320,677 research outputs found
Learning Large-Scale Bayesian Networks with the sparsebn Package
Learning graphical models from data is an important problem with wide
applications, ranging from genomics to the social sciences. Nowadays datasets
often have upwards of thousands---sometimes tens or hundreds of thousands---of
variables and far fewer samples. To meet this challenge, we have developed a
new R package called sparsebn for learning the structure of large, sparse
graphical models with a focus on Bayesian networks. While there are many
existing software packages for this task, this package focuses on the unique
setting of learning large networks from high-dimensional data, possibly with
interventions. As such, the methods provided place a premium on scalability and
consistency in a high-dimensional setting. Furthermore, in the presence of
interventions, the methods implemented here achieve the goal of learning a
causal network from data. Additionally, the sparsebn package is fully
compatible with existing software packages for network analysis.Comment: To appear in the Journal of Statistical Software, 39 pages, 7 figure
On Graphical Models via Univariate Exponential Family Distributions
Undirected graphical models, or Markov networks, are a popular class of
statistical models, used in a wide variety of applications. Popular instances
of this class include Gaussian graphical models and Ising models. In many
settings, however, it might not be clear which subclass of graphical models to
use, particularly for non-Gaussian and non-categorical data. In this paper, we
consider a general sub-class of graphical models where the node-wise
conditional distributions arise from exponential families. This allows us to
derive multivariate graphical model distributions from univariate exponential
family distributions, such as the Poisson, negative binomial, and exponential
distributions. Our key contributions include a class of M-estimators to fit
these graphical model distributions; and rigorous statistical analysis showing
that these M-estimators recover the true graphical model structure exactly,
with high probability. We provide examples of genomic and proteomic networks
learned via instances of our class of graphical models derived from Poisson and
exponential distributions.Comment: Journal of Machine Learning Researc
Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data
We consider learning, from strictly behavioral data, the structure and
parameters of linear influence games (LIGs), a class of parametric graphical
games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic
inference (CSI): Making inferences from causal interventions on stable behavior
in strategic settings. Applications include the identification of the most
influential individuals in large (social) networks. Such tasks can also support
policy-making analysis. Motivated by the computational work on LIGs, we cast
the learning problem as maximum-likelihood estimation (MLE) of a generative
model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation
uncovers the fundamental interplay between goodness-of-fit and model
complexity: good models capture equilibrium behavior within the data while
controlling the true number of equilibria, including those unobserved. We
provide a generalization bound establishing the sample complexity for MLE in
our framework. We propose several algorithms including convex loss minimization
(CLM) and sigmoidal approximations. We prove that the number of exact PSNE in
LIGs is small, with high probability; thus, CLM is sound. We illustrate our
approach on synthetic data and real-world U.S. congressional voting records. We
briefly discuss our learning framework's generality and potential applicability
to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending
publication.) Last conference version: submitted March 30, 2012 to UAI 2012.
First conference version: entitled, Learning Influence Games, initially
submitted on June 1, 2010 to NIPS 201
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