11,315 research outputs found
The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences
Markov networks are models for compactly representing complex probability
distributions. They are composed by a structure and a set of numerical weights.
The structure qualitatively describes independences in the distribution, which
can be exploited to factorize the distribution into a set of compact functions.
A key application for learning structures from data is to automatically
discover knowledge. In practice, structure learning algorithms focused on
"knowledge discovery" present a limitation: they use a coarse-grained
representation of the structure. As a result, this representation cannot
describe context-specific independences. Very recently, an algorithm called
CSPC was designed to overcome this limitation, but it has a high computational
complexity. This work tries to mitigate this downside presenting CSGS, an
algorithm that uses the Grow-Shrink strategy for reducing unnecessary
computations. On an empirical evaluation, the structures learned by CSGS
achieve competitive accuracies and lower computational complexity with respect
to those obtained by CSPC.Comment: 12 pages, and 8 figures. This works was presented in IBERAMIA 201
A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression
Graph-theoretic methods of causal search based in the ideas of Pearl (2000), Spirtes,
Glymour, and Scheines (2000), and others have been applied by a number of researchers
to economic data, particularly by Swanson and Granger (1997) to the problem of finding
a data-based contemporaneous causal order for the structural autoregression (SVAR),
rather than, as is typically done, assuming a weakly justified Choleski order. Demiralp
and Hoover (2003) provided Monte Carlo evidence that such methods were effective,
provided that signal strengths were sufficiently high. Unfortunately, in applications to
actual data, such Monte Carlo simulations are of limited value, since the causal structure
of the true data-generating process is necessarily unknown. In this paper, we present a
bootstrap procedure that can be applied to actual data (i.e., without knowledge of the true
causal structure). We show with an applied example and a simulation study that the
procedure is an effective tool for assessing our confidence in causal orders identified by
graph-theoretic search procedures.vector autoregression (VAR), structural vector autoregression (SVAR),causality, causal order, Choleski order, causal search algorithms, graph-theoretic methods
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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