The paper presents a path algorithm for the generalized lasso problem, which penalizes the $\ell_1$ norm of a matrix $D$ times the coefficient vector. The algorithm is based on solving the dual of the generalized lasso, which facilitates computation of the solution path. For the case where $D = I$ (the usual lasso), the authors draw a connection to the well-known LARS algorithm. For an arbitrary $D$, they derive an unbiased estimate of the degrees of freedom of the generalized lasso fit, which is intuitive in many applications. The introduction motivates the use of a penalty matrix $D$ and provides examples of problems that fit into this framework, including the fused lasso, trend filtering, wavelet smoothing, and outlier detection. The paper then derives the Lagrange dual of the generalized lasso problem, which serves as the foundation for the algorithm. The authors develop the algorithm for the case $X = I$ and then extend it to general design matrices $X$. They also discuss the conditions under which the generalized lasso problem can be transformed into a regular lasso problem. The paper concludes with a discussion of the properties of the solution path, including the primal-dual correspondence and the changes in slope of the primal solution path. The authors provide a geometric argument to prove a result on the degrees of freedom of the generalized lasso fit.The paper presents a path algorithm for the generalized lasso problem, which penalizes the $\ell_1$ norm of a matrix $D$ times the coefficient vector. The algorithm is based on solving the dual of the generalized lasso, which facilitates computation of the solution path. For the case where $D = I$ (the usual lasso), the authors draw a connection to the well-known LARS algorithm. For an arbitrary $D$, they derive an unbiased estimate of the degrees of freedom of the generalized lasso fit, which is intuitive in many applications. The introduction motivates the use of a penalty matrix $D$ and provides examples of problems that fit into this framework, including the fused lasso, trend filtering, wavelet smoothing, and outlier detection. The paper then derives the Lagrange dual of the generalized lasso problem, which serves as the foundation for the algorithm. The authors develop the algorithm for the case $X = I$ and then extend it to general design matrices $X$. They also discuss the conditions under which the generalized lasso problem can be transformed into a regular lasso problem. The paper concludes with a discussion of the properties of the solution path, including the primal-dual correspondence and the changes in slope of the primal solution path. The authors provide a geometric argument to prove a result on the degrees of freedom of the generalized lasso fit.