相关论文: Majorization-minimization for Sparse Nonnegative M…
Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic…
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…
Non-negative matrix factorization is a problem of dimensionality reduction and source separation of data that has been widely used in many fields since it was studied in depth in 1999 by Lee and Seung, including in compression of data,…
We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
Robust matrix factorization (RMF), which uses the $\ell_1$-loss, often outperforms standard matrix factorization using the $\ell_2$-loss, particularly when outliers are present. The state-of-the-art RMF solver is the RMF-MM algorithm,…
Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data…
Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main…
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Dropout is a simple yet effective algorithm for regularizing neural networks by randomly dropping out units through Bernoulli multiplicative noise, and for some restricted problem classes, such as linear or logistic regression, several…
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…