An Ordered Lasso and Sparse Time-Lagged Regression
This incremental method addresses regression problems where coefficient ordering is natural, such as in financial time series or patient outcome prediction.
The authors tackled regression with ordered coefficients by proposing an order-constrained L1-regularized method, efficiently solved using the Pool Adjacent Violators Algorithm, and applied it to time-lagged regression with decaying coefficients, demonstrating results on real and simulated data.
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.