Authors:
Torpong Nitayanont
;
Cheng Lu
and
Dorit Hochbaum
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA, U.S.A.
Keyword(s):
Fused Lasso, Path of Solutions, Minimum Cut, Hyperparameter Selection, Signal Processing.
Abstract:
In a fused lasso problem on sequential data, the objective consists of two competing terms: the fidelity term and the regularization term. The two terms are often balanced with a tradeoff parameter, the value of which affects the solution, yet the extent of the effect is not a priori known. To address this, there is an interest in generating the path of solutions which maps values of this parameter to a solution. Even though there are infinite values of the parameter, we show that for the fused lasso problem with convex piecewise linear fidelity functions, the number of different solutions is bounded by n 2 q where n is the number of variables and q is the number of breakpoints in the fidelity functions. Our path of solutions algorithm, PoS, is based on an efficient minimum cut technique. We compare our PoS algorithm with a state-of-the-art solver, Gurobi, on synthetic data. The results show that PoS generates all solutions whereas Gurobi identifies less than 22% of the number of sol
utions, on comparable running time. Even allowing for hundreds of times factor increase in time limit, compared with PoS, Gurobi still cannot generate all the solutions.
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