Related papers: Optimal Structured Matrix Approximation for Robust…
Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
We design optimal $2 \times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are…
This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving the LM linear system inexactly, subject to specific…
We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimizations. While many efficient…
Tracking and approximating data matrices in streaming fashion is a fundamental challenge. The problem requires more care and attention when data comes from multiple distributed sites, each receiving a stream of data. This paper considers…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
We propose a learning algorithm for cell-load approximation in wireless networks. The proposed algorithm is robust in the sense that it is designed to cope with the uncertainty arising from a small number of training samples. This scenario…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
One popular assumption regarding biological systems is that traits have evolved to be optimized with respect to function. This is a standard goal in evolutionary computation, and while not always embraced in the biological sciences, is an…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…