Related papers: A Non-convex One-Pass Framework for Generalized Fa…
Factorization machine (FM) is a popular machine learning model to capture the second order feature interactions. The optimal learning guarantee of FM and its generalized version is not yet developed. For a rank $k$ generalized FM of $d$…
In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
Efficiently representing real world data in a succinct and parsimonious manner is of central importance in many fields. We present a generalized greedy pursuit framework, allowing us to efficiently solve structured matrix factorization…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
Factorization Machine (FM) is a supervised learning approach with a powerful capability of feature engineering. It yields state-of-the-art performance in various batch learning tasks where all the training data is made available prior to…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
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…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the…
A fundamental problem in machine learning is to understand how neural networks make accurate predictions, while seemingly bypassing the curse of dimensionality. A possible explanation is that common training algorithms for neural networks…
Context-aware recommendation algorithms focus on refining recommendations by considering additional information, available to the system. This topic has gained a lot of attention recently. Among others, several factorization methods were…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…