A New Algorithm to Determine Covariance in Statistical Maximum for Gaussian Mixture Model

Daiki AZUMA; Shuji TSUKIYAMA

doi:10.1587/transfun.E100.A.2834

A New Algorithm to Determine Covariance in Statistical Maximum for Gaussian Mixture Model

Daiki AZUMA, Shuji TSUKIYAMA

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In statistical approaches such as statistical static timing analysis, the distribution of the maximum of plural distributions is computed by repeating a maximum operation of two distributions. Moreover, since each distribution is represented by a linear combination of several explanatory random variables so as to handle correlations efficiently, sensitivity of the maximum of two distributions to each explanatory random variable, that is, covariance between the maximum and an explanatory random variable, must be calculated in every maximum operation. Since distribution of the maximum of two Gaussian distributions is not a Gaussian, Gaussian mixture model is used for representing a distribution. However, if Gaussian mixture models are used, then it is not always possible to make both variance and covariance of the maximum correct simultaneously. We propose a new algorithm to determine covariance without deteriorating the accuracy of variance of the maximum, and show experimental results to evaluate its performance.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2834-2841

Publication Date: 2017/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2834

Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)

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Authors

Daiki AZUMA
Chuo University
Shuji TSUKIYAMA
Chuo University

Keyword

statistical maximum, Gaussian mixture model, covariance, sensitivity, performance evaluation

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Daiki AZUMA, Shuji TSUKIYAMA, "A New Algorithm to Determine Covariance in Statistical Maximum for Gaussian Mixture Model" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 12, pp. 2834-2841, December 2017, doi: 10.1587/transfun.E100.A.2834.
Abstract: In statistical approaches such as statistical static timing analysis, the distribution of the maximum of plural distributions is computed by repeating a maximum operation of two distributions. Moreover, since each distribution is represented by a linear combination of several explanatory random variables so as to handle correlations efficiently, sensitivity of the maximum of two distributions to each explanatory random variable, that is, covariance between the maximum and an explanatory random variable, must be calculated in every maximum operation. Since distribution of the maximum of two Gaussian distributions is not a Gaussian, Gaussian mixture model is used for representing a distribution. However, if Gaussian mixture models are used, then it is not always possible to make both variance and covariance of the maximum correct simultaneously. We propose a new algorithm to determine covariance without deteriorating the accuracy of variance of the maximum, and show experimental results to evaluate its performance.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2834/_p

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@ARTICLE{e100-a_12_2834,
author={Daiki AZUMA, Shuji TSUKIYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Algorithm to Determine Covariance in Statistical Maximum for Gaussian Mixture Model},
year={2017},
volume={E100-A},
number={12},
pages={2834-2841},
abstract={In statistical approaches such as statistical static timing analysis, the distribution of the maximum of plural distributions is computed by repeating a maximum operation of two distributions. Moreover, since each distribution is represented by a linear combination of several explanatory random variables so as to handle correlations efficiently, sensitivity of the maximum of two distributions to each explanatory random variable, that is, covariance between the maximum and an explanatory random variable, must be calculated in every maximum operation. Since distribution of the maximum of two Gaussian distributions is not a Gaussian, Gaussian mixture model is used for representing a distribution. However, if Gaussian mixture models are used, then it is not always possible to make both variance and covariance of the maximum correct simultaneously. We propose a new algorithm to determine covariance without deteriorating the accuracy of variance of the maximum, and show experimental results to evaluate its performance.},
keywords={},
doi={10.1587/transfun.E100.A.2834},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - A New Algorithm to Determine Covariance in Statistical Maximum for Gaussian Mixture Model
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2834
EP - 2841
AU - Daiki AZUMA
AU - Shuji TSUKIYAMA
PY - 2017
DO - 10.1587/transfun.E100.A.2834
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - In statistical approaches such as statistical static timing analysis, the distribution of the maximum of plural distributions is computed by repeating a maximum operation of two distributions. Moreover, since each distribution is represented by a linear combination of several explanatory random variables so as to handle correlations efficiently, sensitivity of the maximum of two distributions to each explanatory random variable, that is, covariance between the maximum and an explanatory random variable, must be calculated in every maximum operation. Since distribution of the maximum of two Gaussian distributions is not a Gaussian, Gaussian mixture model is used for representing a distribution. However, if Gaussian mixture models are used, then it is not always possible to make both variance and covariance of the maximum correct simultaneously. We propose a new algorithm to determine covariance without deteriorating the accuracy of variance of the maximum, and show experimental results to evaluate its performance.
ER -