Related papers: Hierarchical sparsity priors for regression models
Meta-analytic-predictive (MAP) priors have been proposed as a generic approach to deriving informative prior distributions, where external empirical data are processed to learn about certain parameter distributions. The use of MAP priors is…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
While there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
For many practical problems, the regression models follow the strong heredity property (also known as the marginality), which means they include parent main effects when a second-order effect is present. Existing methods rely mostly on…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous…
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are…
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…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Understanding what makes high-dimensional data learnable is a fundamental question in machine learning. On the one hand, it is believed that the success of deep learning lies in its ability to build a hierarchy of representations that…
We address a classical problem in statistics: adding two-way interaction terms to a regression model. As the covariate dimension increases quadratically, we develop an estimator that adapts well to this increase, while providing accurate…
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This…
This work focuses on learning optimization problems with quadratical interactions between variables, which go beyond the additive models of traditional linear learning. We investigate more specifically two different methods encountered in…
We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…