Discrete nonhomogeneous and nonstationary logistic and Markov regression models for spatiotemporal data with unresolved external influences

Wiljes, Jana de; Putzig, Lars; Horenko, Illia

doi:10.2140/camcos.2014.9.1

Cited by 15 publications

(14 citation statements)

References 28 publications

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“…By covariate we not only mean external forcings (for a more complete discussion see the companion paper by Franzke et al 2015) but also unresolved physical processes and scales such as due to EOF truncation. This may then introduce problems when applying the standard stationary approaches common to machine learning and statistics (Wiljes et al 2014). In the context of this paper, this issue plays a very important role when analyzing atmospheric data since many of the potentiallyrelevant covariates might not be available explicitly in the set of covariates that we have chosen for testing.…”

Section: Methodsmentioning

confidence: 99%

On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere

et al. 2015

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We identify the dynamical drivers of systematic changes in persistent quasi-stationary states (regimes) of the Southern Hemisphere troposphere and their secular trends. We apply a purely data-driven approach, whereby a multiscale approximation to nonstationary dynamical processes is achieved through optimal sequences of locally stationary fast vector autoregressive factor processes, to examine a high resolution atmospheric reanalysis over the period encompassing 1958–2013. This approach identifies regimes and their secular trends in terms of the predictability of the flow and is Granger causal. A comprehensive set of diagnostics on both isentropic and isobaric surfaces is employed to examine teleconnections over the full hemisphere and for a set of regional domains. Composite states for the hemisphere obtained from nonstationary nonparametric cluster analysis reveal patterns consistent with a circumglobal wave 3 (polar)–wave 5 (subtropical) pattern, while regional composites reveal the Pacific South American pattern and blocking modes. The respective roles of potential vorticity sources, stationary Rossby waves and baroclinic instability on the dynamics of these circulation modes are shown to be reflected by the seasonal variations of the waveguides, where Rossby wave sources and baroclinic disturbances are largely contained within the waveguides and with little direct evidence of sustained remote tropical influences on persistent synoptic features. Warm surface temperature anomalies are strongly connected with regions of upper level divergence and anticyclonic Rossby wave sources. The persistent states identified reveal significant variability on interannual to decadal time scales with large secular trends identified in all sectors apart from a region close to South America

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Section: Methodsmentioning

confidence: 99%

On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere

et al. 2015

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“…A resulting problem becomes well-posed, robust, and uniquely solvable and the impact of unresolved scales is then essentially modeled via a stationary and homogeneous Bernoulli process with a time-independent probability α. If the impact of u is significantly time-dependent, this assumption might be overstringent and can lead to biased results (9).…”

Section: The Model Of Causality With Unresolved Scalesmentioning

confidence: 99%

“…However, in a context of multiscale and multiphysics models, the presence of unresolved scale quantities u t (that are not statistically independent or identically distributed) may result in the nonstationarity and nonhomogeneity of the resulting data-driven discrete state models and may manifest itself in the presence of secular trends and/or in regime-transition behavior (9). Application of the standard stationary discrete state modeling approaches common to machine learning and statistics (e.g., methods like artificial neuronal networks, support vector machines, and generalized linear models) may lead to biased results (9) and wrong inference of underlying causality (i.e., in the attribution of regressors x t i in terms of their importance or unimportance for explaining the model variable y). Moreover, the standard continuous instruments of causality identification based on correlation [e.g., cross-correlation and cross-covariance (10)] or linear predictability [such as the concept of Granger causality (11-13)]…”

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confidence: 99%

On inference of causality for discrete state models in a multiscale context

Gerber

Horenko

2014

Proc. Natl. Acad. Sci. U.S.A.

