András Fülöp

Nicolas Chopin, Andras Fulop, Jeremy Heng et al.

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.

Dóra Babicz, Soma Kontár, Márk Pető et al.

The pooling operation is a cornerstone element of convolutional neural networks. These elements generate receptive fields for neurons, in which local perturbations should have minimal effect on the output activations, increasing robustness and invariance of the network. In this paper we will present an altered version of the most commonly applied method, maximum pooling, where pooling in theory is substituted by a continuous time differential equation, which generates a location sensitive pooling operation, more similar to biological receptive fields. We will present how this continuous method can be approximated numerically using discrete operations which fit ideally on a GPU. In our approach the kernel size is substituted by diffusion strength which is a continuous valued parameter, this way it can be optimized by gradient descent algorithms. We will evaluate the effect of continuous pooling on accuracy and computational need using commonly applied network architectures and datasets.