A.Kostin, Tula State University, Russia

A unified variational approach to data analysis. Dynamic programming
procedures.

Abstract
There are many data processing problems of transformation source data
array into other one with same structure but elements, generally
speaking, of different nature. Such problems can be solved in terms of
so called Unified Variational Approach to data analysis.
The essence of the approach will be depicted and very efficient
procedures for optimization of objective functions with treelike graph
of variables neighborhood will be expound, then parametric dynamic
programming procedure for minimization of quadratic pairwise separable
objective functions will be proposed. Three applications (estimation of
non-stationary regression coefficients, smoothing of signals,
autoregression and time-frequency analysis) of the procedure will be
demonstrated.