Universal Approximation Using Shuffled Linear Models

TL;DR

This paper introduces Shuffled Linear Models (SLMs), a novel local linear modeling approach that acts as a universal approximator, extending existing machine learning frameworks with proven theoretical guarantees.

Contribution

It presents the SLM as a new universal approximation method, connecting it to Extreme Learning Machines and Takagi-Sugeno fuzzy models, with mathematical proofs and an efficient algorithm.

Findings

Proves universal approximation capability of SLMs.

Provides an upper bound on the number of models needed.

Offers an efficient algorithm for implementing SLMs.

Abstract

This paper proposes a specific type of Local Linear Model, the Shuffled Linear Model (SLM), that can be used as a universal approximator. Local operating points are chosen randomly and linear models are used to approximate a function or system around these points. The model can also be interpreted as an extension to Extreme Learning Machines with Radial Basis Function nodes, or as a specific way of using Takagi-Sugeno fuzzy models. Using the available theory of Extreme Learning Machines, universal approximation of the SLM and an upper bound on the number of models are proved mathematically, and an efficient algorithm is proposed.