An Ordered Lasso and Sparse Time-Lagged Regression

TL;DR

This paper introduces an ordered Lasso method for time-lagged regression that enforces a natural order constraint on coefficients, improving prediction in time series and clinical data by assuming coefficient decay over time.

Contribution

It develops an efficient ordered Lasso approach using the Pool Adjacent Violators Algorithm, specifically tailored for time-lagged regression with ordered coefficients.

Findings

Effective in predicting time series and clinical outcomes.

Demonstrates improved accuracy over traditional methods.

Applicable to financial and healthcare data.

Abstract

We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of L1-regularized regression for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main application of this idea is time-lagged regression, where we predict an outcome at time t from features at the previous K time points. In this setting it is natural to assume that the coefficients decay as we move farther away from t, and hence the order constraint is reasonable. Potential applications include financial time series and prediction of dynamic patient out- comes based on clinical measurements. We illustrate this idea on real and simulated data.