Getting the value of a matrix argument post maximizing a function.

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Deepankar Vishwakarma 2021-4-25

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回答： Nipun 2024-5-16

Hello there,

I was stuck on a problem of maximinzing a posterior probability and wanted the value of 'w' at which it is maximized.

The posterior function is -

posterior = ((2*pi)^(-M/2)) * (det(SIGMA)^(-1/2)) * exp((-1/2) * (w-mu)' * isigma * (w-mu));

where mu, M, SIGMA, isigma are constant. Also, w, SIGMA, isigma, mu are matrices of suitable dimentions.

I could not find a particular solution to the problem. Any help is appreciated.

Thanks

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Thiago Henrique Gomes Lobato 2021-4-25

This posteriori is a multivariate Gaussian, the maximum is when w=mu, so if you have mu you already have the maximum.

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Answer 1

Nipun 2024-5-16

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Hi Deepankar,

I understand that you are trying to find the value of (w) that maximizes the posterior probability described by a multivariate Gaussian distribution. The maximum of this distribution occurs at its mean (\mu), which means the value of (w) you are looking for is equal to (\mu).

Here is a concise MATLAB code snippet that assigns the value of (\mu) to (w), assuming you have already defined (\mu) and other necessary variables:

% Assuming mu is defined and represents the mean vector of your distribution
w = mu; % This assigns the maximizing value to w

Given the nature of the problem, there is no need for further optimization routines or calculations. The result is derived from the mathematical properties of the multivariate Gaussian distribution, where the density function is maximized at the mean (\mu).

Hope this helps.

Regards,

Nipun