---
title: "model class"
type: concept
related: [Normalizing Flow, Model Fitting, Generative Model, Gaussian Mixture Model, Probability Density Function]
source: https://www.jemoka.com/posts/kbhmodel_class/
confidence: high
status: active
---

Goal: we need to find a model that is &ldquo;expressive enough&rdquo;: we need to have enough parameters to help match the shape of the data we collect. to help match the shape of the data we collect.
constituents requirements additional information selecting parameters see model fitting
increasing expressiveness mixure model We could mix distributions into a . See Gaussian mixture model.
transforming distributions Suppose you start with:
\begin{equation} Z \sim \mathcal{N}\qty(0,1) \end{equation}
we can sample \(k\) points \(k \sim Z\), and then transform them across a function \(x_{j}=f(k_{j})\). We now want to know the destruction of \(x_{j}\). Turns out, if \(f\) is invertible and differential, we have:
\begin{equation} p_{x}\qty(x) = p_{z}\qty(g(x)) | g&rsquo;(x) | \end{equation}
where \(g(x) = f^{-1}\qty(x)\).
This new \(p_{x}\) is now the PDF of our transformed distribution.
&hellip;but how do you pick \(f\)
Normalizing Flow!
generative model see generative model
