Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization

• URL: http://arxiv.org/abs/2501.17354v1
• Date: Wed, 29 Jan 2025 00:29:36 GMT
• Title: Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization
• Authors: Yihong Gu, Cong Fang, Yang Xu, Zijian Guo, Jianqing Fan,
• Abstract summary: 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.
• Score: 11.940138507727577
• License:
• Abstract: Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as ICP [Peters et al., 2016] and EILLS [Fan et al., 2024] that can attain sample-efficient estimation are based on exponential time algorithms. In this paper, we show that such a problem is intrinsically hard in computation: the decision problem, testing whether a non-trivial prediction-invariant solution exists across two environments, is NP-hard even for the linear causal relationship. In the world where P$\neq$NP, our results imply that the estimation error rate can be arbitrarily slow using any computationally efficient algorithm. This suggests that pursuing causality is fundamentally harder than detecting associations when no prior assumption is pre-offered. Given there is almost no hope of computational improvement under the worst case, this paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions. Furthermore, our estimator is a distributionally robust estimator with an ellipse-shaped uncertain set where more uncertainty is placed on spurious directions than invariant directions, resulting in a smooth interpolation between the most predictive solution and the causal solution by varying the invariance hyper-parameter. Non-asymptotic results and empirical applications support the claim.

Related papers

• Causal Invariance Learning via Efficient Optimization of a Nonconvex Objective [12.423111378195667]
  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.
  arXiv  Detail & Related papers  (2024-12-16T15:11:02Z)
• Partially factorized variational inference for high-dimensional mixed models [0.0]
  Variational inference is a popular way to perform such computations, especially in the Bayesian context. We show that standard mean-field variational inference dramatically underestimates posterior uncertainty in high-dimensions. We then show how appropriately relaxing the mean-field assumption leads to methods whose uncertainty quantification does not deteriorate in high-dimensions.
  arXiv  Detail & Related papers  (2023-12-20T16:12:37Z)
• Scalable method for Bayesian experimental design without integrating over posterior distribution [0.0]
  We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems. A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design. This study presents a novel likelihood-free approach to the A-optimal experimental design.
  arXiv  Detail & Related papers  (2023-06-30T12:40:43Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Posterior and Computational Uncertainty in Gaussian Processes [52.26904059556759]
  Gaussian processes scale prohibitively with the size of the dataset. Many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. We develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended.
  arXiv  Detail & Related papers  (2022-05-30T22:16:25Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• 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)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Non-Asymptotic Performance Guarantees for Neural Estimation of $\mathsf{f}$-Divergences [22.496696555768846]
  Statistical distances quantify the dissimilarity between probability distributions. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs.
  arXiv  Detail & Related papers  (2021-03-11T19:47:30Z)

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.