1,161 research outputs found
Scaling Nonparametric Bayesian Inference via Subsample-Annealing
We describe an adaptation of the simulated annealing algorithm to
nonparametric clustering and related probabilistic models. This new algorithm
learns nonparametric latent structure over a growing and constantly churning
subsample of training data, where the portion of data subsampled can be
interpreted as the inverse temperature beta(t) in an annealing schedule. Gibbs
sampling at high temperature (i.e., with a very small subsample) can more
quickly explore sketches of the final latent state by (a) making longer jumps
around latent space (as in block Gibbs) and (b) lowering energy barriers (as in
simulated annealing). We prove subsample annealing speeds up mixing time N^2 ->
N in a simple clustering model and exp(N) -> N in another class of models,
where N is data size. Empirically subsample-annealing outperforms naive Gibbs
sampling in accuracy-per-wallclock time, and can scale to larger datasets and
deeper hierarchical models. We demonstrate improved inference on million-row
subsamples of US Census data and network log data and a 307-row hospital rating
dataset, using a Pitman-Yor generalization of the Cross Categorization model.Comment: To appear in AISTATS 201
Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference
The problem of modulation classification for a multiple-antenna (MIMO) system
employing orthogonal frequency division multiplexing (OFDM) is investigated
under the assumption of unknown frequency-selective fading channels and
signal-to-noise ratio (SNR). The classification problem is formulated as a
Bayesian inference task, and solutions are proposed based on Gibbs sampling and
mean field variational inference. The proposed methods rely on a selection of
the prior distributions that adopts a latent Dirichlet model for the modulation
type and on the Bayesian network formalism. The Gibbs sampling method converges
to the optimal Bayesian solution and, using numerical results, its accuracy is
seen to improve for small sample sizes when switching to the mean field
variational inference technique after a number of iterations. The speed of
convergence is shown to improve via annealing and random restarts. While most
of the literature on modulation classification assume that the channels are
flat fading, that the number of receive antennas is no less than that of
transmit antennas, and that a large number of observed data symbols are
available, the proposed methods perform well under more general conditions.
Finally, the proposed Bayesian methods are demonstrated to improve over
existing non-Bayesian approaches based on independent component analysis and on
prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog
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
Monte Carlo likelihood inference for missing data models
We describe a Monte Carlo method to approximate the maximum likelihood
estimate (MLE), when there are missing data and the observed data likelihood is
not available in closed form. This method uses simulated missing data that are
independent and identically distributed and independent of the observed data.
Our Monte Carlo approximation to the MLE is a consistent and asymptotically
normal estimate of the minimizer of the Kullback--Leibler
information, as both Monte Carlo and observed data sample sizes go to infinity
simultaneously. Plug-in estimates of the asymptotic variance are provided for
constructing confidence regions for . We give Logit--Normal
generalized linear mixed model examples, calculated using an R package.Comment: Published at http://dx.doi.org/10.1214/009053606000001389 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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