Related papers: Structured prior distributions for the covariance …

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables $p$ diverges as the number of serially dependent observations $n$ increases. In this paper, we…

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…

When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…

In many applications, it is of interest to assess the dependence structure in multivariate longitudinal data. Discovering such dependence is challenging due to the dimensionality involved. By concatenating the random effects from component…

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

This paper makes a selective survey on the recent development of the factor model and its application on statistical learnings. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to…

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\pi(Y,X)$, rather than a purely conditional model, $\pi(Y \mid X)$, where $Y$ is a scalar response variable and…

Modeling and forecasting covariance matrices of asset returns play a crucial role in finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the…

We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…

Latent factor GARCH models are difficult to estimate using Bayesian methods because standard Markov chain Monte Carlo samplers produce slowly mixing and inefficient draws from the posterior distributions of the model parameters. This paper…

Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…

This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with…

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited…

A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects…

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…