68,431 research outputs found
Sparse Linear Identifiable Multivariate Modeling
In this paper we consider sparse and identifiable linear latent variable
(factor) and linear Bayesian network models for parsimonious analysis of
multivariate data. We propose a computationally efficient method for joint
parameter and model inference, and model comparison. It consists of a fully
Bayesian hierarchy for sparse models using slab and spike priors (two-component
delta-function and continuous mixtures), non-Gaussian latent factors and a
stochastic search over the ordering of the variables. The framework, which we
call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and
bench-marked on artificial and real biological data sets. SLIM is closest in
spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in
inference, Bayesian network structure learning and model comparison.
Experimentally, SLIM performs equally well or better than LiNGAM with
comparable computational complexity. We attribute this mainly to the stochastic
search strategy used, and to parsimony (sparsity and identifiability), which is
an explicit part of the model. We propose two extensions to the basic i.i.d.
linear framework: non-linear dependence on observed variables, called SNIM
(Sparse Non-linear Identifiable Multivariate modeling) and allowing for
correlations between latent variables, called CSLIM (Correlated SLIM), for the
temporal and/or spatial data. The source code and scripts are available from
http://cogsys.imm.dtu.dk/slim/.Comment: 45 pages, 17 figure
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
Effective and efficient structure learning with pruning and model averaging strategies
Learning the structure of a Bayesian Network (BN) with score-based solutions
involves exploring the search space of possible graphs and moving towards the
graph that maximises a given objective function. Some algorithms offer exact
solutions that guarantee to return the graph with the highest objective score,
while others offer approximate solutions in exchange for reduced computational
complexity. This paper describes an approximate BN structure learning
algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines
two novel strategies with hill-climbing search. The algorithm starts by pruning
the search space of graphs, where the pruning strategy can be viewed as an
aggressive version of the pruning strategies that are typically applied to
combinatorial optimisation structure learning problems. It then performs model
averaging in the hill-climbing search process and moves to the neighbouring
graph that maximises the objective function, on average, for that neighbouring
graph and over all its valid neighbouring graphs. Comparisons with other
algorithms spanning different classes of learning suggest that the combination
of aggressive pruning with model averaging is both effective and efficient,
particularly in the presence of data noise
Scalable Exact Parent Sets Identification in Bayesian Networks Learning with Apache Spark
In Machine Learning, the parent set identification problem is to find a set
of random variables that best explain selected variable given the data and some
predefined scoring function. This problem is a critical component to structure
learning of Bayesian networks and Markov blankets discovery, and thus has many
practical applications, ranging from fraud detection to clinical decision
support. In this paper, we introduce a new distributed memory approach to the
exact parent sets assignment problem. To achieve scalability, we derive
theoretical bounds to constraint the search space when MDL scoring function is
used, and we reorganize the underlying dynamic programming such that the
computational density is increased and fine-grain synchronization is
eliminated. We then design efficient realization of our approach in the Apache
Spark platform. Through experimental results, we demonstrate that the method
maintains strong scalability on a 500-core standalone Spark cluster, and it can
be used to efficiently process data sets with 70 variables, far beyond the
reach of the currently available solutions
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