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mml-book / mml-book.github.io

Companion webpage to the book "Mathematics For Machine Learning"
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clarification about 11.2.2, point 11.21b on page 319 #661

Open javismiles opened 3 years ago

javismiles commented 3 years ago

congratulations for a great book, quick clarification if possible. in section 11.2.2, in point 11.21b, we are calculating the derivative of the normal distribution in relation to the mean, this is equal to the transpose of (x_n - mean_k) times the inverse of the covariance matrix_k, what confuses me is why is all of that then multiplied again by the same normal distribution? shoudnt the derivative be simply the above without further multiplying it again by the same normal distribution? thank you for any clarification

mpd37 commented 3 years ago

This basically comes from the exponential in the definition of the normal distribution: For example:

d/dx exp(-x^2) = -2x exp(-x^2)