Related papers: Progress in Self-Certified Neural Networks

The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian…

Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…

Recently, there is growing concern that machine-learning models, which currently assist or even automate decision making, reproduce, and in the worst case reinforce, bias of the training data. The development of tools and techniques for…

In the emerging paradigm of edge learning, neural networks (NNs) are partitioned across distributed edge devices that collaboratively perform inference via wireless transmission. However, deploying NNs for edge inference over wireless…

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we…

PAC-Bayes is a popular and efficient framework for obtaining generalization guarantees in situations involving uncountable hypothesis spaces. Unfortunately, in its classical formulation, it only provides guarantees on the expected risk of a…

We give a general recipe for derandomising PAC-Bayesian bounds using margins, with the critical ingredient being that our randomised predictions concentrate around some value. The tools we develop straightforwardly lead to margin bounds for…

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

In this review, we assess the use of Bayesian methods in model predictive control (MPC), focusing on neural-network-based modeling, control design, and uncertainty quantification. We systematically analyze individual studies and how they…

Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such…

Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the…

Actor-critic algorithms address the dual goals of reinforcement learning (RL), policy evaluation and improvement via two separate function approximators. The practicality of this approach comes at the expense of training instability, caused…

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…

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

Deep learning models excel at capturing complex representations through sequential layers of linear and non-linear transformations, yet their inherent black-box nature and multi-modal training landscape raise critical concerns about…

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of…

We investigate the problem of establishing finite-time probabilistic safety guarantees for discrete-time stochastic dynamical systems subject to unknown disturbance distributions, using barrier certificate methods. Our approach develops a…

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems,…

We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm…