5,602 research outputs found
Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior
In recent years a number of methods have been developed for automatically
learning the (sparse) connectivity structure of Markov Random Fields. These
methods are mostly based on L1-regularized optimization which has a number of
disadvantages such as the inability to assess model uncertainty and expensive
cross-validation to find the optimal regularization parameter. Moreover, the
model's predictive performance may degrade dramatically with a suboptimal value
of the regularization parameter (which is sometimes desirable to induce
sparseness). We propose a fully Bayesian approach based on a "spike and slab"
prior (similar to L0 regularization) that does not suffer from these
shortcomings. We develop an approximate MCMC method combining Langevin dynamics
and reversible jump MCMC to conduct inference in this model. Experiments show
that the proposed model learns a good combination of the structure and
parameter values without the need for separate hyper-parameter tuning.
Moreover, the model's predictive performance is much more robust than L1-based
methods with hyper-parameter settings that induce highly sparse model
structures.Comment: Accepted in the Conference on Uncertainty in Artificial Intelligence
(UAI), 201
Monte Carlo Algorithms for the Partition Function and Information Rates of Two-Dimensional Channels
The paper proposes Monte Carlo algorithms for the computation of the
information rate of two-dimensional source/channel models. The focus of the
paper is on binary-input channels with constraints on the allowed input
configurations. The problem of numerically computing the information rate, and
even the noiseless capacity, of such channels has so far remained largely
unsolved. Both problems can be reduced to computing a Monte Carlo estimate of a
partition function. The proposed algorithms use tree-based Gibbs sampling and
multilayer (multitemperature) importance sampling. The viability of the
proposed algorithms is demonstrated by simulation results
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
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