Related papers: PAC-Bayes bounds for stable algorithms with instan…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

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…

The PAC-Bayesian framework has significantly advanced the understanding of statistical learning, particularly for majority voting methods. Despite its successes, its application to multi-view learning -- a setting with multiple…

We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…

Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…

Thompson sampling and other Bayesian sequential decision-making algorithms are among the most popular approaches to tackle explore/exploit trade-offs in (contextual) bandits. The choice of prior in these algorithms offers flexibility to…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using…

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 --…

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…

We present new fast-rate PAC-Bayesian generalization bounds for multi-task and meta-learning in the unbalanced setting, i.e. when the tasks have training sets of different sizes, as is typically the case in real-world scenarios. Previously,…

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…

Despite its wide use and empirical successes, the theoretical understanding and study of the behaviour and performance of the variational autoencoder (VAE) have only emerged in the past few years. We contribute to this recent line of work…

We present a PAC-Bayesian analysis of lifelong learning. In the lifelong learning problem, a sequence of learning tasks is observed one-at-a-time, and the goal is to transfer information acquired from previous tasks to new learning tasks.…

This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of the mean of a vector or a matrix, with applications to least…

In robotics, optimizing controller parameters under safety constraints is an important challenge. Safe Bayesian optimization (BO) quantifies uncertainty in the objective and constraints to safely guide exploration in such settings.…

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…