A Simple Algorithm for Approximation by Nomographic Functions

Abstract

This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate continuous inner functions. We show that a suitable approximation can be obtained by solving a cone-constrained Rayleigh-Quotient optimization problem. The proposed approach is based on a combination of a dimensionwise function decomposition known as Analysis of Variance (ANOVA) and optimization over a class of monotone polynomials. An example is given to show that the proposed algorithm can be applied to solve problems in distributed function computation over multiple-access channels.

6 pages, 7 figures, 2 tables. v2: various improvements and minor corrections, added references