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This paper introduces the kernel mixture network, a new method fornonparametric estimation of conditional probability densities using neuralnetworks. We model arbitrarily complex conditional densities as linearcombinations of a family of kernel functions centered at a subset of trainingpoints. The weights are determined by the outer layer of a deep neural network,trained by minimizing the negative log likelihood. This generalizes the popularquantized softmax approach, which can be seen as a kernel mixture network withsquare and non-overlapping kernels. We test the performance of our method ontwo important applications, namely Bayesian filtering and generative modeling.In the Bayesian filtering example, we show that the method can be used tofilter complex nonlinear and non-Gaussian signals defined on manifolds. Theresulting kernel mixture network filter outperforms both the quantized softmaxfilter and the extended Kalman filter in terms of model likelihood. Finally,our experiments on generative models show that, given the same architecture,the kernel mixture network leads to higher test set likelihood, lessoverfitting and more diversified and realistic generated samples than thequantized softmax approach.

The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables