Related papers: Matrix Factorization in Tropical and Mixed Tropica…

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…

The increasing size of data generated by smartphones and IoT devices motivated the development of Federated Learning (FL), a framework for on-device collaborative training of machine learning models. First efforts in FL focused on learning…

Factorization machines (FMs) are widely used in recommender systems due to their adaptability and ability to learn from sparse data. However, for the ubiquitous non-interactive features in sparse data, existing FMs can only estimate the…

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In…

We propose the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the $\ell_2$-regularizer and…

We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…

In an effort to develop topic modeling methods that can be quickly applied to large data sets, we revisit the problem of maximum-likelihood estimation in topic models. It is known, at least informally, that maximum-likelihood estimation in…

Bayesian Matrix Factorization (BMF) is a powerful technique for recommender systems because it produces good results and is relatively robust against overfitting. Yet BMF is more computationally intensive and thus more challenging to…

Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…

Recommender system is currently widely used in many e-commerce systems, such as Amazon, eBay, and so on. It aims to help users to find items which they may be interested in. In literature, neighborhood-based collaborative filtering and…

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on…

In this paper, we propose the use of in-training matrix factorization to reduce the model size for neural machine translation. Using in-training matrix factorization, parameter matrices may be decomposed into the products of smaller…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn…