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This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…
We prove a lower bound on the size of bottlenecks in uniform quadrangulations, valid at all scales simultaneously. We use it to establish upper bounds on the uniform mixing time of the lazy random walk on uniform quadrangulations, as well…
This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a…
Variational approximation techniques and inference for stochastic models in machine learning has gained much attention the last years. Especially in the case of Gaussian Processes (GP) and their deep versions, Deep Gaussian Processes…
PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen…
Using the argument of Geiss, Montgomery-Smith and Saksman \cite{GMSS}, and a new martingale inequality, the $L^p$--norms of certain Fourier multipliers in $\R^d$, $d\geq 2$, are identified. These include, among others, the second order…
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…
Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…
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 study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…
We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
Using martingale methods, we provide bounds for the entropy of a probability measure on $\mathbb {R}^d$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev…
We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…
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,…
Many practical machine learning tasks can be framed as Structured prediction problems, where several output variables are predicted and considered interdependent. Recent theoretical advances in structured prediction have focused on…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…