On a convergence property of a geometrical algorithm for statistical manifolds
This work addresses convergence guarantees for a derivative-free algorithm in statistical inference, which is incremental as it builds on existing geometrical methods.
The paper tackles the problem of guaranteeing convergence for a geometrical projection algorithm used in statistical inference, deriving a bound on the learning rate to ensure local convergence and providing specific forms of this bound for m-mixture and e-mixture estimation problems.
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.