Related papers: Empirical PAC-Bayes Bounds for Markov Chains
By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably…
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
PAC-Bayes has recently re-emerged as an effective theory with which one can derive principled learning algorithms with tight performance guarantees. However, applications of PAC-Bayes to bandit problems are relatively rare, which is a great…
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…
Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…
We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is…
We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration,…
Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses…
In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…
We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance,…
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…
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison…
Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some…
We prove a version of McDiarmid's bounded differences inequality for Markov chains, with constants proportional to the mixing time of the chain. We also show variance bounds and Bernstein-type inequalities for empirical averages of Markov…
Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov chains are: (i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to…
This paper presents a PAC-Bayes framework for learning controllers for unknown stochastic linear discrete-time systems, where the system parameters are drawn from a fixed but unknown distribution. We derive a data-dependent high probability…
We introduce a new framework that yields spectral bounds on norms of functions of transition maps for finite, homogeneous Markov chains. The techniques employed work for bounded semigroups, in particular for classical as well as for quantum…
We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a sequence of finite Markov chains with…