4 papers
Initialization of a Polyharmonic Cascade, Launch and Testing
Yuriy N. Bakhvalov
This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of rand…
Polyharmonic Cascade
Yuriy N. Bakhvalov
This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from…
Polyharmonic Spline Packages: Composition, Efficient Procedures for Computation and Differentiation
Yuriy N. Bakhvalov
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically deriv…
Solving a Machine Learning Regression Problem Based on the Theory of Random Functions
Yuriy N. Bakhvalov
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a…