Related papers: Bayesian factorization via $L_{1/2}$ shrinkage
In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…
We present a novel framework for concomitant dimension reduction and clustering. This framework is based on a novel class of Bayesian clustering factor models. These models assume a factor model structure where the vectors of common factors…
The main objective of this paper is to apply linear and pretest shrinkage estimation techniques to estimating the parameters of two 2-parameter Burr-XII distributions. Further more, predictions for future observations are made using both…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
Scientific computer simulations cannot represent all scales in realistic applications. To bridge this model-data gap, parameters are injected into models and constrained with noisy data using Bayesian inversion. To reduce the number of…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…
Randomized controlled clinical trials provide the gold standard for evidence generation in relation to the efficacy of a new treatment in medical research. Relevant information from previous studies may be desirable to incorporate in the…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…
The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…