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Discrete state models are a common tool of modeling in many areas. E.g., Markov state models as a particular representative of this model family became one of the major instruments for analysis and understanding of processes in molecular dynamics (MD). Here we extend the scope of discrete state models to the case of systematically missing scales, resulting in a nonstationary and nonhomogeneous formulation of the inference problem. We demonstrate how the recently developed tools of nonstationary data analysis and information theory can be used to identify the simultaneously most optimal (in terms of describing the given data) and most simple (in terms of complexity and causality) discrete state models. We apply the resulting formalism to a problem from molecular dynamics and show how the results can be used to understand the spatial and temporal causality information beyond the usual assumptions. We demonstrate that the most optimal explanation for the appropriately discretized/ coarse-grained MD torsion angles data in a polypeptide is given by the causality that is localized both in time and in space, opening new possibilities for deploying percolation theory and stochastic subgridscale modeling approaches in the area of MD.multiscale systems | probabilistic networks | Granger causality | nonstationarity | regularization D iscrete state modeling is a powerful tool in many areas of science such as in computational biophysics [where it is mostly used in a form of Markov state models (1-4)], materials science [e.g., deployed in percolation theory and Ising models (5)], bioinformatics [e.g., as probabilistic Boolean models for analysis and control of complex biological networks (6)], and geosciences [e.g., used in the form of the generalized linear regression models (7)]. A central issue of discrete state modeling is the identification of an optimal model for the discrete quantity of interest y (e.g., being a Boolean variable or a probability measure) expressed as a function of other available discrete quantities x 1 , x 2 , . . . , x n (being also Boolean variables or probability measures) and of all other potentially relevant quantities u (being discrete and/or continuous variables). Inference of causality then implies identification of all x i that have a statistically significant impact on y and distinguishing them from all those x j that are insignificant for y. To give a concrete example, in the context of molecular dynamics variable y may describe a probability for a certain torsion angle (e.g., from the protein backbone) to be in one of the discrete conformational states; x 1 , x 2 , . . . , x n can be the values of probabilities for all torsion angles of this protein in previous times and variable u may represent all of the positions and velocities of individual atoms, simulation settings (e.g., temperature), and force-field and solvent properties, etc. Understanding the causality in this situation will mean, for example, identification of the memory depth (e.g., in the context of Markov state models, where...

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“…This subproblem strongly depends on the model choice, and its computational complexity can range from a simple computation of a deterministic analytic expression (e.g., geometric clustering problem (2.5)) to quadratic optimization problems with linear equality and inequality constraints (see [9] for examples).…”

Section: Numerical Approach and Computational Complexitymentioning

confidence: 99%

“…Step 2 (see lines [8][9] of the subspace algorithm on the other hand depends on the choice of the underlying model class (2.1). In the following we will consider the example model function (2.2) with model distance function (2.5).…”

Section: Numerical Approach and Computational Complexitymentioning

confidence: 99%

An Adaptive Markov Chain Monte Carlo Approach to Time Series Clustering of Processes with Regime Transition Behavior

Wiljes¹,

Majda²,

Horenko³

2013

Multiscale Model. Simul.

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A numerical framework for clustering of time series via a Markov chain Monte Carlo (MCMC) method is presented. It combines concepts from recently introduced variational time series analysis and regularized clustering functional minimization [I. Horenko, SIAM J. Sci. Comput., 32 (2010), pp. 62-83] with MCMC. A conceptual advantage of the presented combined framework is that it allows us to address the two main problems of the existent clustering methods, e.g., the nonconvexity and the ill-posedness of the respective functionals, in a unified way. Clustering of the time series and minimization of the regularized clustering functional are based on the generation of samples from an appropriately chosen Boltzmann distribution in the space of cluster affiliation paths using simulated annealing and the Metropolis algorithm. The presented method is applied to sets of generic ill-posed clustering problems, and the results are compared to those obtained by the standard methods. As demonstrated in numerical examples, the presented MCMC formulation of the regularized clustering problem allows us to avoid the locality of the obtained minimizers, provides good clustering results even for very ill-posed problems with overlapping clusters, and is the computationally superior method for long time series. Introduction.Cluster modeling is widely used in many application areas such as computational and statistical physics [42,15], climate/weather research [22,23,10,12,13,45,8], and finance [21,38,48]. In the context of time series analysis, the aim is usually to detect a hidden process switching between different regimes of a system's behavior, which helps to predict a certain outcome of future events. In most cases the only given information is observation data, which we can regard as a time series. Then the determination of the model and the data-based description of the regime behavior can be formulated as an optimization problem [3,16]. The main issue thereby is to compute a hidden path, weighting the influence of the data on the various possible cluster models and, therefore, specifying the transitions between the regimes.This can be rather difficult since (i) the underlying problem is ill-posed, due to the high number of unknowns in relation to the known parameters, and (ii) the results obtained with a local minimization algorithm depend on the initial parameters, since

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Discrete nonhomogeneous and nonstationary logistic and Markov regression models for spatiotemporal data with unresolved external influences

Cited by 15 publications

References 28 publications

On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere

On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere

On inference of causality for discrete state models in a multiscale context

An Adaptive Markov Chain Monte Carlo Approach to Time Series Clustering of Processes with Regime Transition Behavior

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