1,396 research outputs found
Particle Gibbs Split-Merge Sampling for Bayesian Inference in Mixture Models
This paper presents a new Markov chain Monte Carlo method to sample from the
posterior distribution of conjugate mixture models. This algorithm relies on a
flexible split-merge procedure built using the particle Gibbs sampler. Contrary
to available split-merge procedures, the resulting so-called Particle Gibbs
Split-Merge sampler does not require the computation of a complex acceptance
ratio, is simple to implement using existing sequential Monte Carlo libraries
and can be parallelized. We investigate its performance experimentally on
synthetic problems as well as on geolocation and cancer genomics data. In all
these examples, the particle Gibbs split-merge sampler outperforms
state-of-the-art split-merge methods by up to an order of magnitude for a fixed
computational complexity
A sticky HDP-HMM with application to speaker diarization
We consider the problem of speaker diarization, the problem of segmenting an
audio recording of a meeting into temporal segments corresponding to individual
speakers. The problem is rendered particularly difficult by the fact that we
are not allowed to assume knowledge of the number of people participating in
the meeting. To address this problem, we take a Bayesian nonparametric approach
to speaker diarization that builds on the hierarchical Dirichlet process hidden
Markov model (HDP-HMM) of Teh et al. [J. Amer. Statist. Assoc. 101 (2006)
1566--1581]. Although the basic HDP-HMM tends to over-segment the audio
data---creating redundant states and rapidly switching among them---we describe
an augmented HDP-HMM that provides effective control over the switching rate.
We also show that this augmentation makes it possible to treat emission
distributions nonparametrically. To scale the resulting architecture to
realistic diarization problems, we develop a sampling algorithm that employs a
truncated approximation of the Dirichlet process to jointly resample the full
state sequence, greatly improving mixing rates. Working with a benchmark NIST
data set, we show that our Bayesian nonparametric architecture yields
state-of-the-art speaker diarization results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS395 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation
We present a discriminative nonparametric latent feature relational model
(LFRM) for link prediction to automatically infer the dimensionality of latent
features. Under the generic RegBayes (regularized Bayesian inference)
framework, we handily incorporate the prediction loss with probabilistic
inference of a Bayesian model; set distinct regularization parameters for
different types of links to handle the imbalance issue in real networks; and
unify the analysis of both the smooth logistic log-loss and the piecewise
linear hinge loss. For the nonconjugate posterior inference, we present a
simple Gibbs sampler via data augmentation, without making restricting
assumptions as done in variational methods. We further develop an approximate
sampler using stochastic gradient Langevin dynamics to handle large networks
with hundreds of thousands of entities and millions of links, orders of
magnitude larger than what existing LFRM models can process. Extensive studies
on various real networks show promising performance.Comment: Accepted by AAAI 201
Bayesian Nonparametric Hidden Semi-Markov Models
There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous
Hidden Markov Model for learning from sequential and time-series data. However,
in many settings the HDP-HMM's strict Markovian constraints are undesirable,
particularly if we wish to learn or encode non-geometric state durations. We
can extend the HDP-HMM to capture such structure by drawing upon
explicit-duration semi-Markovianity, which has been developed mainly in the
parametric frequentist setting, to allow construction of highly interpretable
models that admit natural prior information on state durations.
In this paper we introduce the explicit-duration Hierarchical Dirichlet
Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for
efficient posterior inference. The methods we introduce also provide new
methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs
sampling methods can be embedded in samplers for larger hierarchical Bayesian
models, adding semi-Markov chain modeling as another tool in the Bayesian
inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference
methods on both synthetic and real experiments
Data augmentation for models based on rejection sampling
We present a data augmentation scheme to perform Markov chain Monte Carlo
inference for models where data generation involves a rejection sampling
algorithm. Our idea, which seems to be missing in the literature, is a simple
scheme to instantiate the rejected proposals preceding each data point. The
resulting joint probability over observed and rejected variables can be much
simpler than the marginal distribution over the observed variables, which often
involves intractable integrals. We consider three problems, the first being the
modeling of flow-cytometry measurements subject to truncation. The second is a
Bayesian analysis of the matrix Langevin distribution on the Stiefel manifold,
and the third, Bayesian inference for a nonparametric Gaussian process density
model. The latter two are instances of problems where Markov chain Monte Carlo
inference is doubly-intractable. Our experiments demonstrate superior
performance over state-of-the-art sampling algorithms for such problems.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1311.090
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