A Convex Approach to Frisch-Kalman Problem

TL;DR

This paper introduces a convex optimization method for the Frisch-Kalman problem, effectively identifying linear relations among variables from noisy data and outperforming existing heuristics in low-noise scenarios.

Contribution

It presents a novel convex approach to a longstanding rank minimization problem, providing improved accuracy over traditional heuristics.

Findings

The convex method accurately identifies relations in noisy data.

It outperforms common heuristics when noise is small.

The approach is computationally efficient and reliable.

Abstract

This paper proposes a convex approach to the Frisch-Kalman problem that identifies the linear relations among variables from noisy observations. The problem was proposed by Ragnar Frisch in 1930s, and was promoted and further developed by Rudolf Kalman later in 1980s. It is essentially a rank minimization problem with convex constraints. Regarding this problem, analytical results and heuristic methods have been pursued over a half century. The proposed convex method in this paper is shown to be accurate and demonstrated to outperform several commonly adopted heuristics when the noise components are relatively small compared with the underlying data.