Related papers: Parametrizing the mixing matrix : A unified approa…
The multiplicative update (MU) algorithm has been extensively used to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizers. However, theoretical…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
The world is rarely static -- many problems need not only be solved once but repeatedly, under changing conditions. This setting is addressed by the "multistage" view on computational problems. We study the "diverse multistage" variant,…
We consider the problem of consistently matching multiple sets of elements to each other, which is a common task in fields such as computer vision. To solve the underlying NP-hard objective, existing methods often relax or approximate it,…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
We obtain a general parametrization for the neutrino Majorana mass matrix in which all possible deviations from tribimaximal mixing are given by three complex parameters, and the deviation from each tribimaximal mixing eigenvector is…
Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…
It turns out that a parametrization of degenerate density matrices requires a parametrization of $\mathfrak{F}=U(n)/({U(k_1)\times U(k_2)\times \cdots \times U(k_m)})\quad n=k_1 +\cdots + k_m $ where $U(k)$ denotes the set of all unitary…
Matrix and tensor-guided parametrization for Natural Language Processing (NLP) models is fundamentally useful for the improvement of the model's systematic efficiency. However, the internal links between these two algebra structures and…
In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…
In this paper, we analyze the process of "assembling" new matrix geometric means from existing ones, through function composition or limit processes. We show that for n=4 a new matrix mean exists which is simpler to compute than the…
Merging has become a widespread way to cheaply combine individual models into a single model that inherits their capabilities and attains better performance. This popularity has spurred rapid development of many new merging methods, which…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
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…
We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates design and operational phases, which are represented by a mixed-integer program and discounted-cost…