Universal Switching Linear Least Squares Prediction

We consider sequential regression of individual sequences under the square error loss. Using a competitive algorithm framework, we construct a sequential algorithm that can achieve the performance of the best piecewise (in time) linear regression algorithm tuned to the underlying individual sequence. The sequential algorithm we construct does not need the data length, number of piecewise linear regions, or the locations of the transition times, however, it can asymptotically achieve the performance of the best piecewise (in time) linear regressor that can choose number of segments, duration of these segments and best regressor in each segment, based on observation of the whole sequence in advance. We use a transition diagram similar to that of [Willems '96] to effectively combine an exponential number of competing algorithms, with a complexity that is only linear in the data length. We demonstrate that the regret of this approach is at most O(4 ln(n)) per transition for not knowin...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Suleyman Serdar Kozat, Andrew C. Singer
• Keywords: Algorithms, Linear, Sequential Algorithm, TSP 2008