Deterministic Stretchy Regression

TL;DR

This paper introduces a novel deterministic stretchy regression method that extends regularized least-squares by incorporating stretchable parameters, enabling effective high-dimensional data learning.

Contribution

It presents a closed-form solution for ridge regression with stretchable parameters, including primal and dual forms, and proposes an input transformation to keep computations real.

Findings

Effective in high-dimensional compressive learning

Demonstrated success on synthetic and real-world datasets

Provides a new approach to parameter stretching in regression

Abstract

An extension of the regularized least-squares in which the estimation parameters are stretchable is introduced and studied in this paper. The solution of this ridge regression with stretchable parameters is given in primal and dual spaces and in closed-form. Essentially, the proposed solution stretches the covariance computation by a power term, thereby compressing or amplifying the estimation parameters. To maintain the computation of power root terms within the real space, an input transformation is proposed. The results of an empirical evaluation in both synthetic and real-world data illustrate that the proposed method is effective for compressive learning with high-dimensional data.