Related papers: Max vs Min: Tensor Decomposition and ICA with near…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer…
We propose a new algorithm for tensor decomposition, based on Jennrich's algorithm, and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our first contribution is a simple and efficient algorithm to…
Finding overcomplete latent representations of data has applications in data analysis, signal processing, machine learning, theoretical neuroscience and many other fields. In an overcomplete representation, the number of latent features…
We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…
We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
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…
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…
We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
We consider the problem of clustering mixtures of mean-separated Gaussians in high dimensions. We are given samples from a mixture of $k$ identity covariance Gaussians, so that the minimum pairwise distance between any two pairs of means is…
Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…