Related papers: A quantum-inspired algorithm for approximating sta…
We study symmetric tensor decompositions, i.e. decompositions of the input symmetric tensor T of order 3 as sum of r 3rd-order tensor powers of u_i where u_i are vectors in \C^n. In order to obtain efficient decomposition algorithms, it is…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\times n$ efficiently such that $A\approx QLP$, where $L$ is the rank-$k$…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic…
We analyze the convergence rate of the unregularized natural policy gradient algorithm with log-linear policy parametrizations in infinite-horizon discounted Markov decision processes. In the deterministic case, when the Q-value is known…
In this paper, we aim to develop stochastic hard thresholding algorithms for the important problem of AUC maximization in imbalanced classification. The main challenge is the pairwise loss involved in AUC maximization. We overcome this…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…
Higher-order $U$-statistics abound in fields such as statistics, machine learning, and computer science, but are known to be highly time-consuming to compute in practice. Despite their widespread appearance, a comprehensive study of their…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
We present new algorithms for computing the log-determinant of symmetric, diagonally dominant matrices. Existing algorithms run with cubic complexity with respect to the size of the matrix in the worst case. Our algorithm computes an…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations,…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large…