8,995 research outputs found
Probabilistic Meta-Representations Of Neural Networks
Existing Bayesian treatments of neural networks are typically characterized
by weak prior and approximate posterior distributions according to which all
the weights are drawn independently. Here, we consider a richer prior
distribution in which units in the network are represented by latent variables,
and the weights between units are drawn conditionally on the values of the
collection of those variables. This allows rich correlations between related
weights, and can be seen as realizing a function prior with a Bayesian
complexity regularizer ensuring simple solutions. We illustrate the resulting
meta-representations and representations, elucidating the power of this prior.Comment: presented at UAI 2018 Uncertainty In Deep Learning Workshop (UDL AUG.
2018
Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples
We examine some differential geometric approaches to finding approximate
solutions to the continuous time nonlinear filtering problem. Our primary focus
is a new projection method for the optimal filter infinite dimensional
Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric
and on a family of normal mixtures. We compare this method to earlier
projection methods based on the Hellinger distance/Fisher metric and
exponential families, and we compare the L2 mixture projection filter with a
particle method with the same number of parameters, using the Levy metric. We
prove that for a simple choice of the mixture manifold the L2 mixture
projection filter coincides with a Galerkin method, whereas for more general
mixture manifolds the equivalence does not hold and the L2 mixture filter is
more general. We study particular systems that may illustrate the advantages of
this new filter over other algorithms when comparing outputs with the optimal
filter. We finally consider a specific software design that is suited for a
numerically efficient implementation of this filter and provide numerical
examples.Comment: Updated and expanded version published in the Journal reference
below. Preprint updates: January 2016 (v3) added projection of Zakai Equation
and difference with projection of Kushner-Stratonovich (section 4.1). August
2014 (v2) added Galerkin equivalence proof (Section 5) to the March 2013 (v1)
versio
- …