اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStatistical paleoclimate reconstructions via Markov random fields
198
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Understanding centennial scale climate variability requires data sets that are accurate, long, continuous and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be reconstructed using paleoclimate archives, known as proxies. Various climate field reconstructions (CFR) methods have been proposed to relate past temperature to such proxy networks. In this work, we propose a new CFR method, called GraphEM, based on Gaussian Markov random fields embedded within an EM algorithm. Gaussian Markov random fields provide a natural and flexible framework for modeling high-dimensional spatial fields. At the same time, they provide the parameter reduction necessary for obtaining precise and well-conditioned estimates of the covariance structure, even in the sample-starved setting common in paleoclimate applications. In this paper, we propose and compare the performance of different methods to estimate the graphical structure of climate fields, and demonstrate how the GraphEM algorithm can be used to reconstruct past climate variations. The performance of GraphEM is compared to the widely used CFR method RegEM with regularization via truncated total least squares, using synthetic data. Our results show that GraphEM can yield significant improvements, with uniform gains over space, and far better risk properties. We demonstrate that the spatial structure of temperature fields can be well estimated by graphs where each neighbor is only connected to a few geographically close neighbors, and that the increase in performance is directly related to recovering the underlying sparsity in the covariance of the spatial field. Our work demonstrates how significant improvements can be made in climate reconstruction methods by better modeling the covariance structure of the climate field.
قيم البحث
اقرأ أيضاً
The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMises stress for each of the more than 94,000 tetrahedra
within the finite element discretization. In this paper, we define an intricate statistical model for the spatial field of vonMises stress which uses the given grain geometry in a fundamental way. Our model relates the three-dimensional field to integrals of latent stochastic processes defined on the vertices of the one- and two-dimensional grain boundaries. An intuitive neighborhood structure of said boundary nodes suggested the use of a latent Gaussian Markov random field (GMRF). However, despite the potential for computational gains afforded by GMRFs, the integral nature of our model and the sheer number of data points pose substantial challenges for a full Bayesian analysis. To overcome these problems and encourage efficient exploration of the posterior distribution, a number of techniques are now combined: parallel computing, sparse matrix methods, and a modification of a block update strategy within the sampling routine. In addition, we use an auxiliary variables approach to accommodate the presence of outliers in the data.
Traditional voxel-level multiple testing procedures in neuroimaging, mostly $p$-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based p
rocedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimers or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimers Disease Neuroimaging Initiative.
The Potts model is frequently used to describe the behavior of image classes, since it allows to incorporate contextual information linking neighboring pixels in a simple way. Its isotropic version has only one real parameter beta, known as smoothnes
s parameter or inverse temperature, which regulates the classes map homogeneity. The classes are unavailable, and estimating them is central in important image processing procedures as, for instance, image classification. Methods for estimating the classes which stem from a Bayesian approach under the Potts model require to adequately specify a value for beta. The estimation of such parameter can be efficiently made solving the Pseudo Maximum likelihood (PML) equations in two different schemes, using the prior or the posterior model. Having only radiometric data available, the first scheme needs the computation of an initial segmentation, while the second uses both the segmentation and the radiometric data to make the estimation. In this paper, we compare these two PML estimators by computing the mean square error (MSE), bias, and sensitivity to deviations from the hypothesis of the model. We conclude that the use of extra data does not improve the accuracy of the PML, moreover, under gross deviations from the model, this extra information introduces unpredictable distortions and bias.
In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying MRFs rely on
the regularized maximum likelihood estimation (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing MRFs. The proposed optimization problem is formulated based on the exact $ell_0$ regularization, and can be solved in near-linear time and memory. Moreover, we show that the proposed estimator enjoys a provably small estimation error. As a special case, we derive sharp statistical guarantees for the inference of sparsely-changing Gaussian MRFs (GMRF) in the high-dimensional regime, showing that such problems can be learned with as few as one sample per time. Our proposed method is extremely efficient in practice: it can accurately estimate sparsely-changing graphical models with more than 500 million variables in less than one hour.
We consider general discrete Markov Random Fields(MRFs) with additional bottleneck potentials which penalize the maximum (instead of the sum) over local potential value taken by the MRF-assignment. Bottleneck potentials or analogous constructions hav
e been considered in (i) combinatorial optimization (e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree problem, bottleneck function minimization in greedoids), (ii) inverse problems with $L_{infty}$-norm regularization, and (iii) valued constraint satisfaction on the $(min,max)$-pre-semirings. Bottleneck potentials for general discrete MRFs are a natural generalization of the above direction of modeling work to Maximum-A-Posteriori (MAP) inference in MRFs. To this end, we propose MRFs whose objective consists of two parts: terms that factorize according to (i) $(min,+)$, i.e. potentials as in plain MRFs, and (ii) $(min,max)$, i.e. bottleneck potentials. To solve the ensuing inference problem, we propose high-quality relaxations and efficient algorithms for solving them. We empirically show efficacy of our approach on large scale seismic horizon tracking problems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
