相关论文: PAC-Bayesian theory for stochastic LTI systems

Analysing statistical properties of neural networks is a central topic in statistics and machine learning. However, most results in the literature focus on the properties of the neural network minimizing the training error. The goal of this…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

We introduce a new PAC-Bayes oracle bound for unbounded losses that extends Cram\'er-Chernoff bounds to the PAC-Bayesian setting. The proof technique relies on controlling the tails of certain random variables involving the Cram\'er…

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…

We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…

We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction…

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties…

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…

Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

In this paper, we present refined probabilistic bounds on empirical reward estimates for off-policy learning in bandit problems. We build on the PAC-Bayesian bounds from Seldin et al. (2010) and improve on their results using a new…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \emph{PAC learning quantum process}, and study…

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke & Zakynthinou (2020), this framework leads to bounds that depend on the conditional…

We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial…

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…