5,654 research outputs found
Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks
Undirected graphical models are widely used in statistics, physics and
machine vision. However Bayesian parameter estimation for undirected models is
extremely challenging, since evaluation of the posterior typically involves the
calculation of an intractable normalising constant. This problem has received
much attention, but very little of this has focussed on the important practical
case where the data consists of noisy or incomplete observations of the
underlying hidden structure. This paper specifically addresses this problem,
comparing two alternative methodologies. In the first of these approaches
particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently
explore the parameter space, combined with the exchange algorithm (Murray et
al., 2006) for avoiding the calculation of the intractable normalising constant
(a proof showing that this combination targets the correct distribution in
found in a supplementary appendix online). This approach is compared with
approximate Bayesian computation (Pritchard et al., 1999). Applications to
estimating the parameters of Ising models and exponential random graphs from
noisy data are presented. Each algorithm used in the paper targets an
approximation to the true posterior due to the use of MCMC to simulate from the
latent graphical model, in lieu of being able to do this exactly in general.
The supplementary appendix also describes the nature of the resulting
approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and
Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm
Copula-like Variational Inference
This paper considers a new family of variational distributions motivated by
Sklar's theorem. This family is based on new copula-like densities on the
hypercube with non-uniform marginals which can be sampled efficiently, i.e.
with a complexity linear in the dimension of state space. Then, the proposed
variational densities that we suggest can be seen as arising from these
copula-like densities used as base distributions on the hypercube with Gaussian
quantile functions and sparse rotation matrices as normalizing flows. The
latter correspond to a rotation of the marginals with complexity . We provide some empirical evidence that such a variational family can
also approximate non-Gaussian posteriors and can be beneficial compared to
Gaussian approximations. Our method performs largely comparably to
state-of-the-art variational approximations on standard regression and
classification benchmarks for Bayesian Neural Networks.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS
2019), Vancouver, Canad
- …