Efficient learning of smooth probability functions from Bernoulli tests with guarantees

TL;DR

This paper introduces a scalable, guaranteed method for learning smooth probability functions from Bernoulli tests, including contextual features, with proven convergence rates and superior empirical performance.

Contribution

The paper presents a novel scalable algorithm with rigorous guarantees for learning smooth probability functions, extending to contextual features with provable inference methods.

Findings

Proves convergence rate of the posterior update in L2-norm.

Demonstrates empirical convergence matches theoretical predictions.

Shows superiority over state-of-the-art in handling contextual features.

Abstract

We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate of our posterior update rule to the true probability function in L2-norm. Moreover, we allow the Bernoulli tests to depend on contextual features and provide a modified inference engine with provable guarantees for this novel setting. Numerical results show that the empirical convergence rates match the theory, and illustrate the superiority of our approach in handling contextual features over the state-of-the-art.