Efficient learning of smooth probability functions from Bernoulli tests with guarantees
This work addresses a fundamental problem in statistical learning with applications in areas like medical testing or recommendation systems, though it appears incremental by extending existing methods to contextual settings.
The paper tackles the problem of learning an unknown smooth probability function from Bernoulli tests, providing a scalable algorithm with rigorous convergence guarantees in L2-norm, including a modified inference engine for contextual features. Numerical results show empirical convergence rates matching theory and superiority over state-of-the-art in handling contextual features.
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.