Sparse Polynomial Regression under Anomalous Data

TL;DR

This paper introduces a novel optimization-based approach for sparse polynomial regression that effectively filters anomalous data, reformulating the problem into a fractional program and proposing an efficient solution algorithm.

Contribution

It presents a new formulation of sparse polynomial regression with anomalous data filtering as a fractional program and develops a two-step convex relaxation algorithm for improved computational efficiency.

Findings

The proposed TS-CRR algorithm outperforms benchmark models in computational experiments.

Reformulating the problem as a fractional program improves computational properties.

The method effectively filters anomalous data in polynomial regression tasks.

Abstract

This paper starts with the general form of the polynomial regression model. We reformulate the Sparse Polynomial Regression Model (SPRM) with anomalous data filtering as Mixed-Integer Linear Program (MILP). This MILP is then converted to a non-convex Quadratically Constrained Quadratic Program (QCQP). Through a proposed mapping, the derived QCQP is reformulated as a Fractional Program (FP). We theoretically show that the reformulated FP has better computational properties than the original QCQP. We then suggest a conic-relaxation-based algorithm to solve the proposed FP. A Two-Step Convex Relaxation and Recovery (TS-CRR) algorithm is proposed for sparse polynomial regression with anomalous data filtering. Through a series of comprehensive computational experiments (using two different datasets), we have compared the results of our proposed TS-CRR algorithm with the results from several regression and artificial intelligent models. The numerical results show the promising performance of our proposed TS-CRR algorithm as compared to those studied benchmark models.