# Bayesian binary classification using partitions of unity

Sunday afternoon project. I think it is possible to get topological garanties for the reconstruction of the classification boundary using the Nash-Tognoli theorem.

# 1. The problem

Points $x_i$, $i=1\dots, N$ are distributed on some space $\mathbb{M}$ and associated a label $\ell_i\in \{0,1\}$. It is assumed that

$\ell_i \sim \text{Ber}(p(x_i)), \qquad (1)$

where $p: \mathbb{M} \rightarrow [0,1]$ is some unknown integrable function. Estimating $p$ from the data $\{(x_i,\ell_i)\,|\, i=1,2,\dots, N\}$ allows us to predict $\ell_{n+1}$ given $x_{n+1}$.Read More »