4,183 research outputs found
Factorial graphical lasso for dynamic networks
Dynamic networks models describe a growing number of important scientific
processes, from cell biology and epidemiology to sociology and finance. There
are many aspects of dynamical networks that require statistical considerations.
In this paper we focus on determining network structure. Estimating dynamic
networks is a difficult task since the number of components involved in the
system is very large. As a result, the number of parameters to be estimated is
bigger than the number of observations. However, a characteristic of many
networks is that they are sparse. For example, the molecular structure of genes
make interactions with other components a highly-structured and therefore
sparse process.
Penalized Gaussian graphical models have been used to estimate sparse
networks. However, the literature has focussed on static networks, which lack
specific temporal constraints. We propose a structured Gaussian dynamical
graphical model, where structures can consist of specific time dynamics, known
presence or absence of links and block equality constraints on the parameters.
Thus, the number of parameters to be estimated is reduced and accuracy of the
estimates, including the identification of the network, can be tuned up. Here,
we show that the constrained optimization problem can be solved by taking
advantage of an efficient solver, logdetPPA, developed in convex optimization.
Moreover, model selection methods for checking the sensitivity of the inferred
networks are described. Finally, synthetic and real data illustrate the
proposed methodologies.Comment: 30 pp, 5 figure
Exponential asymptotics and Stokes lines in a partial differential equation
A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution identifies asymptotic contributions from saddle points, end points and poles, and the Stokes lines across which these may be switched on and off. These results are then derived directly from the equation by optimally truncating the naïve perturbation expansion and smoothing the Stokes discontinuities. The analysis reveals two new types of Stokes switching: a higher-order Stokes line which is a Stokes line in the approximation of the late terms of the asymptotic series, and which switches on or off Stokes lines themselves; and a second-generation Stokes line, in which a subdominant exponential switched on at a primary Stokes line is itself responsible for switching on another smaller exponential. The ‘new’ Stokes lines discussed by Berk et al. (Berk et al. 1982 J. Math. Phys.23, 988–1002) are second-generation Stokes lines, while the ‘vanishing’ Stokes lines discussed by Aoki et al. (Aoki et al. 1998 In Microlocal analysis and complex Fourier analysis (ed. K. F. T. Kawai), pp. 165–176) are switched off by a higher-order Stokes line
Large Scale Variational Bayesian Inference for Structured Scale Mixture Models
Natural image statistics exhibit hierarchical dependencies across multiple
scales. Representing such prior knowledge in non-factorial latent tree models
can boost performance of image denoising, inpainting, deconvolution or
reconstruction substantially, beyond standard factorial "sparse" methodology.
We derive a large scale approximate Bayesian inference algorithm for linear
models with non-factorial (latent tree-structured) scale mixture priors.
Experimental results on a range of denoising and inpainting problems
demonstrate substantially improved performance compared to MAP estimation or to
inference with factorial priors.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Reconstruction of primordial density fields
The Monge-Ampere-Kantorovich (MAK) reconstruction is tested against
cosmological N-body simulations. Using only the present mass distribution
sampled with particles, and the assumption of homogeneity of the primordial
distribution, MAK recovers for each particle the non-linear displacement field
between its present position and its Lagrangian position on a primordial
uniform grid. To test the method, we examine a standard LCDM N-body simulation
with Gaussian initial conditions and 6 models with non-Gaussian initial
conditions: a chi-squared model, a model with primordial voids and four weakly
non-Gaussian models. Our extensive analyses of the Gaussian simulation show
that the level of accuracy of the reconstruction of the nonlinear displacement
field achieved by MAK is unprecedented, at scales as small as about 3 Mpc. In
particular, it captures in a nontrivial way the nonlinear contribution from
gravitational instability, well beyond the Zel'dovich approximation. This is
also confirmed by our analyses of the non-Gaussian samples. Applying the
spherical collapse model to the probability distribution function of the
divergence of the displacement field, we also show that from a
well-reconstructed displacement field, such as that given by MAK, it is
possible to accurately disentangle dynamical contributions induced by
gravitational clustering from possible initial non-Gaussianities, allowing one
to efficiently test the non-Gaussian nature of the primordial fluctuations. In
addition, a simple application of MAK using the Zel'dovich approximation allows
one to also recover accurately the present-day peculiar velocity field on
scales of about 8 Mpc.Comment: Version to appear in MNRAS, 24 pages, 21 figures appearing (uses 35
figure files), 1 tabl
The relationship between noise and annoyance around Orly
The extent to which annoyance estimated by an isopsophic index is a good forecaster for annoyance perceived near airport approaches was investigated. An index of sensed annoyance is constructed, and the relationship between the annoyance index and the isopsophic index is studied
Penalized estimation in large-scale generalized linear array models
Large-scale generalized linear array models (GLAMs) can be challenging to
fit. Computation and storage of its tensor product design matrix can be
impossible due to time and memory constraints, and previously considered design
matrix free algorithms do not scale well with the dimension of the parameter
vector. A new design matrix free algorithm is proposed for computing the
penalized maximum likelihood estimate for GLAMs, which, in particular, handles
nondifferentiable penalty functions. The proposed algorithm is implemented and
available via the R package \verb+glamlasso+. It combines several ideas --
previously considered separately -- to obtain sparse estimates while at the
same time efficiently exploiting the GLAM structure. In this paper the
convergence of the algorithm is treated and the performance of its
implementation is investigated and compared to that of \verb+glmnet+ on
simulated as well as real data. It is shown that the computation time fo
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