Sequential Nonparametric Regression
This work addresses the challenge of efficient regression in streaming data scenarios, which is incremental but important for real-time applications.
The authors tackled the problem of nonparametric regression with sequentially arriving data by developing a linear-time algorithm that dynamically adjusts bandwidths for each new data point, achieving the optimal minimax convergence rate, and using online expert mixing to adapt to unknown smoothness, with simulations confirming theoretical results.
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.