An efficient algorithm for a class of fused lasso problems
An efficient algorithm for a class of fused lasso problems
复制标题
DOI：
10.1145/1835804.1835847
复制
发表时间：
2010-07
期刊：
影响因子：
--
通讯作者：
Jun Liu;Lei Yuan;Jieping Ye
中科院分区：
文献类型：
--
作者：
Jun Liu;Lei Yuan;Jieping Ye
融合的Lasso惩罚在系数和它们的连续差中强制稀疏性，这对于以某种有意义的方式排序的特征的应用是理想的。然而，由此产生的问题是具有挑战性的解决，因为融合的Lasso惩罚是非光滑和不可分离的。现有的算法具有高的计算复杂度，不扩展到大规模的问题。在本文中，我们提出了一个有效的融合套索算法（EFLA）优化这类问题。EFLA中的一个关键构建块是融合Lasso信号近似器（FLSA）。为了有效地解决FLSA，我们建议重新制定它的问题，找到一个“适当的”次梯度的融合罚款在最小值，并开发一个次梯度发现算法（SFA）。我们进一步设计了一个重新启动技术，以加快收敛的SFA，利用特殊的“结构”的原始和重新FLSA问题。我们的实证评估表明，SFA和EFLA显着优于现有的解决方案。我们还演示了融合的套索的几个应用程序。
The fused Lasso penalty enforces sparsity in both the coefficients and their successive differences, which is desirable for applications with features ordered in some meaningful way. The resulting problem is, however, challenging to solve, as the fused Lasso penalty is both non-smooth and non-separable. Existing algorithms have high computational complexity and do not scale to large-size problems. In this paper, we propose an Efficient Fused Lasso Algorithm (EFLA) for optimizing this class of problems. One key building block in the proposed EFLA is the Fused Lasso Signal Approximator (FLSA). To efficiently solve FLSA, we propose to reformulate it as the problem of finding an "appropriate" subgradient of the fused penalty at the minimizer, and develop a Subgradient Finding Algorithm (SFA). We further design a restart technique to accelerate the convergence of SFA, by exploiting the special "structures" of both the original and the reformulated FLSA problems. Our empirical evaluations show that, both SFA and EFLA significantly outperform existing solvers. We also demonstrate several applications of the fused Lasso.