151 research outputs found
Epitope profiling via mixture modeling of ranked data
We propose the use of probability models for ranked data as a useful
alternative to a quantitative data analysis to investigate the outcome of
bioassay experiments, when the preliminary choice of an appropriate
normalization method for the raw numerical responses is difficult or subject to
criticism. We review standard distance-based and multistage ranking models and
in this last context we propose an original generalization of the Plackett-Luce
model to account for the order of the ranking elicitation process. The
usefulness of the novel model is illustrated with its maximum likelihood
estimation for a real data set. Specifically, we address the heterogeneous
nature of experimental units via model-based clustering and detail the
necessary steps for a successful likelihood maximization through a hybrid
version of the Expectation-Maximization algorithm. The performance of the
mixture model using the new distribution as mixture components is compared with
those relative to alternative mixture models for random rankings. A discussion
on the interpretation of the identified clusters and a comparison with more
standard quantitative approaches are finally provided.Comment: (revised to properly include references
A review on Estimation of Distribution Algorithms in Permutation-based Combinatorial Optimization Problems
Estimation of Distribution Algorithms (EDAs) are a set of algorithms
that belong to the field of Evolutionary Computation. Characterized by the use of
probabilistic models to represent the solutions and the dependencies between the
variables of the problem, these algorithms have been applied to a wide set of academic
and real-world optimization problems, achieving competitive results in most
scenarios. Nevertheless, there are some optimization problems, whose solutions can
be naturally represented as permutations, for which EDAs have not been extensively
developed. Although some work has been carried out in this direction, most
of the approaches are adaptations of EDAs designed for problems based on integer
or real domains, and only a few algorithms have been specifically designed to
deal with permutation-based problems. In order to set the basis for a development
of EDAs in permutation-based problems similar to that which occurred in other
optimization fields (integer and real-value problems), in this paper we carry out a
thorough review of state-of-the-art EDAs applied to permutation-based problems.
Furthermore, we provide some ideas on probabilistic modeling over permutation
spaces that could inspire the researchers of EDAs to design new approaches for
these kinds of problems
Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes
In this paper we propose a Bayesian nonparametric model for clustering
partial ranking data. We start by developing a Bayesian nonparametric extension
of the popular Plackett-Luce choice model that can handle an infinite number of
choice items. Our framework is based on the theory of random atomic measures,
with the prior specified by a completely random measure. We characterise the
posterior distribution given data, and derive a simple and effective Gibbs
sampler for posterior simulation. We then develop a Dirichlet process mixture
extension of our model and apply it to investigate the clustering of
preferences for college degree programmes amongst Irish secondary school
graduates. The existence of clusters of applicants who have similar preferences
for degree programmes is established and we determine that subject matter and
geographical location of the third level institution characterise these
clusters.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS717 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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