8,500 research outputs found
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
Strategies for online inference of model-based clustering in large and growing networks
In this paper we adapt online estimation strategies to perform model-based
clustering on large networks. Our work focuses on two algorithms, the first
based on the SAEM algorithm, and the second on variational methods. These two
strategies are compared with existing approaches on simulated and real data. We
use the method to decipher the connexion structure of the political websphere
during the US political campaign in 2008. We show that our online EM-based
algorithms offer a good trade-off between precision and speed, when estimating
parameters for mixture distributions in the context of random graphs.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS359 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Message-Passing Inference on a Factor Graph for Collaborative Filtering
This paper introduces a novel message-passing (MP) framework for the
collaborative filtering (CF) problem associated with recommender systems. We
model the movie-rating prediction problem popularized by the Netflix Prize,
using a probabilistic factor graph model and study the model by deriving
generalization error bounds in terms of the training error. Based on the model,
we develop a new MP algorithm, termed IMP, for learning the model. To show
superiority of the IMP algorithm, we compare it with the closely related
expectation-maximization (EM) based algorithm and a number of other matrix
completion algorithms. Our simulation results on Netflix data show that, while
the methods perform similarly with large amounts of data, the IMP algorithm is
superior for small amounts of data. This improves the cold-start problem of the
CF systems in practice. Another advantage of the IMP algorithm is that it can
be analyzed using the technique of density evolution (DE) that was originally
developed for MP decoding of error-correcting codes
Regularized Wasserstein Means for Aligning Distributional Data
We propose to align distributional data from the perspective of Wasserstein
means. We raise the problem of regularizing Wasserstein means and propose
several terms tailored to tackle different problems. Our formulation is based
on the variational transportation to distribute a sparse discrete measure into
the target domain. The resulting sparse representation well captures the
desired property of the domain while reducing the mapping cost. We demonstrate
the scalability and robustness of our method with examples in domain
adaptation, point set registration, and skeleton layout
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