17,218 research outputs found
The IBMAP approach for Markov networks structure learning
In this work we consider the problem of learning the structure of Markov
networks from data. We present an approach for tackling this problem called
IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC
algorithm, designed for avoiding important limitations of existing
independence-based algorithms. These algorithms proceed by performing
statistical independence tests on data, trusting completely the outcome of each
test. In practice tests may be incorrect, resulting in potential cascading
errors and the consequent reduction in the quality of the structures learned.
IBMAP contemplates this uncertainty in the outcome of the tests through a
probabilistic maximum-a-posteriori approach. The approach is instantiated in
the IBMAP-HC algorithm, a structure selection strategy that performs a
polynomial heuristic local search in the space of possible structures. We
present an extensive empirical evaluation on synthetic and real data, showing
that our algorithm outperforms significantly the current independence-based
algorithms, in terms of data efficiency and quality of learned structures, with
equivalent computational complexities. We also show the performance of IBMAP-HC
in a real-world application of knowledge discovery: EDAs, which are
evolutionary algorithms that use structure learning on each generation for
modeling the distribution of populations. The experiments show that when
IBMAP-HC is used to learn the structure, EDAs improve the convergence to the
optimum
Spatial modeling of extreme snow depth
The spatial modeling of extreme snow is important for adequate risk
management in Alpine and high altitude countries. A natural approach to such
modeling is through the theory of max-stable processes, an infinite-dimensional
extension of multivariate extreme value theory. In this paper we describe the
application of such processes in modeling the spatial dependence of extreme
snow depth in Switzerland, based on data for the winters 1966--2008 at 101
stations. The models we propose rely on a climate transformation that allows us
to account for the presence of climate regions and for directional effects,
resulting from synoptic weather patterns. Estimation is performed through
pairwise likelihood inference and the models are compared using penalized
likelihood criteria. The max-stable models provide a much better fit to the
joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generalized Network Psychometrics: Combining Network and Latent Variable Models
We introduce the network model as a formal psychometric model,
conceptualizing the covariance between psychometric indicators as resulting
from pairwise interactions between observable variables in a network structure.
This contrasts with standard psychometric models, in which the covariance
between test items arises from the influence of one or more common latent
variables. Here, we present two generalizations of the network model that
encompass latent variable structures, establishing network modeling as parts of
the more general framework of Structural Equation Modeling (SEM). In the first
generalization, we model the covariance structure of latent variables as a
network. We term this framework Latent Network Modeling (LNM) and show that,
with LNM, a unique structure of conditional independence relationships between
latent variables can be obtained in an explorative manner. In the second
generalization, the residual variance-covariance structure of indicators is
modeled as a network. We term this generalization Residual Network Modeling
(RNM) and show that, within this framework, identifiable models can be obtained
in which local independence is structurally violated. These generalizations
allow for a general modeling framework that can be used to fit, and compare,
SEM models, network models, and the RNM and LNM generalizations. This
methodology has been implemented in the free-to-use software package lvnet,
which contains confirmatory model testing as well as two exploratory search
algorithms: stepwise search algorithms for low-dimensional datasets and
penalized maximum likelihood estimation for larger datasets. We show in
simulation studies that these search algorithms performs adequately in
identifying the structure of the relevant residual or latent networks. We
further demonstrate the utility of these generalizations in an empirical
example on a personality inventory dataset.Comment: Published in Psychometrik
A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Process
This paper develops a unified, accurate and computationally efficient method
for change-point inference in non-stationary spatio-temporal processes. By
modeling a non-stationary spatio-temporal process as a piecewise stationary
spatio-temporal process, we consider simultaneous estimation of the number and
locations of change-points, and model parameters in each segment. A composite
likelihood-based criterion is developed for change-point and parameters
estimation. Asymptotic theories including consistency and distribution of the
estimators are derived under mild conditions. In contrast to classical results
in fixed dimensional time series that the asymptotic error of change-point
estimator is , exact recovery of true change-points is guaranteed in
the spatio-temporal setting. More surprisingly, the consistency of change-point
estimation can be achieved without any penalty term in the criterion function.
A computational efficient pruned dynamic programming algorithm is developed for
the challenging criterion optimization problem. Simulation studies and an
application to U.S. precipitation data are provided to demonstrate the
effectiveness and practicality of the proposed method
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