Related papers: Bayesian inference of vector autoregressions with …

Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the…

VAR models are a type of multi-equation model that have been widely applied in econometrics. With the arrival of Big Data, huge amounts of data are being collected in numerous fields, making feasible the application of these kind of…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on…

Tensor decomposition has emerged as a powerful framework for feature extraction in multi-modal biomedical data. In this review, we present a comprehensive analysis of tensor decomposition methods such as Tucker, CANDECOMP/PARAFAC, spiked…

Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…

Structural vector autoregressive (SVAR) models are widely used to analyze the simultaneous relationships between multiple time-dependent data. Various statistical inference methods have been studied to overcome the identification problems…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…

Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling…

The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision,…

We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…

Time-series classification is an important domain of machine learning and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series…

Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with…

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…

We propose a family of novel hierarchical Bayesian deep auto-encoder models capable of identifying disentangled factors of variability in data. While many recent attempts at factor disentanglement have focused on sophisticated learning…