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Topology selection in graphical models of autoregressive processes
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2010
"... An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series. The graph topology of the model represents the sparsity pattern of the inverse spectrum of the time series and characterizes conditional independence relations between the variables. The meth ..."
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An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series. The graph topology of the model represents the sparsity pattern of the inverse spectrum of the time series and characterizes conditional independence relations between the variables. The method proposed in the paper is based on an ℓ1type nonsmooth regularization of the conditional maximum likelihood estimation problem. We show that this reduces to a convex optimization problem and describe a largescale algorithm that solves the dual problem via the gradient projection method. Results of experiments with randomly generated and real data sets are also included.
Causality and graphical models in time series
 Richardson (Eds.), Highly Structured Stochastic Systems
, 2003
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Direct or indirect? Graphical models for neural oscillators
, 2006
"... Univariate and bivariate time series analysis techniques have enabled new insights into neural processes. However, these techniques are not feasible to distinguish direct and indirect interrelations in multivariate systems. To this aim multivariate times series techniques are presented and investiga ..."
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Univariate and bivariate time series analysis techniques have enabled new insights into neural processes. However, these techniques are not feasible to distinguish direct and indirect interrelations in multivariate systems. To this aim multivariate times series techniques are presented and investigated by means of simulated as well as physiological time series. Pitfalls and limitations of these techniques are discussed.
Contents lists available at ScienceDirect
"... journal homepage: www.elsevier.com/locate/neulet Tremorcorrelated neuronal activity in the subthalamic nucleus of Parkinsonian patients ..."
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journal homepage: www.elsevier.com/locate/neulet Tremorcorrelated neuronal activity in the subthalamic nucleus of Parkinsonian patients
Statistical Memory Effects in Time Series Dynamics: Application to Parkinson’s Disease
 NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
, 2006
"... In this work we present a new approach to the problem of diagnosing and forecasting various states in patients with Parkinson’s disease. Recently we have achieved the following result. In real complex systems the nonMarkovity parameter (NMP) can serve as a reliable quantitative measure of the curre ..."
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In this work we present a new approach to the problem of diagnosing and forecasting various states in patients with Parkinson’s disease. Recently we have achieved the following result. In real complex systems the nonMarkovity parameter (NMP) can serve as a reliable quantitative measure of the current state of a complex system and can help to estimate the deviation of this state from the normal one. Our preliminary studies of real complex systems in cardiology, neurophysiology, epidemiology and seismology have shown, that the NMP has diverse frequency dependence. It testifies to the competition between Markov and nonMarkov, random and regular processes and makes a transfer from one relaxation scenario to the other possible. On this basis we can formulate the new method of diagnosing deflections in the central nervous system caused by Parkinson’s disease. We suggest the statistical theory of discrete nonMarkov stochastic processes to calculate the NMP and the quantitative evaluation of various dynamic states of real complex systems. With the help of NMP we have found evident manifestation of Markov effects in a normal (healthy) state of the studied live system and its sharp decrease in the nonMarkov states in the period of crises and catastrophes and various human diseases. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson’s disease, in particular.
Article Quantitative Assessment of Parkinsonian Tremor Based on an Inertial Measurement Unit
, 2015
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Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems
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GRAPHICAL INTERACTION MODELS FOR TIME SERIES: PARAMETER ESTIMATION AND MODEL SELECTION
"... Abstract. We present a parametric approach for graphical interaction modelling in multivariate stationary time series. In these models, the possible dependencies between the components of the process are represented by edges in an undirected graph. We consider vector autoregressive models and propos ..."
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Abstract. We present a parametric approach for graphical interaction modelling in multivariate stationary time series. In these models, the possible dependencies between the components of the process are represented by edges in an undirected graph. We consider vector autoregressive models and propose a parametrization in terms of inverse covariances, which are contrained to zero for missing edges. The parameter can be estimated by minimization of Whittle’s loglikelihood, which leads to similar likelihood equation as for covariance selection models. We discuss the problem of model selection and prove asymptotic efficiency of AIClike criteria. 1.
Central Tremor Oscillators – a Directionality Study
"... This study investigates the relation of causality between the two central putative oscillators of the bilateral postural hand tremor. For this, we used a photic driving paradigm that induced at the visual cortical level a specific oscillatory activity. Having the particular functional relation betwe ..."
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This study investigates the relation of causality between the two central putative oscillators of the bilateral postural hand tremor. For this, we used a photic driving paradigm that induced at the visual cortical level a specific oscillatory activity. Having the particular functional relation between the hand motor system and the visual system, we assumed that changes in the last one were reflected in the central tremor oscillatory activity too. The stimuli frequencies were particularly chosen out of the alpha frequency band (7 Hz, 19 Hz), thus preventing the cortical driven oscillations to interfere with the spontaneous cortical rhythm. Physiological postural hand tremor was recorded bilaterally while the visual stimuli were delivered – either concurrently, either alternatively –, in the two visual hemifields. To track the causal functional interdependence between the two tremor central oscillators accompanying the corresponding changes induced in the cognitive state, we applied the partial directed coherence analysis.