1
$\begingroup$

Is there a way around the numerical problem of calculating the denominator of the Multivariate Gaussian distribution of high dimensional vectors?
Given the following formula $$f_{\mathbf X}(x_1,\ldots,x_k) = \frac{\exp\left(-\frac 1 2 ({\mathbf x}-{\boldsymbol\mu})^\mathrm{T}{\boldsymbol\Sigma}^{-1}({\mathbf x}-{\boldsymbol\mu})\right)}{\sqrt{(2\pi)^k|\boldsymbol\Sigma|}}$$ With a feature vector of size, $>128$ the denominator cannot be computed with normal precision(64 bit) frameworks. My feature vectors are $1024$ long, and I haven't found a way to come across the problem.

$\endgroup$

1 Answer 1

1
$\begingroup$

It's better to operate on log domain in such cases. There are implementations (employing factorizations like Cholesky, LU) available in common languages:

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.