6,600 research outputs found
Dynamic density estimation with diffusive Dirichlet mixtures
We introduce a new class of nonparametric prior distributions on the space of
continuously varying densities, induced by Dirichlet process mixtures which
diffuse in time. These select time-indexed random functions without jumps,
whose sections are continuous or discrete distributions depending on the choice
of kernel. The construction exploits the widely used stick-breaking
representation of the Dirichlet process and induces the time dependence by
replacing the stick-breaking components with one-dimensional Wright-Fisher
diffusions. These features combine appealing properties of the model, inherited
from the Wright-Fisher diffusions and the Dirichlet mixture structure, with
great flexibility and tractability for posterior computation. The construction
can be easily extended to multi-parameter GEM marginal states, which include,
for example, the Pitman--Yor process. A full inferential strategy is detailed
and illustrated on simulated and real data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ681 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture
This paper presents a novel algorithm, based upon the dependent Dirichlet
process mixture model (DDPMM), for clustering batch-sequential data containing
an unknown number of evolving clusters. The algorithm is derived via a
low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM,
and provides a hard clustering with convergence guarantees similar to those of
the k-means algorithm. Empirical results from a synthetic test with moving
Gaussian clusters and a test with real ADS-B aircraft trajectory data
demonstrate that the algorithm requires orders of magnitude less computational
time than contemporary probabilistic and hard clustering algorithms, while
providing higher accuracy on the examined datasets.Comment: This paper is from NIPS 2013. Please use the following BibTeX
citation: @inproceedings{Campbell13_NIPS, Author = {Trevor Campbell and Miao
Liu and Brian Kulis and Jonathan P. How and Lawrence Carin}, Title = {Dynamic
Clustering via Asymptotics of the Dependent Dirichlet Process}, Booktitle =
{Advances in Neural Information Processing Systems (NIPS)}, Year = {2013}
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