scholarly journals Analysis of Probing Techniques for Sparse Approximation and Trace Estimation of Decaying Matrix Functions

2021 ◽  
Vol 42 (3) ◽  
pp. 1290-1318
Author(s):  
Andreas Frommer ◽  
Claudia Schimmel ◽  
Marcel Schweitzer
Keyword(s):  
Sparse Approximation ◽  
Matrix Functions ◽  
Trace Estimation

Sparse Approximation of Gram Matrices for GMMN-based Speech Synthesis

2019 ◽  
Author(s):  
Tomoki Koriyama ◽  
Shinnosuke Takamichi ◽  
Takao Kobayashi
Keyword(s):  
Speech Synthesis ◽  
Sparse Approximation ◽  
Gram Matrices

scholarly journals Sparse Approximation via Generating Point Sets

2019 ◽  
Vol 15 (3) ◽  
pp. 1-16
Author(s):  
Avrim Blum ◽  
Sariel Har-Peled ◽  
Benjamin Raichel
Keyword(s):  
Sparse Approximation ◽  
Point Sets

Shifted extended global Lanczos processes for trace estimation with application to network analysis

CALCOLO ◽  
2021 ◽  
Vol 58 (1) ◽  
Author(s):  
A. H. Bentbib ◽  
M. El Ghomari ◽  
K. Jbilou ◽  
L. Reichel
Keyword(s):  
Network Analysis ◽  
Trace Estimation

scholarly journals On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

2021 ◽  
Author(s):  
Alice Cortinovis ◽  
Daniel Kressner
Keyword(s):  
Large Scale ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Random Vectors ◽  
Symmetric Positive Definite ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Trace Estimation ◽  
Scale Matrix ◽  
Existing Result

AbstractRandomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of $$x^T Bx$$ x T B x for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number of applications give rise to indefinite B. Most notably, this is the case for log-determinant estimation, a task that features prominently in statistical learning, for instance in maximum likelihood estimation for Gaussian process regression. The analysis of randomized trace estimates, including tail bounds, has mostly focused on the SPD case. In this work, we derive new tail bounds for randomized trace estimates applied to indefinite B with Rademacher or Gaussian random vectors. These bounds significantly improve existing results for indefinite B, reducing the number of required samples by a factor n or even more, where n is the size of B. Even for an SPD matrix, our work improves an existing result by Roosta-Khorasani and Ascher (Found Comput Math, 15(5):1187–1212, 2015) for Rademacher vectors. This work also analyzes the combination of randomized trace estimates with the Lanczos method for approximating the trace of f(B). Particular attention is paid to the matrix logarithm, which is needed for log-determinant estimation. We improve and extend an existing result, to not only cover Rademacher but also Gaussian random vectors.

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