End-to-End Learning of Gaussian Mixture Proposals Using Differentiable Particle Filters and Neural Networks

We introduce a new method, named PropMixNN, that uses a neural network to learn the proposal distribution of a particle filter. The optimal proposal distribution is approximated as a multivariate Gaussian mixture, so the proposed method aims at learning the means and covariance matrices of the S components that characterise the mixture. This unsupervised method is trained to target the log-likelihood, which does not require knowledge of the hidden state. The performance of the method is assessed in a stochastic Lorenz 96 model, which presents a non-linear chaotic behaviour. The proposed method reduces estimation errors in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.