Related papers: A Note on the PAC Bayesian Theorem

This paper proves the Baum--Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties of slowly varying…

In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…

Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…

We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…

Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Mat\'ern covariance function,…

Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…

We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…

This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.

We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in…

We formulate and establish the central limit theorem for products of i.i.d. random variables on arbitrary simply connected nilpotent Lie groups, allowing a possible bias. Two new phenomena arise in the presence of a bias: (a) the walk…

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

In this note, using the derangement polynomials and their umbral representation, we give another simple proof of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory.

Standard Bayesian learning is known to have suboptimal generalization capabilities under misspecification and in the presence of outliers. PAC-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a…

In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…