Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models

• URL: http://arxiv.org/abs/2305.17076v2
• Date: Mon, 6 Nov 2023 10:14:26 GMT
• Title: Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models
• Authors: Wa\"iss Azizian (DAO), Franck Iutzeler (DAO), J\'er\^ome Malick (DAO)
• Abstract summary: Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. We show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems.

Related papers

• Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering [55.15192437680943]
  Generative models lack rigorous statistical guarantees for their outputs. We propose a sequential conformal prediction method producing prediction sets that satisfy a rigorous statistical guarantee. This guarantee states that with high probability, the prediction sets contain at least one admissible (or valid) example.
  arXiv  Detail & Related papers  (2024-10-02T15:26:52Z)
• Calibrated Probabilistic Forecasts for Arbitrary Sequences [58.54729945445505]
  Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors. We present a forecasting framework ensuring valid uncertainty estimates regardless of how data evolves.
  arXiv  Detail & Related papers  (2024-09-27T21:46:42Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Rejection via Learning Density Ratios [50.91522897152437]
  Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. We propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance. Our framework is tested empirically over clean and noisy datasets.
  arXiv  Detail & Related papers  (2024-05-29T01:32:17Z)
• Universal generalization guarantees for Wasserstein distributionally robust models [10.036727981085223]
  We present a novel proof technique that combines nonsmooth analysis rationale with classical concentration results. Our approach is general enough to extend to the recent versions Wasserstein/Sinkhorn distributionally robust problems that involve (double) regularizations.
  arXiv  Detail & Related papers  (2024-02-19T09:27:47Z)
• Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition [7.811916700683125]
  We introduce a bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions.
  arXiv  Detail & Related papers  (2022-10-21T21:24:37Z)
• Convergence of score-based generative modeling for general data distributions [9.953088581242845]
  We give convergence guarantees for denoising diffusion models that do not rely on the data distribution satisfying functional inequalities or strong smoothness assumptions. We obtain Wasserstein distance guarantees for any distributions of bounded support or sufficiently decaying tails, as well as TV guarantees for distributions with further smoothness assumptions.
  arXiv  Detail & Related papers  (2022-09-26T02:38:36Z)
• Evaluating Aleatoric Uncertainty via Conditional Generative Models [15.494774321257939]
  We study conditional generative models for aleatoric uncertainty estimation. We introduce two metrics to measure the discrepancy between two conditional distributions. We demonstrate numerically how our metrics provide correct measurements of conditional distributional discrepancies.
  arXiv  Detail & Related papers  (2022-06-09T05:39:04Z)
• Wasserstein Robust Support Vector Machines with Fairness Constraints [15.004754864933705]
  We use a type-$infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty. We numerically demonstrate that our proposed approach improves fairness with negligible loss of predictive accuracy.
  arXiv  Detail & Related papers  (2021-03-11T17:53:54Z)
• Estimating Generalization under Distribution Shifts via Domain-Invariant Representations [75.74928159249225]
  We use a set of domain-invariant predictors as a proxy for the unknown, true target labels. The error of the resulting risk estimate depends on the target risk of the proxy model.
  arXiv  Detail & Related papers  (2020-07-06T17:21:24Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)

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.