Additive models with trend filtering

Additive Models with Trend Filtering

We consider additive models built with trend filtering, i.e., additive models whose components are each regularized by the (discrete) total variation of their (k+1)st (discrete) derivative, for a chosen integer k ≥ 0. This results in kth degree piecewise polynomial components, (e.g., k = 0 gives piecewise constant components, k = 1 gives piecewise linear, k = 2 gives piecewise quadratic, etc.)....

l1 Trend Filtering

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l1 trend filtering method substitutes a sum of absolute values (i.e., an l1-norm) for the sum of squares used in H-P filtering to penalize variations in the estimated ...

1 Trend Filtering

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick–Prescott (H-P) filtering, a widely used method for trend estimation. The proposed !1 trend filtering method substitutes a sum of absolute values (i.e., !1 norm) for the sum of squares used in H-P filtering to penalize variations in the estimated tre...

Trend Filtering on Graphs

Yu-Xiang Wang1,2 [email protected] James Sharpnack3 [email protected] Alexander J. Smola1,4 [email protected] Ryan J. Tibshirani1,2 [email protected] 1 Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213 2 Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213 3 Mathematics Department, University of California at San Diego, La Jolla, CA 10280 ...

Target setting in additive models with preferences and interval data