相关论文: Tighter risk certificates for neural networks

A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network…

This paper presents four theoretical contributions that improve the usability of risk certificates for neural networks based on PAC-Bayes bounds. First, two bounds on the KL divergence between Bernoulli distributions enable the derivation…

We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second…

Recent works have investigated deep learning models trained by optimising PAC-Bayes bounds, with priors that are learnt on subsets of the data. This combination has been shown to lead not only to accurate classifiers, but also to remarkably…

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial…

Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by…

Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes training, updates the model toward minimizing these bounds.…

We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of…

We derive a novel PAC-Bayesian generalization bound for reinforcement learning that explicitly accounts for Markov dependencies in the data, through the chain's mixing time. This contributes to overcoming challenges in obtaining…

Analysing statistical properties of neural networks is a central topic in statistics and machine learning. However, most results in the literature focus on the properties of the neural network minimizing the training error. The goal of this…

Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…

We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…

The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing…

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke & Zakynthinou (2020), this framework leads to bounds that depend on the conditional…

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and…

Adversarial examples pose a security threat to many critical systems built on neural networks. While certified training improves robustness, it also decreases accuracy noticeably. Despite various proposals for addressing this issue, the…

Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…

This paper presents an approach for learning vision-based planners that provably generalize to novel environments (i.e., environments unseen during training). We leverage the Probably Approximately Correct (PAC)-Bayes framework to obtain an…