A new similarity measure for covariate shift with applications to nonparametric regression

• URL: http://arxiv.org/abs/2202.02837v1
• Date: Sun, 6 Feb 2022 19:14:50 GMT
• Title: A new similarity measure for covariate shift with applications to nonparametric regression
• Authors: Reese Pathak and Cong Ma and Martin J. Wainwright
• Abstract summary: We introduce a new measure of distribution mismatch based on the integrated ratio of probabilities of balls at a given radius. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence.
• Score: 43.457497490211985
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions that is based on the integrated ratio of probabilities of balls at a given radius. We use the scaling of this measure with respect to the radius to characterize the minimax rate of estimation over a family of H\"older continuous functions under covariate shift. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence and is more fine-grained. We accompany our theory with concrete instances of covariate shift that illustrate this sharp difference.

Related papers

• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression [109.69084997173196]
  Deepscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. Recent works show that this may result in sub-optimal convergence due to the challenges associated with covariance estimation. We study two questions: (1) Does the predicted covariance truly capture the randomness of the predicted mean? Our results show that not only does TIC accurately learn the covariance, it additionally facilitates an improved convergence of the negative log-likelihood.
  arXiv  Detail & Related papers  (2023-10-29T09:54:03Z)
• Robust Covariate Shift Adaptation for Density-Ratio Estimation [10.470114319701576]
  We propose a doubly robust estimator for covariate shift adaptation via importance weighting. Our estimator reduces the bias arising from the density ratio estimation errors. Notably, our estimator remains consistent if either the density ratio estimator or the regression function is consistent.
  arXiv  Detail & Related papers  (2023-10-25T13:38:29Z)
• Function-space regularized R\'enyi divergences [6.221019624345409]
  We propose a new family of regularized R'enyi divergences parametrized by a variational function space. We prove several properties of these new divergences, showing that they interpolate between the classical R'enyi divergences and IPMs. We show that the proposed regularized R'enyi divergences inherit features from IPMs such as the ability to compare distributions that are not absolutely continuous.
  arXiv  Detail & Related papers  (2022-10-10T19:18:04Z)
• Optimally tackling covariate shift in RKHS-based nonparametric regression [43.457497490211985]
  We show that a kernel ridge regression estimator with a carefully chosen regularization parameter is minimax rate-optimal. We also show that a naive estimator, which minimizes the empirical risk over the function class, is strictly sub-optimal. We propose a reweighted KRR estimator that weights samples based on a careful truncation of the likelihood ratios.
  arXiv  Detail & Related papers  (2022-05-06T02:33:24Z)
• Decorrelated Variable Importance [0.0]
  We propose a method for mitigating the effect of correlation by defining a modified version of LOCO. This new parameter is difficult to estimate nonparametrically, but we show how to estimate it using semiparametric models.
  arXiv  Detail & Related papers  (2021-11-21T16:31:36Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Reducing the Variance of Variational Estimates of Mutual Information by Limiting the Critic's Hypothesis Space to RKHS [0.0]
  Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Recent methods realize parametric probability distributions or critic as a neural network to approximate unknown density ratios. We argue that the high variance characteristic is due to the uncontrolled complexity of the critic's hypothesis space.
  arXiv  Detail & Related papers  (2020-11-17T14:32:48Z)
• Minimax Optimal Estimation of KL Divergence for Continuous Distributions [56.29748742084386]
  Esting Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor between these samples.
  arXiv  Detail & Related papers  (2020-02-26T16:37:37Z)

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.