How Does Bayes Error Limit Probabilistic Robust Accuracy

• URL: http://arxiv.org/abs/2405.14923v1
• Date: Thu, 23 May 2024 17:51:36 GMT
• Title: How Does Bayes Error Limit Probabilistic Robust Accuracy
• Authors: Ruihan Zhang, Jun Sun,
• Abstract summary: Adversarial examples pose a security threat to many critical systems built on neural networks. Probability of having same label with a vicinity is $ge 1-kappa$. Training methods for probabilistic robustness still experience non-trivial accuracy loss.
• Score: 3.350980549219263
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having the same label with a vicinity is $\ge 1-\kappa$) has been proposed as a promising way of achieving robustness whilst maintaining accuracy. However, existing training methods for probabilistic robustness still experience non-trivial accuracy loss. It is unclear whether there is an upper bound on the accuracy when optimising towards probabilistic robustness, and whether there is a certain relationship between $\kappa$ and this bound. This work studies these problems from a Bayes error perspective. We find that while Bayes uncertainty does affect probabilistic robustness, its impact is smaller than that on deterministic robustness. This reduced Bayes uncertainty allows a higher upper bound on probabilistic robust accuracy than that on deterministic robust accuracy. Further, we prove that with optimal probabilistic robustness, each probabilistically robust input is also deterministically robust in a smaller vicinity. We also show that voting within the vicinity always improves probabilistic robust accuracy and the upper bound of probabilistic robust accuracy monotonically increases as $\kappa$ grows. Our empirical findings also align with our results.

Related papers

• Rigorous Probabilistic Guarantees for Robust Counterfactual Explanations [80.86128012438834]
  We show for the first time that computing the robustness of counterfactuals with respect to plausible model shifts is NP-complete. We propose a novel probabilistic approach which is able to provide tight estimates of robustness with strong guarantees.
  arXiv  Detail & Related papers  (2024-07-10T09:13:11Z)
• Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors [3.350980549219263]
  certified training improves robustness but also decreases accuracy noticeably. It is not clear whether there is a certain fundamental limit on achieving robustness whilst maintaining accuracy. By adopting Bayes error to robustness analysis, we investigate the limit of certified robust accuracy.
  arXiv  Detail & Related papers  (2024-05-19T13:23:05Z)
• Robustness Guarantees for Credal Bayesian Networks via Constraint Relaxation over Probabilistic Circuits [16.997060715857987]
  We develop a method to quantify the robustness of decision functions with respect to credal Bayesian networks. We show how to obtain a guaranteed upper bound on MARmax in linear time in the size of the circuit.
  arXiv  Detail & Related papers  (2022-05-11T22:37:07Z)
• 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)
• Dense Uncertainty Estimation via an Ensemble-based Conditional Latent Variable Model [68.34559610536614]
  We argue that the aleatoric uncertainty is an inherent attribute of the data and can only be correctly estimated with an unbiased oracle model. We propose a new sampling and selection strategy at train time to approximate the oracle model for aleatoric uncertainty estimation. Our results show that our solution achieves both accurate deterministic results and reliable uncertainty estimation.
  arXiv  Detail & Related papers  (2021-11-22T08:54:10Z)
• Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits [18.740781076082044]
  We propose an approach to overcome the independence assumption behind most of the approaches dealing with a large class of probabilistic reasoning. We provide an algorithm for Bayesian learning from sparse, albeit complete, observations. Each leaf of such circuits is labelled with a beta-distributed random variable that provides us with an elegant framework for representing uncertain probabilities.
  arXiv  Detail & Related papers  (2021-02-22T10:03:15Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)
• Labels Are Not Perfect: Improving Probabilistic Object Detection via Label Uncertainty [12.531126969367774]
  We leverage our previously proposed method for estimating uncertainty inherent in ground truth bounding box parameters. Experimental results on the KITTI dataset show that our method surpasses both the baseline model and the models based on simple uncertaintys by up to 3.6% in terms of Average Precision.
  arXiv  Detail & Related papers  (2020-08-10T14:49:49Z)
• Provable tradeoffs in adversarially robust classification [96.48180210364893]
  We develop and leverage new tools, including recent breakthroughs from probability theory on robust isoperimetry. Our results reveal fundamental tradeoffs between standard and robust accuracy that grow when data is imbalanced.
  arXiv  Detail & Related papers  (2020-06-09T09:58:19Z)
• Estimation of Accurate and Calibrated Uncertainties in Deterministic models [0.8702432681310401]
  We devise a method to transform a deterministic prediction into a probabilistic one. We show that for doing so, one has to compromise between the accuracy and the reliability (calibration) of such a model. We show several examples both with synthetic data, where the underlying hidden noise can accurately be recovered, and with large real-world datasets.
  arXiv  Detail & Related papers  (2020-03-11T04:02:56Z)
• Hidden Cost of Randomized Smoothing [72.93630656906599]
  In this paper, we point out the side effects of current randomized smoothing. Specifically, we articulate and prove two major points: 1) the decision boundaries of smoothed classifiers will shrink, resulting in disparity in class-wise accuracy; 2) applying noise augmentation in the training process does not necessarily resolve the shrinking issue due to the inconsistent learning objectives.
  arXiv  Detail & Related papers  (2020-03-02T23:37:42Z)

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.