arXiv research

New method clusters matrix-variate data with outliers.

In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-w…

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-var…

A distributed framework for reducing high-dimensional matrix-variate time series data.

Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one…

Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive poste…

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable a…

Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised and supervised classification. Although dimension reduction in the area of clus…

New method infers graph from dependent matrix data.

A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.

The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations…

We face network data from various sources, such as protein interactions and online social networks. A critical problem is to model network interactions and identify latent groups of network nodes. This problem is challenging due to many reasons. For example, the network nodes are interdependent instead of independent o…

We propose a novel hierarchical model for multitask bipartite ranking. The proposed approach combines a matrix-variate Gaussian process with a generative model for task-wise bipartite ranking. In addition, we employ a novel trace constrained variational inference approach to impose low rank structure on the posterior m…

Proposes a robust factor analysis for matrix data.

Estimates covariance matrices for matrix-variate data via core covariance geometry.

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

This paper proposes robust matrix variate regression models with rank constraints and vector regularization.

RFPCA improves robustness of FPCA for matrix data.

New distribution simplifies covariance matrix inference.

Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also…

MMM model clusters mixed-type longitudinal data efficiently.

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…

This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorith…

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between …

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior distribution where we explicitly model the covariance among the input and output dimensions…

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…

Learning probability distributions on the weights of neural networks (NNs) has recently proven beneficial in many applications. Bayesian methods, such as Stein variational gradient descent (SVGD), offer an elegant framework to reason about NN model uncertainty. However, by assuming independent Gaussian priors for the i…

This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distribu…

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate appr…

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples…

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm …

Ordinal data is omnipresent in almost all multiuser-generated feedback - questionnaires, preferences etc. This paper investigates modelling of ordinal data with Gaussian restricted Boltzmann machines (RBMs). In particular, we present the model architecture, learning and inference procedures for both vector-variate and …

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction mo…

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive w…

MSFA clusters high-dimensional spatial data using spline-based covariance structures.

EiGLasso speeds up sparse Kronecker-sum covariance estimation.

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability, which extends from the previous work of Nguyen [2013] and Chen [1995] to address…

This paper considers the problem of isolating a small number of exchange traded funds (ETFs) that suffice to capture the fundamental dimensions of variation in U.S. financial markets. First, the data is fit to a vector-valued Bayesian regression model, which is a matrix-variate generalization of the well known stochast…

Future advancement of engineering applications is dependent on design of novel materials with desired properties. Enormous size of known chemical space necessitates use of automated high throughput screening to search the desired material. The high throughput screening uses quantum chemistry calculations to predict mat…

Enhances traffic forecasting with dynamic regression incorporating error modeling.

Bayesian approach for learning spatiotemporal systems from noisy data.

Paper proposes a deep learning method for better covariance matrix forecasting.

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes m…

Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further extensions of such algorithms. One of the new approaches to the probabilistic D…

New algorithm estimates matrix-valued regression parameters efficiently.

A new framework uses matrix flows to unify frequentist and Bayesian approaches for sparse GGMs.

SpINNEr uses matrix regression to analyze brain connectivity, improving accuracy over other methods.

Bayesian parametric matrix models provide uncertainty quantification for spectral learning.