An Homotopy Algorithm for the Lasso with Online Observations
An Homotopy Algorithm for the Lasso with Online Observations
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DOI：
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发表时间：
2008-12
期刊：
影响因子：
2.1
通讯作者：
Pierre Garrigues;L. Ghaoui
中科院分区：
文献类型：
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作者：
Pierre Garrigues;L. Ghaoui
已经表明，通常被称为Lasso或Basis Pursuit DeNoising的l1惩罚最小二乘回归问题导致稀疏的解决方案，因此实现了模型选择。在本文中，我们提出了RecLasso，一个算法来解决Lasso与在线（顺序）的意见。我们引入一个优化问题，使我们能够计算从当前的解决方案的同伦的解决方案后，观察一个新的数据点。我们比较我们的方法拉尔斯和坐标下降，并提出了一个应用程序的压缩感知与顺序观察。我们的方法可以很容易地扩展到计算同伦从当前的解决方案的解决方案，对应于删除一个数据点，这导致了一个有效的算法留一交叉验证。我们还提出了一个算法，自动更新正则化参数后，观察到一个新的数据点。
It has been shown that the problem of l1-penalized least-square regression commonly referred to as the Lasso or Basis Pursuit DeNoising leads to solutions that are sparse and therefore achieves model selection. We propose in this paper RecLasso, an algorithm to solve the Lasso with online (sequential) observations. We introduce an optimization problem that allows us to compute an homotopy from the current solution to the solution after observing a new data point. We compare our method to Lars and Coordinate Descent, and present an application to compressive sensing with sequential observations. Our approach can easily be extended to compute an homotopy from the current solution to the solution that corresponds to removing a data point, which leads to an efficient algorithm for leave-one-out cross-validation. We also propose an algorithm to automatically update the regularization parameter after observing a new data point.