Context models on sequences of covers

TL;DR

This paper introduces a novel class of non-parametric Bayesian models that perform exact, incremental inference on sequences of covers, enabling efficient conditional density estimation with a new probabilistic framework.

Contribution

It presents a new approach using sequences of covers and random walks for tractable, exact Bayesian inference in conditional measures, applied to density estimation.

Findings

First closed-form non-parametric Bayesian method for conditional density estimation

Achieves polynomial-time, incremental inference

Demonstrates effectiveness on density estimation problems

Abstract

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem.