1,530 research outputs found
A Tutorial on Bayesian Nonparametric Models
A key problem in statistical modeling is model selection, how to choose a
model at an appropriate level of complexity. This problem appears in many
settings, most prominently in choosing the number ofclusters in mixture models
or the number of factors in factor analysis. In this tutorial we describe
Bayesian nonparametric methods, a class of methods that side-steps this issue
by allowing the data to determine the complexity of the model. This tutorial is
a high-level introduction to Bayesian nonparametric methods and contains
several examples of their application.Comment: 28 pages, 8 figure
Stochastic Variational Inference
We develop stochastic variational inference, a scalable algorithm for
approximating posterior distributions. We develop this technique for a large
class of probabilistic models and we demonstrate it with two probabilistic
topic models, latent Dirichlet allocation and the hierarchical Dirichlet
process topic model. Using stochastic variational inference, we analyze several
large collections of documents: 300K articles from Nature, 1.8M articles from
The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can
easily handle data sets of this size and outperforms traditional variational
inference, which can only handle a smaller subset. (We also show that the
Bayesian nonparametric topic model outperforms its parametric counterpart.)
Stochastic variational inference lets us apply complex Bayesian models to
massive data sets
A nonparametric Bayesian approach toward robot learning by demonstration
In the past years, many authors have considered application of machine learning methodologies to effect robot learning by demonstration. Gaussian mixture regression (GMR) is one of the most successful methodologies used for this purpose. A major limitation of GMR models concerns automatic selection of the proper number of model states, i.e., the number of model component densities. Existing methods, including likelihood- or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Under this motivation, to resolve the aforementioned issues of GMR-based methods for robot learning by demonstration, in this paper we introduce a nonparametric Bayesian formulation for the GMR model, the Dirichlet process GMR model. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally investigate its efficacy as a robot learning by demonstration methodology, considering a number of demanding robot learning by demonstration scenarios
Location Dependent Dirichlet Processes
Dirichlet processes (DP) are widely applied in Bayesian nonparametric
modeling. However, in their basic form they do not directly integrate
dependency information among data arising from space and time. In this paper,
we propose location dependent Dirichlet processes (LDDP) which incorporate
nonparametric Gaussian processes in the DP modeling framework to model such
dependencies. We develop the LDDP in the context of mixture modeling, and
develop a mean field variational inference algorithm for this mixture model.
The effectiveness of the proposed modeling framework is shown on an image
segmentation task
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