On a convergence property of a geometrical algorithm for statistical manifolds

TL;DR

This paper analyzes a geometrical projection algorithm for statistical inference, providing convergence guarantees and practical bounds, especially for mixture estimation problems, useful in nonparametric contexts.

Contribution

It introduces a derivative-free, representation-free geometrical algorithm with convergence bounds applicable to mixture estimation.

Findings

Derived a learning rate bound for local convergence

Calculated specific bounds for m-mixture and e-mixture estimation

Demonstrated the algorithm's applicability in nonparametric cases

Abstract

In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive a bound of learning rate to guarantee local convergence. In special cases of m-mixture and e-mixture estimation problems, we calculate specific forms of the bound that can be used easily in practice.