Related papers: Factoring Multidimensional Data to Create a Sophis…
A standard tool for model selection in a Bayesian framework is the Bayes factor which compares the marginal likelihood of the data under two given different models. In this paper, we consider the class of hierarchical loglinear models for…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A…
Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and its full…
We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any…
Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…
One of the central themes in the classification task is the estimation of class posterior probability at a new point $\bf{x}$. The vast majority of classifiers output a score for $\bf{x}$, which is monotonically related to the posterior…
This paper proposes a computationally efficient Bayesian factor model for multiple grouped count data. Adopting the link function approach, the proposed model can capture the association within and between the at-risk probabilities and…
We address the problem of data clustering by introducing an unsupervised, parameter free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information,…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We propose an efficient method for Bayesian network inference in models with functional dependence. We generalize the multiplicative factorization method originally designed by Takikawa and D Ambrosio(1999) FOR models WITH independence OF…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source.…
We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either…
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…