Related papers: Joint Bayesian Parameter and Model Order Estimatio…
Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of…
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…
Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation…
Learning the joint probability of random variables (RVs) is the cornerstone of statistical signal processing and machine learning. However, direct nonparametric estimation for high-dimensional joint probability is in general impossible, due…
Estimating the joint probability mass function (PMF) of a set of random variables lies at the heart of statistical learning and signal processing. Without structural assumptions, such as modeling the variables as a Markov chain, tree, or…
In this article, a Probability Mass Function (PMF) estimation method which tames the curse of dimensionality is proposed. This method, called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D, has for principle to partially…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to…
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…
Deep neural networks typically impose significant computational loads and memory consumption. Moreover, the large parameters pose constraints on deploying the model on edge devices such as embedded systems. Tensor decomposition offers a…
Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
We study nonparametric estimation of a probability mass function (PMF) on a large discrete support, where the PMF is multi-modal and heavy-tailed. The core idea is to treat the empirical PMF as a signal on a line graph and apply a…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…