相关论文: PAC-Bayesian Transportation Bound

Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid…

The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares…

We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike most previous literature on this topic, our bounds are anytime-valid (i.e., time-uniform), meaning that they hold at all stopping times, not only for a…

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is…

In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by…

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…

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…

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Early-exit neural networks enable adaptive computation by allowing confident predictions to exit at intermediate layers, achieving 2-8$\times$ inference speedup. Despite widespread deployment, their generalization properties lack…

We develop a unified Data Processing Inequality PAC-Bayesian framework -- abbreviated DPI-PAC-Bayesian -- for deriving generalization error bounds in the supervised learning setting. By embedding the Data Processing Inequality (DPI) into…

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…

We present novel upper and lower bounds to estimate the collision probability of motion plans for autonomous agents with discrete-time linear Gaussian dynamics. Motion plans generated by planning algorithms cannot be perfectly executed by…

The core of generalization theory was developed for independent observations. Some PAC and PAC-Bayes bounds are available for data that exhibit a temporal dependence. However, there are constants in these bounds that depend on properties of…

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

Most PAC-Bayesian bounds hold in the batch learning setting where data is collected at once, prior to inference or prediction. This somewhat departs from many contemporary learning problems where data streams are collected and the…

Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…

Let $f(\theta, X_1),$ $ \dots,$ $ f(\theta, X_n)$ be a sequence of random elements, where $f$ is a fixed scalar function, $X_1, \dots, X_n$ are independent random variables (data), and $\theta$ is a random parameter distributed according to…

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous…

This paper introduces a new principled approach for off-policy learning in contextual bandits. Unlike previous work, our approach does not derive learning principles from intractable or loose bounds. We analyse the problem through the…

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…