An introduction to Density Ratio Estimation and its applications with Missing Data
Published:
Density ratio estimation is a highly useful field of mathematics with many applications. This post describes my research undertaken alongside my supervisors Song Liu and Henry Reeve which aims to make density ratio estimation robust to missing data. This work was recently published in proceedings for AISTATS 2023.
Density Ratio Estimation
Definition
As the name suggests, density ratio estimation is simply the task of estimating the ratio between two probability densities. More precisely for two RVs (Random Variables) $Z^0, Z^1$ on some space $\mathcal{Z}$ with probability density functions (PDFs) $p_0, p_1$ respectively, the density ratio is the function $r^{*}:\mathcal{Z}\rightarrow\mathbb{R}$ defined by \(r^{*}(z):=\frac{p_0(z)}{p_1(z)}\)