Related papers: NGS Based Haplotype Assembly Using Matrix Completi…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
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…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
Genome assembly from the high-throughput sequencing (HTS) reads is a fundamental yet challenging computational problem. An intrinsic challenge is the uncertainty caused by the widespread repetitive elements. Here we get around the…
Sparse general matrix multiplication (SpGEMM) is a fundamental building block in numerous scientific applications. One critical task of SpGEMM is to compute or predict the structure of the output matrix (i.e., the number of nonzero elements…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
Complete deconvolution analysis for bulk RNAseq data is important and helpful to distinguish whether the difference of disease-associated GEPs (gene expression profiles) in tissues of patients and normal controls are due to changes in…
A ternary/binary data coding algorithm and conditions under which Hopfield networks implement optimal convolutional or Hamming decoding algorithms has been described. Using the coding/decoding approach (an optimal Binary Signal Detection…
This paper aims to understand how neural networks learn algorithmic reasoning by addressing two questions: How faithful are learned algorithms when they are effective, and why do neural networks fail to learn effective algorithms otherwise?…
Learning to autonomously assemble shapes is a crucial skill for many robotic applications. While the majority of existing part assembly methods focus on correctly posing semantic parts to recreate a whole object, we interpret assembly more…
Protein Structure Prediction (PSP) is an unsolved problem in the field of computational biology. The problem of protein structure prediction is about predicting the native conformation of a protein, while its sequence of amino acids is…
We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel Structured Newton-Like…
We present several new results pertaining to haplotyping. These results concern the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype fragments. We consider the complexity of the…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…