11,493 research outputs found
Probabilistic Latent Tensor Factorization Model for Link Pattern Prediction in Multi-relational Networks
This paper aims at the problem of link pattern prediction in collections of
objects connected by multiple relation types, where each type may play a
distinct role. While common link analysis models are limited to single-type
link prediction, we attempt here to capture the correlations among different
relation types and reveal the impact of various relation types on performance
quality. For that, we define the overall relations between object pairs as a
\textit{link pattern} which consists in interaction pattern and connection
structure in the network, and then use tensor formalization to jointly model
and predict the link patterns, which we refer to as \textit{Link Pattern
Prediction} (LPP) problem. To address the issue, we propose a Probabilistic
Latent Tensor Factorization (PLTF) model by introducing another latent factor
for multiple relation types and furnish the Hierarchical Bayesian treatment of
the proposed probabilistic model to avoid overfitting for solving the LPP
problem. To learn the proposed model we develop an efficient Markov Chain Monte
Carlo sampling method. Extensive experiments are conducted on several real
world datasets and demonstrate significant improvements over several existing
state-of-the-art methods.Comment: 19pages, 5 figure
Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes
Probabilistic matrix factorization (PMF) is a powerful method for modeling
data associated with pairwise relationships, finding use in collaborative
filtering, computational biology, and document analysis, among other areas. In
many domains, there is additional information that can assist in prediction.
For example, when modeling movie ratings, we might know when the rating
occurred, where the user lives, or what actors appear in the movie. It is
difficult, however, to incorporate this side information into the PMF model. We
propose a framework for incorporating side information by coupling together
multiple PMF problems via Gaussian process priors. We replace scalar latent
features with functions that vary over the space of side information. The GP
priors on these functions require them to vary smoothly and share information.
We successfully use this new method to predict the scores of professional
basketball games, where side information about the venue and date of the game
are relevant for the outcome.Comment: 18 pages, 4 figures, Submitted to UAI 201
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis
Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.Comment: 49 pages including appendi
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