Related papers: A Majorization-Minimization Algorithm for Computin…
Let $M$ be a representation of an acyclic quiver $Q$ over an infinite field $k$. We establish a deterministic algorithm for computing the Harder-Narasimhan filtration of $M$. The algorithm is polynomial in the dimensions of $M$, the weights…
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
Logistic linear mixed model is widely used in experimental designs and genetic analysis with binary traits. Motivated by modern applications, we consider the case with many groups of random effects and each group corresponds to a variance…
We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
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…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
An algorithm framework is proposed for minimizing nonsmooth functions. The framework is variable-metric in that, in each iteration, a step is computed using a symmetric positive definite matrix whose value is updated as in a quasi-Newton…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…
The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where the measurements consist of only the magnitude of linear function of the unknown signal, and the noise in the measurements follow Poisson…
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…
The Krasnosel'skii-Mann (KM) algorithm is the most fundamental iterative scheme designed to find a fixed point of an averaged operator in the framework of a real Hilbert space, since it lies at the heart of various numerical algorithms for…