXiv  Detail & Related papers  (2025-01-29T00:29:36Z)
• Statistical ranking with dynamic covariates [6.729750785106628]
  We introduce an efficient alternating algorithm to compute the likelihood estimator (MLE) A comprehensive numerical study is conducted to corroborate our theoretical findings and demonstrate the application of the proposed model to real-world datasets, including horse racing and tennis competitions.
  arXiv  Detail & Related papers  (2024-06-24T10:26:05Z)
• Robust Estimation of Causal Heteroscedastic Noise Models [7.568978862189266]
  Student's $t$-distribution is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.
  arXiv  Detail & Related papers  (2023-12-15T02:26:35Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Optimization-based Causal Estimation from Heterogenous Environments [35.74340459207312]
  CoCo is an optimization algorithm that bridges the gap between pure prediction and causal inference. We describe the theoretical foundations of this approach and demonstrate its effectiveness on simulated and real datasets.
  arXiv  Detail & Related papers  (2021-09-24T14:21:58Z)
• Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flows [74.85071867225533]
  Causal mechanisms can be described by structural causal models. One major drawback of state-of-the-art artificial intelligence is its lack of explainability.
  arXiv  Detail & Related papers  (2021-09-06T14:52:58Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Robust, Accurate Stochastic Optimization for Variational Inference [68.83746081733464]
  We show that common optimization methods lead to poor variational approximations if the problem is moderately large. Motivated by these findings, we develop a more robust and accurate optimization framework by viewing the underlying algorithm as producing a Markov chain.
  arXiv  Detail & Related papers  (2020-09-01T19:12:11Z)
• Efficient Ensemble Model Generation for Uncertainty Estimation with Bayesian Approximation in Segmentation [74.06904875527556]
  We propose a generic and efficient segmentation framework to construct ensemble segmentation models. In the proposed method, ensemble models can be efficiently generated by using the layer selection method. We also devise a new pixel-wise uncertainty loss, which improves the predictive performance.
  arXiv  Detail & Related papers  (2020-05-21T16:08:38Z)

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.