Monotonic Risk Relationships under Distribution Shifts for Regularized Risk Minimization

• URL: http://arxiv.org/abs/2210.11589v2
• Date: Thu, 20 Jul 2023 18:48:37 GMT
• Title: Monotonic Risk Relationships under Distribution Shifts for Regularized Risk Minimization
• Authors: Daniel LeJeune, Jiayu Liu, Reinhard Heckel
• Abstract summary: Machine learning systems are often applied to data that is drawn from a different distribution than the training distribution. Recent work has shown that for a variety of classification and signal reconstruction problems, the out-of-distribution performance is strongly linearly correlated with the in-distribution performance.
• Score: 24.970274256061376
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Machine learning systems are often applied to data that is drawn from a different distribution than the training distribution. Recent work has shown that for a variety of classification and signal reconstruction problems, the out-of-distribution performance is strongly linearly correlated with the in-distribution performance. If this relationship or more generally a monotonic one holds, it has important consequences. For example, it allows to optimize performance on one distribution as a proxy for performance on the other. In this paper, we study conditions under which a monotonic relationship between the performances of a model on two distributions is expected. We prove an exact asymptotic linear relation for squared error and a monotonic relation for misclassification error for ridge-regularized general linear models under covariate shift, as well as an approximate linear relation for linear inverse problems.

Related papers

• Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
  In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data. We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
  arXiv  Detail & Related papers  (2024-06-07T14:29:21Z)
• Supervised Contrastive Learning with Heterogeneous Similarity for Distribution Shifts [3.7819322027528113]
  We propose a new regularization using the supervised contrastive learning to prevent such overfitting and to train models that do not degrade their performance under the distribution shifts. Experiments on benchmark datasets that emulate distribution shifts, including subpopulation shift and domain generalization, demonstrate the advantage of the proposed method.
  arXiv  Detail & Related papers  (2023-04-07T01:45:09Z)
• A Unified Analysis of Multi-task Functional Linear Regression Models with Manifold Constraint and Composite Quadratic Penalty [0.0]
  The power of multi-task learning is brought in by imposing additional structures over the slope functions. We show the composite penalty induces a specific norm, which helps to quantify the manifold curvature. A unified convergence upper bound is obtained and specifically applied to the reduced-rank model and the graph Laplacian regularized model.
  arXiv  Detail & Related papers  (2022-11-09T13:32:23Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• The Interplay Between Implicit Bias and Benign Overfitting in Two-Layer Linear Networks [51.1848572349154]
  neural network models that perfectly fit noisy data can generalize well to unseen test data. We consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk.
  arXiv  Detail & Related papers  (2021-08-25T22:01:01Z)
• Why do classifier accuracies show linear trends under distribution shift? [58.40438263312526]
  accuracies of models on one data distribution are approximately linear functions of the accuracies on another distribution. We assume the probability that two models agree in their predictions is higher than what we can infer from their accuracy levels alone. We show that a linear trend must occur when evaluating models on two distributions unless the size of the distribution shift is large.
  arXiv  Detail & Related papers  (2020-12-31T07:24:30Z)
• Understanding Double Descent Requires a Fine-Grained Bias-Variance Decomposition [34.235007566913396]
  We describe an interpretable, symmetric decomposition of the variance into terms associated with the labels. We find that the bias decreases monotonically with the network width, but the variance terms exhibit non-monotonic behavior. We also analyze the strikingly rich phenomenology that arises.
  arXiv  Detail & Related papers  (2020-11-04T21:04:02Z)
• Accounting for Unobserved Confounding in Domain Generalization [107.0464488046289]
  This paper investigates the problem of learning robust, generalizable prediction models from a combination of datasets. Part of the challenge of learning robust models lies in the influence of unobserved confounders. We demonstrate the empirical performance of our approach on healthcare data from different modalities.
  arXiv  Detail & Related papers  (2020-07-21T08:18:06Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

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.