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Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
Topic models have been extensively used to organize and interpret the contents of large, unstructured corpora of text documents. Although topic models often perform well on traditional training vs. test set evaluations, it is often the case…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…
Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…
The convergence of DP Fourier series which are neither strongly convergent nor strongly divergent is discussed in terms of the Taylor series of the corresponding inner analytic functions. These are the cases in which the maximum disk of…
In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
Various Non-negative Matrix factorization (NMF) based methods add new terms to the cost function to adapt the model to specific tasks, such as clustering, or to preserve some structural properties in the reduced space (e.g., local…
To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are…
Many sequential decision making problems, including pool-based active learning and adaptive viral marketing, can be formulated as an adaptive submodular maximization problem. Most of existing studies on adaptive submodular optimization…
In this article almost semi-continuous processes with stationary independent increments on a finite irreducible Markov chain are considered. For these processes the components of matrix factorization identity are concretely defined. On the…
We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,\tau})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…
Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…