6 papers
Local Invertibility of Integral Operators with Analytic Kernels
Nikolay Balov
The invertibility of integral linear operators is a major problem of both theoretical and practical importance. In this paper we investigate the relation between an operator invert…
Consistent Model Selection of Discrete Bayesian Networks from Incomplete Data
Nikolay H. Balov
A maximum likelihood based model selection of discrete Bayesian networks is considered. The model selection is performed through scoring function , which, for a given network $G…
On the Stochastic Rank of Metric Functions
Nikolay H. Balov
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochast…
Comparing and interpolating distributions on manifold
Nikolay H. Balov
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and find…
Covariance fields
Nikolay H. Balov
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,…
Covariance of centered distributions on manifold
Nikolay H. Balov
We define and study a family of distributions with domain complete Riemannian manifold. They are obtained by projection onto a fixed tangent space via the inverse exponential map.…