Fused Lasso and trend filtering
function fit(FusedLasso, y, λ)Fits the fused Lasso model:
\[\underset{\beta}{\operatorname{argmin}} \frac{1}{2} \sum_{k=1}^N(y_k - \beta_k)^2 + \lambda \sum_{k=2}^N |\beta_k - \beta_{k-1}|\]
The model coefficients can be obtained by calling $coef$ on the returned model object.
For details of the algorithm, see Johnson, N. A. (2013). A dynamic programming algorithm for the fused lasso and L0-segmentation. Journal of Computational and Graphical Statistics, 22(2), 246–260. doi:10.1080/10618600.2012.681238
function fit(TrendFilter, y, order, λ)Fits the trend filter model:
\[\underset{\beta}{\operatorname{argmin}} \frac{1}{2} \sum_{k=1}^N(y_k - \beta_k)^2 + \lambda \|D^{(k+1)}\beta_k\|_1\]
Where $D^{(k+1)}$ is the discrete difference operator of order k+1. The model coefficients can be obtained by calling $coef$ on the returned model object.
For details of the algorithm, see Ramdas, A., & Tibshirani, R. J. (2014). Fast and flexible ADMM algorithms for trend filtering. arXiv Preprint arXiv:1406.2082. Retrieved from http://arxiv.org/abs/1406.2082