Shashanka Ubaru

Fast Estimation of

The problem of estimating the trace of matrix functions appears in applications ranging from machine learning and scientific computing, to computational biology. This paper presents an inexpensive method to estimate the trace of

tr(f(A))

f(A)

via Stochastic Lanczos Quadrature

for cases where

Fast Estimation of Approximate Matrix Ranks Using Spectral Densities

f

Improving the incoherence of a learned dictionary via rank shrinkage

is analytic inside a closed interval and

Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and Hardness

A

Group testing schemes from low-weight codewords of BCH codes

is a symmetric positive definite matrix. The method combines three key ingredients, namely, the stochastic trace estimator, Gaussian quadrature, and the Lanczos algorithm. As examples, we consider the problems of estimating the log-determinant (

Applications of Trace Estimation Techniques

f(t)=\log(t)

Gray Scales by Cross Pairing of Select and Data Voltages in Multi-Line Addressed Liquid Crystal Displays

), the Schatten

Fast methods for estimating the numerical rank of large matrices

p