We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is dynamically changing. We propose a linear time algorithm that adjusts the bandwidth for each new data point, and show that the estimator achieves the optimal minimax rate of convergence. We also propose the use of online expert mixing algorithms to adapt to unknown smoothness of the regression function. We provide simulations that confirm the theoretical results, and demonstrate the effectiveness of the methods.
- Pub Date:
- June 2012
- Statistics - Methodology;
- Astrophysics - Instrumentation and Methods for Astrophysics;
- Computer Science - Machine Learning
- Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)