Multivariate online kernel density estimation with Gaussian kernels

We propose a novel approach to online estimation of probability density functions, which is based on kernel density estimation (KDE). The method maintains and updates a non-parametric model of the observed data, from which the KDE can be calculated. We propose an online bandwidth estimation approach and a compression/revitalization scheme which maintains the KDE's complexity low. We compare the proposed online KDE to the state-of-the-art approaches on examples of estimating stationary and non-stationary distributions, and on examples of classification. The results show that the online KDE outperforms or achieves a comparable performance to the state-of-the-art and produces models with a significantly lower complexity while allowing online adaptation.

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► We propose a solution for online estimation of probability density functions.
► We extend the batch kernel density estimators (KDE) to online KDEs (oKDE).
► oKDE's complexity scales sublinearly with the number of samples.
► oKDE outperforms batch KDEs in non-stationary distribution estimation.
► oKDE achieves comparable classification performance to a batch SVM.