# Path of Solutions for Fused Lasso Problems

### Torpong Nitayanont, Cheng Lu, Dorit Hochbaum

#### 2024

#### 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 solutions, 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.

Download#### Paper Citation

#### in Harvard Style

Nitayanont T., Lu C. and Hochbaum D. (2024). **Path of Solutions for Fused Lasso Problems**. In *Proceedings of the 13th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM*; ISBN 978-989-758-684-2, SciTePress, pages 107-118. DOI: 10.5220/0012433200003654

#### in Bibtex Style

@conference{icpram24,

author={Torpong Nitayanont and Cheng Lu and Dorit Hochbaum},

title={Path of Solutions for Fused Lasso Problems},

booktitle={Proceedings of the 13th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM},

year={2024},

pages={107-118},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012433200003654},

isbn={978-989-758-684-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM

TI - Path of Solutions for Fused Lasso Problems

SN - 978-989-758-684-2

AU - Nitayanont T.

AU - Lu C.

AU - Hochbaum D.

PY - 2024

SP - 107

EP - 118

DO - 10.5220/0012433200003654

PB - SciTePress