Abstract

We consider a regression scenario where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of `1-regularized regression (lasso) for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Vio-lators Algorithm as its proximal operator. The main application of this idea is to 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 appli-cation areas include financial time series and prediction of dynamic patient outcomes based on clinical measurements. We illustrate this idea on real and simulated data. 1