The Ensemble Epanechnikov Mixture Filter
This work addresses the problem of high-dimensional density estimation for researchers in statistics and machine learning, offering a practical and cost-efficient alternative to Gaussian methods, though it appears incremental as it builds on existing kernel and filtering frameworks.
The paper tackled the suboptimality of Gaussian mixture kernel density estimates in high-dimensional settings by proposing the ensemble Epanechnikov mixture filter (EnEMF), which uses the optimal multivariate Epanechnikov kernel for sequential filtering, resulting in a significant reduction in error per particle on the 40-variable Lorenz '96 system.
In the high-dimensional setting, Gaussian mixture kernel density estimates become increasingly suboptimal. In this work we aim to show that it is practical to instead use the optimal multivariate Epanechnikov kernel. We make use of this optimal Epanechnikov mixture kernel density estimate for the sequential filtering scenario through what we term the ensemble Epanechnikov mixture filter (EnEMF). We provide a practical implementation of the EnEMF that is as cost efficient as the comparable ensemble Gaussian mixture filter. We show on a static example that the EnEMF is robust to growth in dimension, and also that the EnEMF has a significant reduction in error per particle on the 40-variable Lorenz '96 system.