Multivariate Online Kernel Density Estimation

We propose an approach for online kernel density estimation (KDE) which enables building probability density functions from data by observing only a single data-point at a time. The method maintains a non-parametric model of the data itself and uses this model to calculate the corresponding KDE. We propose an new automatic bandwidth selection rule, which can be computed directly from the non-parametric model of the data. Low complexity of the model is maintained through a novel compression and refinement scheme. We compare the online KDE to some state-of-the-art batch KDEs on examples of estimating distributions and on an example of classification. The results show that the online KDE generally achieves comparable performance to the batch approaches, while producing models with lower complexity and allowing online updating using only a single observation at a time.