1,768 research outputs found
Poisson Multi-Bernoulli Mapping Using Gibbs Sampling
This paper addresses the mapping problem. Using a conjugate prior form, we
derive the exact theoretical batch multi-object posterior density of the map
given a set of measurements. The landmarks in the map are modeled as extended
objects, and the measurements are described as a Poisson process, conditioned
on the map. We use a Poisson process prior on the map and prove that the
posterior distribution is a hybrid Poisson, multi-Bernoulli mixture
distribution. We devise a Gibbs sampling algorithm to sample from the batch
multi-object posterior. The proposed method can handle uncertainties in the
data associations and the cardinality of the set of landmarks, and is
parallelizable, making it suitable for large-scale problems. The performance of
the proposed method is evaluated on synthetic data and is shown to outperform a
state-of-the-art method.Comment: 14 pages, 6 figure
A unifying representation for a class of dependent random measures
We present a general construction for dependent random measures based on
thinning Poisson processes on an augmented space. The framework is not
restricted to dependent versions of a specific nonparametric model, but can be
applied to all models that can be represented using completely random measures.
Several existing dependent random measures can be seen as specific cases of
this framework. Interesting properties of the resulting measures are derived
and the efficacy of the framework is demonstrated by constructing a
covariate-dependent latent feature model and topic model that obtain superior
predictive performance
Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes
We define a family of probability distributions for random count matrices
with a potentially unbounded number of rows and columns. The three
distributions we consider are derived from the gamma-Poisson, gamma-negative
binomial, and beta-negative binomial processes. Because the models lead to
closed-form Gibbs sampling update equations, they are natural candidates for
nonparametric Bayesian priors over count matrices. A key aspect of our analysis
is the recognition that, although the random count matrices within the family
are defined by a row-wise construction, their columns can be shown to be i.i.d.
This fact is used to derive explicit formulas for drawing all the columns at
once. Moreover, by analyzing these matrices' combinatorial structure, we
describe how to sequentially construct a column-i.i.d. random count matrix one
row at a time, and derive the predictive distribution of a new row count vector
with previously unseen features. We describe the similarities and differences
between the three priors, and argue that the greater flexibility of the gamma-
and beta- negative binomial processes, especially their ability to model
over-dispersed, heavy-tailed count data, makes these well suited to a wide
variety of real-world applications. As an example of our framework, we
construct a naive-Bayes text classifier to categorize a count vector to one of
several existing random count matrices of different categories. The classifier
supports an unbounded number of features, and unlike most existing methods, it
does not require a predefined finite vocabulary to be shared by all the
categories, and needs neither feature selection nor parameter tuning. Both the
gamma- and beta- negative binomial processes are shown to significantly
outperform the gamma-Poisson process for document categorization, with
comparable performance to other state-of-the-art supervised text classification
algorithms.Comment: To appear in Journal of the American Statistical Association (Theory
and Methods). 31 pages + 11 page supplement, 5 figure
On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering
We analyse the exponential stability properties of a class of measure-valued
equations arising in nonlinear multi-target filtering problems. We also prove
the uniform convergence properties w.r.t. the time parameter of a rather
general class of stochastic filtering algorithms, including sequential Monte
Carlo type models and mean eld particle interpretation models. We illustrate
these results in the context of the Bernoulli and the Probability Hypothesis
Density filter, yielding what seems to be the first results of this kind in
this subject
Modeling Infection with Multi-agent Dynamics
Developing the ability to comprehensively study infections in small
populations enables us to improve epidemic models and better advise individuals
about potential risks to their health. We currently have a limited
understanding of how infections spread within a small population because it has
been difficult to closely track an infection within a complete community. The
paper presents data closely tracking the spread of an infection centered on a
student dormitory, collected by leveraging the residents' use of cellular
phones. The data are based on daily symptom surveys taken over a period of four
months and proximity tracking through cellular phones. We demonstrate that
using a Bayesian, discrete-time multi-agent model of infection to model
real-world symptom reports and proximity tracking records gives us important
insights about infec-tions in small populations
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