Kernel Density Estimation by Stagewise Algorithm with a Simple Dictionary
This work addresses density estimation for data analysis, but it appears incremental as it builds on existing kernel methods with algorithmic improvements.
The authors tackled multivariate kernel density estimation by proposing a stagewise minimization algorithm using U-divergence and a simple dictionary, resulting in a sparse estimator with data-adaptive parameters that performs competitively or better than other methods in simulations.
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and realizes a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of estimator obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs competitive to or sometime better than other well-known density estimators.