Related papers: Risk Bounds for the Majority Vote: From a PAC-Baye…
PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester ('98). This framework has the flexibility of deriving distribution- and algorithm-dependent bounds, which are often tighter than…
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns…
We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian…
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…
We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated,…
This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive…
We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for…
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
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…
Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework,…
In boosting, we aim to leverage multiple weak learners to produce a strong learner. At the center of this paradigm lies the concept of building the strong learner as a voting classifier, which outputs a weighted majority vote of the weak…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds. We derive conditional MI bounds as an instance, with special choice of prior, of conditional MAC-Bayesian (Mean Approximately…
Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability --…
We study upper and lower bounds on the sample-complexity of learning near-optimal behaviour in finite-state discounted Markov Decision Processes (MDPs). For the upper bound we make the assumption that each action leads to at most two…
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…
In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for…
When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the PAC-Bayesian…
The dominant term in PAC-Bayes bounds is often the Kullback--Leibler divergence between the posterior and prior. For so-called linear PAC-Bayes risk bounds based on the empirical risk of a fixed posterior kernel, it is possible to minimize…