相关论文: Optimal PAC-Bayesian Posteriors for Stochastic Cla…

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

Optimization problems over discrete or quantized variables are very challenging in general due to the combinatorial nature of their search space. Piecewise-affine regularization (PAR) provides a flexible modeling and computational framework…

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…

We study contrastive learning under the PAC learning framework. While a series of recent works have shown statistical results for learning under contrastive loss, based either on the VC-dimension or Rademacher complexity, their algorithms…

We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…

Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…

Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Sequential multi-class diagnosis, also known as multi-hypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the…

In this paper we develop a Bayesian optimization based hyperparameter tuning framework inspired by statistical learning theory for classifiers. We utilize two key facts from PAC learning theory; the generalization bound will be higher for a…

Off-policy learning (OPL) often involves minimizing a risk estimator based on importance weighting to correct bias from the logging policy used to collect data. However, this method can produce an estimator with a high variance. A common…

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…

We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…

Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms…

This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability…

Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good…