Related papers: Information-theoretic Feature Selection via Tensor…
Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor…
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…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…
Feature selection is a widely used dimension reduction technique to select feature subsets because of its interpretability. Many methods have been proposed and achieved good results, in which the relationships between adjacent data points…
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…
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…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
Many approximations were suggested to circumvent the cubic complexity of kernel-based algorithms, allowing their application to large-scale datasets. One strategy is to consider the primal formulation of the learning problem by mapping the…
Non-Negative Matrix Factorization (NMF) is a widely used dimension reduction method that factorizes a non-negative data matrix into two lower dimensional non-negative matrices: One is the basis or feature matrix which consists of the…
Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…
Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem…
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…
While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…
Feature selection is a process of choosing a subset of relevant features so that the quality of prediction models can be improved. An extensive body of work exists on information-theoretic feature selection, based on maximizing Mutual…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…