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2008

An Homotopy Algorithm for the Lasso with Online Observations

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An Homotopy Algorithm for the Lasso with Online Observations
It has been shown that the problem of 1-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.
Pierre Garrigues, Laurent El Ghaoui
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Pierre Garrigues, Laurent El Ghaoui
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