Bayesian methods based on hierarchical mixture models have demonstrated excellent mean squared error properties in constructing data dependent shrinkage estimators in wavelets, however, subjective elicitation of the hyperparameters is challenging. In this chapter we use an Empirical Bayes approach to estimate the hyperparameters for each level of the wavelet decomposition, bypassing the usual d...

Personalized recommender systems can be classified into three main categories: content-based, mostly used to make suggestions depending on the text of the web documents, collaborative filtering, that use ratings from many users to suggest a document or an action to a given user and hybrid solutions. In the collaborative filtering task we can find algorithms such as the naı̈ve Bayes classifier or...

Empirical Bayes methods use the data from parallel experiments, for instance observations Xk ~ 𝒩 (Θ k , 1) for k = 1, 2, …, N, to estimate the conditional distributions Θ k |Xk . There are two main estimation strategies: modeling on the θ space, called "g-modeling" here, and modeling on the×space, called "f-modeling." The two approaches are de- scribed and compared. A series of computational fo...

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We investigate theoretically some properties of variational Bayes approximations based on estimating the mixing coefficients of known densities. We show that, with probability 1 as the sample size n grows large, the iterative algorithm for the variational Bayes approximation converges locally to the maximum likelihood estimator at the rate of O(1/n). Moreover, the variational posterior distribu...

ÐWe give a short proof of the following result. Let …X; Y † be any distribution on N f0; 1g, and let …X1; Y1†; . . . ; …Xn; Yn† be an i.i.d. sample drawn from this distribution. In discrimination, the Bayes error L ˆ infg Pfg…X† 6ˆ Y g is of crucial importance. Here we show that without further conditions on the distribution of …X; Y †, no rate-of-convergence results can be obtained. Let n…X1; ...

We propose a linear Bayes estimator of the cumulative hazard of a survival distribution, based on iid survival times, possibly right censored and left truncated. The resulting estimator is recognized as an exact Bayes estimator under more restrictive model assumptions and verified to have the minimax property.

The Bayes factor is a useful tool for evaluating sets of inequality and about equality constrainedmodels. In the approach described, the Bayes factor for a constrained model with the encompassing model reduces to the ratio of two proportions, namely the proportion of, respectively, the encompassing prior and posterior in agreement with the constraints. This enables easy and straightforward esti...

In this paper, we investigate the use of multivariate Poisson model and feature weighting to learn naive Bayes text classifier. Our new naive Bayes text classification model assumes that a document is generated by a multivariate Poisson model while the previous works consider a document as a vector of binary term features based on the presence or absence of each term. We also explore the use of...