Notes - Machine Learning MT23, Inverse transform sampling

Created: October 22, 2023

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• [[Course - Machine Learning MT23]]^U

Flashcards

Suppose we want to sample from a distribution $D$. How can you achieve this with inverse transform sampling?

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Sample $x$ from $U[0, 1]$. Then take $F^{-1}(x)$ where $F^{-1}$ is the inverse cumulative distribution function.

Proofs

Prove that inverse transform sampling works, i.e. if $X \sim D$ then $Y = F _ X^{-1}(U)$ where $U \sim U[0, 1]$ has the same distribution.

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Todo, http://www3.eng.cam.ac.uk/~ss248/G12-M01/Week1/ITM.pdf.

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