10,765 research outputs found
Identification of Sparse Reciprocal Graphical Models
In this paper we propose an identification procedure of a sparse graphical
model associated to a Gaussian stationary stochastic process. The
identification paradigm exploits the approximation of autoregressive processes
through reciprocal processes in order to improve the robustness of the
identification algorithm, especially when the order of the autoregressive
process becomes large. We show that the proposed paradigm leads to a
regularized, circulant matrix completion problem whose solution only requires
computations of the eigenvalues of matrices of dimension equal to the dimension
of the process
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
Sparse plus low-rank identification for dynamical latent-variable graphical AR models
This paper focuses on the identification of graphical autoregressive models
with dynamical latent variables. The dynamical structure of latent variables is
described by a matrix polynomial transfer function. Taking account of the
sparse interactions between the observed variables and the low-rank property of
the latent-variable model, a new sparse plus low-rank optimization problem is
formulated to identify the graphical auto-regressive part, which is then
handled using the trace approximation and reweighted nuclear norm minimization.
Afterwards, the dynamics of latent variables are recovered from low-rank
spectral decomposition using the trace norm convex programming method.
Simulation examples are used to illustrate the effectiveness of the proposed
approach
On the Identification of Sparse plus Low-rank Graphical Models
This thesis proposes an identification procedure for periodic, Gaussian, stationary reciprocal processes, under the assumption that the conditional dependence relations among the observed variables are mainly due to a limited number of latent variables. The identification procedure combines the sparse plus low-rank decomposition of the inverse covariance matrix of the process and the maximum entropy solution for the block-circulant band extension problem recently proposed in the literatur
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters
This paper proposes a hierarchical, multi-resolution framework for the
identification of model parameters and their spatially variability from noisy
measurements of the response or output. Such parameters are frequently
encountered in PDE-based models and correspond to quantities such as density or
pressure fields, elasto-plastic moduli and internal variables in solid
mechanics, conductivity fields in heat diffusion problems, permeability fields
in fluid flow through porous media etc. The proposed model has all the
advantages of traditional Bayesian formulations such as the ability to produce
measures of confidence for the inferences made and providing not only
predictive estimates but also quantitative measures of the predictive
uncertainty. In contrast to existing approaches it utilizes a parsimonious,
non-parametric formulation that favors sparse representations and whose
complexity can be determined from the data. The proposed framework in
non-intrusive and makes use of a sequence of forward solvers operating at
various resolutions. As a result, inexpensive, coarse solvers are used to
identify the most salient features of the unknown field(s) which are
subsequently enriched by invoking solvers operating at finer resolutions. This
leads to significant computational savings particularly in problems involving
computationally demanding forward models but also improvements in accuracy. It
is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling
which is embarrassingly parallelizable and circumvents issues with slow mixing
encountered in Markov Chain Monte Carlo schemes
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