Related papers: Redundancy of Exchangeable Estimators
We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring…
The marginal Bayesian predictive classifiers (mBpc) as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and hence tacitly assumes the independence of the observations. However, due to…
Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods…
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…
Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birg\'{e} [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42 (2006) 273--325] to the particular situation of the estimation of…
The evaluation of the error to be attributed to cut efficiencies is a common question in the practice of experimental particle physics. Specifically, the need to evaluate the efficiency of the cuts for background removal, when they are…
We study the redundancy of universally compressing strings $X_1,\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of…
Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over…
We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches…