Related papers: Bayesian Low Rank and Sparse Covariance Matrix Dec…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…

Bayesian factor analysis is routinely used for dimensionality reduction in modeling of high-dimensional covariance matrices. Factor analytic decompositions express the covariance as a sum of a low rank and diagonal matrix. In practice,…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…

The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying…

Understanding covariate-varying interdependencies among features is of great interest in various applications. Motivated by microbiome studies where microbial abundances and interactions vary with environmental factors, we develop a…

We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…

Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

Consider a linear model $y = X \beta + z$, $z \sim N(0, \sigma^2 I_n)$. The Gram matrix $\Theta = \frac{1}{n} X'X$ is non-sparse, but it is approximately the sum of two components, a low-rank matrix and a sparse matrix, where neither…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of…

We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes…

Matrix factorisation methods decompose multivariate observations as linear combinations of latent feature vectors. The Indian Buffet Process (IBP) provides a way to model the number of latent features required for a good approximation in…

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…