Related papers: Estimating Discrete Choice Demand Models with Spar…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
This paper addresses the item ranking problem with associate covariates, focusing on scenarios where the preference scores can not be fully explained by covariates, and the remaining intrinsic scores, are sparse. Specifically, we extend the…
This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumer-level panel data with few purchase events per consumer (i.e., short panel). Consumers are…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
Consider a bipartite network where $N$ consumers choose to buy or not to buy $M$ different products. This paper considers the properties of the logistic regression of the $N\times M$ array of i-buys-j purchase decisions,…
We study consumer demand in large-scale retail settings with many products, multiple categories and repeated purchase behavior. While inertia and brand loyalty are well documented, existing discrete choice models typically focus on single…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the…
In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…
Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional…