Karl Sjöstrand
Coefficient Path Algorithms
In this talk the focus is not on methods for sparse estimation per se, but rather on their efficient computation. Many sparse methods include a regularization parameter which effectively controls the number of non-zero variables, providing an entire range of sparse solutions to select among. Instead of estimating a set of separate solutions for a fixed set of regularization parameter values, we look at algorithms which provide the solutions to all possible such values. Methods where this approach is especially attractive are those where the estimated coefficients are piecewise linear functions of the regularization parameter. We define this class of methods by deriving necessary and sufficient conditions and look at algorithms for recovering the entire regularization path. Suggested reading: Rosset and Zhu, Ann. Statist. Vol 35, Nr 3 (2007), 1012-1030.