# Efficient learning of smooth probability functions from Bernoulli tests with guarantees

arXiv: https://arxiv.org/abs/1812.04428 · HTML: https://mlsanity.com/paper/1812.04428/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2018.

## Built on by (most cited first, 2 of 2)

- [Open Problem: Tight Bounds for Kernelized Multi-Armed Bandits with Bernoulli Rewards](https://mlsanity.com/paper/2407.06321/) (2024)
- [BKP: An R Package for Beta Kernel Process Modeling](https://mlsanity.com/paper/2508.10447/) (2025)

## Abstract (arXiv)

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.