TY - DATA T1 - An Ordered Lasso and Sparse Time-lagged Regression PY - 2015/08/07 AU - Robert Tibshirani AU - Xiaotong Suo UR - https://tandf.figshare.com/articles/journal_contribution/An_Ordered_Lasso_and_Sparse_Time_lagged_Regression/1569557 DO - 10.6084/m9.figshare.1569557.v1 L4 - https://ndownloader.figshare.com/files/2352105 KW - regression KW - coefficient KW - outcome KW - lasso KW - Potential application areas KW - K time points KW - Pool Adjacent Violators Algorithm KW - order constraint N2 - 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 (Lasso) 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 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 application areas include financial time series and prediction of dynamic patient outcomes based on clinical measurements. We illustrate this idea on real and simulated data. ER -