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


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.12   pp.2834-2841
Publication Date: 2017/12/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
statistical maximum,  Gaussian mixture model,  covariance,  sensitivity,  performance evaluation,  

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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.