This paper presents the prior PAC-Bayes bound and explores its capabilities as a tool to provide tight predictions of SVMs’ generalization. The computation of the bound involves estimating a prior of the distribution of classifiers from the available data, and then manipulating this prior in the usual PAC-Bayes generalization bound. We explore two alternatives: to learn the prior from a separat...

This paper analyzes the problem of learning the structure of a Bayes net (BN) in the theoretical framework of Gold’s learning paradigm. Bayes nets are one of the most prominent formalisms for knowledge representation and probabilistic and causal reasoning. We follow constraint-based approaches to learning Bayes net structure, where learning is based on observed conditional dependencies between ...

Small area estimation has received a lot of attention in recent years due to growing demand for reliable small area statistics. Traditional area-specific estimators may not provide adequate precision because sample sizes in small areas are seldom large enough. This makes it necessary to employ indirect estimators based on linking models. Basic area level and unit level models have been extensiv...

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of existing VB algorithms is so far generally restricted to case where variational parameter space Euclidean, which hinders potential broad application methods. This paper extends scope Riemannian manifold. We develop an efficient manifold-based algorithm ...

In this work, fundamental properties of Bayes decision rule using general loss functions are derived analytically and are verified experimentally for automatic speech recognition. It is shown that, for maximum posterior probabilities larger than 1/2, Bayes decision rule with a metric loss function always decides on the posterior maximizing class independent of the specific choice of (metric) lo...