A Fundamental Accuracy--Robustness Trade-off in Regression and Classification

• URL: http://arxiv.org/abs/2411.05853v1
• Date: Wed, 06 Nov 2024 22:03:53 GMT
• Title: A Fundamental Accuracy--Robustness Trade-off in Regression and Classification
• Authors: Sohail Bahmani,
• Abstract summary: We derive a fundamental trade-off between standard and adversarial risk in a general situation. As a concrete example, we evaluate the trade-off in regression with derived ridge functions under mild regularity conditions.
• Score: 0.0
• License:
• Abstract: We derive a fundamental trade-off between standard and adversarial risk in a rather general situation that formalizes the following simple intuition: "If no (nearly) optimal predictor is smooth, adversarial robustness comes at the cost of accuracy." As a concrete example, we evaluate the derived trade-off in regression with polynomial ridge functions under mild regularity conditions.

Related papers

• Conformalized Selective Regression [2.3964255330849356]
  We propose a novel approach to selective regression by leveraging conformal prediction. We show how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-02-26T04:43:50Z)
• Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization [29.24821214671497]
  Training machine learning and statistical models often involve optimizing a data-driven risk criterion. We propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations.
  arXiv  Detail & Related papers  (2024-01-28T21:19:15Z)
• Robust Linear Regression: Phase-Transitions and Precise Tradeoffs for General Norms [29.936005822346054]
  We investigate the impact of test-time adversarial attacks on linear regression models. We determine the optimal level of robustness that any model can reach while maintaining a given level of standard predictive performance (accuracy) We obtain a precise characterization which distinguishes between regimes where robustness is achievable without hurting standard accuracy and regimes where a tradeoff might be unavoidable.
  arXiv  Detail & Related papers  (2023-08-01T13:55:45Z)
• Model-Based Uncertainty in Value Functions [89.31922008981735]
  We focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values.
  arXiv  Detail & Related papers  (2023-02-24T09:18:27Z)
• The Implicit Delta Method [61.36121543728134]
  In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of uncertainty. We show that the change in the evaluation due to regularization is consistent for the variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference.
  arXiv  Detail & Related papers  (2022-11-11T19:34:17Z)
• Robustness and Accuracy Could Be Reconcilable by (Proper) Definition [109.62614226793833]
  The trade-off between robustness and accuracy has been widely studied in the adversarial literature. We find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty.
  arXiv  Detail & Related papers  (2022-02-21T10:36:09Z)
• Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression [91.3373131262391]
  Uncertainty is the only certainty there is. Traditionally, the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. How to model the uncertainty within the present-day technologies for regression remains an open issue.
  arXiv  Detail & Related papers  (2021-03-25T06:56:09Z)
• Distribution-Free Robust Linear Regression [5.532477732693]
  We study random design linear regression with no assumptions on the distribution of the covariates. We construct a non-linear estimator achieving excess risk of order $d/n$ with the optimal sub-exponential tail. We prove an optimal version of the classical bound for the truncated least squares estimator due to Gy"orfi, Kohler, Krzyzak, and Walk.
  arXiv  Detail & Related papers  (2021-02-25T15:10:41Z)
• Don't Just Blame Over-parametrization for Over-confidence: Theoretical Analysis of Calibration in Binary Classification [58.03725169462616]
  We show theoretically that over-parametrization is not the only reason for over-confidence. We prove that logistic regression is inherently over-confident, in the realizable, under-parametrized setting. Perhaps surprisingly, we also show that over-confidence is not always the case.
  arXiv  Detail & Related papers  (2021-02-15T21:38:09Z)
• On Model Identification and Out-of-Sample Prediction of Principal Component Regression: Applications to Synthetic Controls [20.96904429337912]
  We analyze principal component regression (PCR) in a high-dimensional error-in-variables setting with fixed design. We establish non-asymptotic out-of-sample prediction guarantees that improve upon the best known rates.
  arXiv  Detail & Related papers  (2020-10-27T17:07:36Z)
• Understanding and Mitigating the Tradeoff Between Robustness and Accuracy [88.51943635427709]
  Adversarial training augments the training set with perturbations to improve the robust error. We show that the standard error could increase even when the augmented perturbations have noiseless observations from the optimal linear predictor.
  arXiv  Detail & Related papers  (2020-02-25T08:03:01Z)

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.