23,098 research outputs found
Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena
Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is
further complicated by many theoretical issues, such as the I-equivalence among
different structures. In this work, we focus on a specific subclass of BNs,
named Suppes-Bayes Causal Networks (SBCNs), which include specific structural
constraints based on Suppes' probabilistic causation to efficiently model
cumulative phenomena. Here we compare the performance, via extensive
simulations, of various state-of-the-art search strategies, such as local
search techniques and Genetic Algorithms, as well as of distinct regularization
methods. The assessment is performed on a large number of simulated datasets
from topologies with distinct levels of complexity, various sample size and
different rates of errors in the data. Among the main results, we show that the
introduction of Suppes' constraints dramatically improve the inference
accuracy, by reducing the solution space and providing a temporal ordering on
the variables. We also report on trade-offs among different search techniques
that can be efficiently employed in distinct experimental settings. This
manuscript is an extended version of the paper "Structural Learning of
Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018
International Conference on Computational Science
Network inference and community detection, based on covariance matrices, correlations and test statistics from arbitrary distributions
In this paper we propose methodology for inference of binary-valued adjacency
matrices from various measures of the strength of association between pairs of
network nodes, or more generally pairs of variables. This strength of
association can be quantified by sample covariance and correlation matrices,
and more generally by test-statistics and hypothesis test p-values from
arbitrary distributions. Community detection methods such as block modelling
typically require binary-valued adjacency matrices as a starting point. Hence,
a main motivation for the methodology we propose is to obtain binary-valued
adjacency matrices from such pairwise measures of strength of association
between variables. The proposed methodology is applicable to large
high-dimensional data-sets and is based on computationally efficient
algorithms. We illustrate its utility in a range of contexts and data-sets
The Infinite Hierarchical Factor Regression Model
We propose a nonparametric Bayesian factor regression model that accounts for
uncertainty in the number of factors, and the relationship between factors. To
accomplish this, we propose a sparse variant of the Indian Buffet Process and
couple this with a hierarchical model over factors, based on Kingman's
coalescent. We apply this model to two problems (factor analysis and factor
regression) in gene-expression data analysis
Bayesian stochastic blockmodeling
This chapter provides a self-contained introduction to the use of Bayesian
inference to extract large-scale modular structures from network data, based on
the stochastic blockmodel (SBM), as well as its degree-corrected and
overlapping generalizations. We focus on nonparametric formulations that allow
their inference in a manner that prevents overfitting, and enables model
selection. We discuss aspects of the choice of priors, in particular how to
avoid underfitting via increased Bayesian hierarchies, and we contrast the task
of sampling network partitions from the posterior distribution with finding the
single point estimate that maximizes it, while describing efficient algorithms
to perform either one. We also show how inferring the SBM can be used to
predict missing and spurious links, and shed light on the fundamental
limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool
at https://graph-tool.skewed.de . See also the HOWTO at
https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm
Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net
We propose a novel method to directly learn a stochastic transition operator
whose repeated application provides generated samples. Traditional undirected
graphical models approach this problem indirectly by learning a Markov chain
model whose stationary distribution obeys detailed balance with respect to a
parameterized energy function. The energy function is then modified so the
model and data distributions match, with no guarantee on the number of steps
required for the Markov chain to converge. Moreover, the detailed balance
condition is highly restrictive: energy based models corresponding to neural
networks must have symmetric weights, unlike biological neural circuits. In
contrast, we develop a method for directly learning arbitrarily parameterized
transition operators capable of expressing non-equilibrium stationary
distributions that violate detailed balance, thereby enabling us to learn more
biologically plausible asymmetric neural networks and more general non-energy
based dynamical systems. The proposed training objective, which we derive via
principled variational methods, encourages the transition operator to "walk
back" in multi-step trajectories that start at data-points, as quickly as
possible back to the original data points. We present a series of experimental
results illustrating the soundness of the proposed approach, Variational
Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating
superior samples compared to earlier attempts to learn a transition operator.
We also show that although each rapid training trajectory is limited to a
finite but variable number of steps, our transition operator continues to
generate good samples well past the length of such trajectories, thereby
demonstrating the match of its non-equilibrium stationary distribution to the
data distribution. Source Code: http://github.com/anirudh9119/walkback_nips17Comment: To appear at NIPS 201
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