We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of consistency intensity to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer to the Bayes optimal classifier, enabling fair comparisons of the excess risks of d...

Hierarchical Bayes and Empirical Bayes are related by their goals, but quite different by the methods of how these goals are achieved. The attribute hierarchical refers mostly to the modeling strategy, while empirical is referring to the methodology. Both methods are concerned in specifying the distribution at prior level, hierarchical via Bayes inference involving additional degrees of hierarc...

By using the kernel-type density estimation and empirical distribution function in the case of identically distributed and negatively associated samples, the empirical Bayes one-sided test rules for the parameter of inverse exponential distribution are constructed based on negative associate sample under weighted linear loss function, and the asymptotically optimal property is obtained . It is ...

Charles Stein shocked the statistical world in 1955 with his proof that maximum likelihood estimation methods for Gaussian models, in common use for more than a century, were inadmissible beyond simple oneor twodimensional situations. These methods are still in use, for good reasons, but Stein-type estimators have pointed the way toward a radically different empirical Bayes approach to high-dim...

Variational Bayesian (VB) learning is known to be a promising approximation to Bayesian learning with computational efficiency. However, in some applications, e.g., large-scale collaborative filtering and tensor factorization, VB is still computationally too costly. In such cases, looser approximations such as MAP estimation and partially Bayesian (PB) learning, where a part of the parameters a...

In this article, we propose a new method for selecting level dependent threshold in wavelet shrinkage using the empirical Bayes framework. We employ both Bayesian and frequentist testing hypothesis instead of point estimation method. The best test yields the best prior and hence the more appropriate wavelet thresholds. The standard model functions are used to illustrate the performance of the p...

Microarrays are widely used for examining differential gene expression, identifying single nucleotide polymorphisms, and detecting methylation loci. Multiple testing methods in microarray data analysis aim at controlling both Type I and Type II error rates; however, real microarray data do not always fit their distribution assumptions. Smyth's ubiquitous parametric method, for example, inadequa...

Empirical Bayes methods are privileged in data mining because they can absorb prior information on model parameters and are free of choosing tuning parameters. We proposed an iterated conditional modes/medians (ICM/M) algorithm to implement empirical Bayes selection of massive variables while incorporating sparsity or more complicated a priori information. The algorithm is constructed on the ba...

Naive Credal Classifier, which is an imprecise-probability counterpart of Naive Bayes, is rigorously extended to a very general and flexible treatment of incomplete data, yielding a new classifier called Naive Credal Classifier 2 (NCC2). The new classifier delivers classifications that are robust to the presence of small sample sizes and missing values. In particular, some empirical evaluations...