  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.
