31,262 research outputs found
Summary Statistics for Partitionings and Feature Allocations
Infinite mixture models are commonly used for clustering. One can sample from
the posterior of mixture assignments by Monte Carlo methods or find its maximum
a posteriori solution by optimization. However, in some problems the posterior
is diffuse and it is hard to interpret the sampled partitionings. In this
paper, we introduce novel statistics based on block sizes for representing
sample sets of partitionings and feature allocations. We develop an
element-based definition of entropy to quantify segmentation among their
elements. Then we propose a simple algorithm called entropy agglomeration (EA)
to summarize and visualize this information. Experiments on various infinite
mixture posteriors as well as a feature allocation dataset demonstrate that the
proposed statistics are useful in practice.Comment: Accepted to NIPS 2013:
https://nips.cc/Conferences/2013/Program/event.php?ID=376
Partial Identification in Matching Models for the Marriage Market
We study partial identification of the preference parameters in models of
one-to-one matching with perfectly transferable utilities, without imposing
parametric distributional restrictions on the unobserved heterogeneity and with
data on one large market. We provide a tractable characterisation of the
identified set, under various classes of nonparametric distributional
assumptions on the unobserved heterogeneity. Using our methodology, we
re-examine some of the relevant questions in the empirical literature on the
marriage market which have been previously studied under the Multinomial Logit
assumption
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