Related papers: PAC-Bayesian-Like Error Bound for a Class of Linea…

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors.…

In this work, we provide deterministic error bounds for the actual state evolution of nonlinear systems embedded with the linear parametric variable (LPV) formulation and steered by model predictive control (MPC). The main novelty concerns…

Online Passive-Aggressive (PA) learning is a class of online margin-based algorithms suitable for a wide range of real-time prediction tasks, including classification and regression. PA algorithms are formulated in terms of deterministic…

We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system…

In this paper, we consider the state estimation problem for nonlinear stochastic discrete-time systems. We combine Lyapunov's method in control theory and deep reinforcement learning to design the state estimator. We theoretically prove the…

Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes training, updates the model toward minimizing these bounds.…

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…

This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven…

Application of deep neural networks to medical imaging tasks has in some sense become commonplace. Still, a "thorn in the side" of the deep learning movement is the argument that deep networks are prone to overfitting and are thus unable to…

We develop the concept of exponential stochastic inequality (ESI), a novel notation that simultaneously captures high-probability and in-expectation statements. It is especially well suited to succinctly state, prove, and reason about…

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…

Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.

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 --…

We present reduced basis approximations and rigorous a posteriori error bounds for the instationary Stokes equations. We shall discuss both a method based on the standard formulation as well as a method based on a penalty approach, which…

Transfer learning has received a lot of attention in the machine learning community over the last years, and several effective algorithms have been developed. However, relatively little is known about their theoretical properties,…

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an…