Fused Lasso

The fused Lasso adds an L1 norm penalty on adjacent coefficient differences to a squared-error objective, optionally together with an L1 norm penalty on the coefficients themselves. The differences penalty encourages neighbouring coefficients to coincide.

This version of the fused Lasso penalizes only adjacent differences. It estimates a piecewise-constant signal while preserving an unpenalized constant level. Larger penalties generally favour fewer fitted changes.