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25
Beyond independent components: trees and clusters
 Journal of Machine Learning Research
, 2003
"... We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysi ..."
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Cited by 52 (0 self)
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We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find “clusters ” of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate treestructured dependencies among multiple time series.
Graphical modelling of multivariate time series
, 2001
"... Abstract. We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with nonlinear dependencies. The models are derived ..."
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Cited by 15 (9 self)
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Abstract. We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with nonlinear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Grangercausal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Grangercausal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.
Finding clusters in independent component analysis
 IN: 4TH INTL. SYMP. ON INDEPENDENT COMPONENT ANALYSIS AND SIGNAL SEPARATION (ICA2003
, 2003
"... We present a class of algorithms that find clusters in independent component analysis: the data are linearly transformed so that the resulting components can be grouped into clusters, such that components are dependent within clusters and independent between clusters. In order to find such clusters, ..."
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Cited by 15 (0 self)
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We present a class of algorithms that find clusters in independent component analysis: the data are linearly transformed so that the resulting components can be grouped into clusters, such that components are dependent within clusters and independent between clusters. In order to find such clusters, we look for a transform that fits the estimated sources to a foreststructured graphical model. In the nonGaussian, temporally independent case, the optimal transform is found by minimizing a contrast function based on mutual information that directly extends the contrast function used for classical ICA. We also derive a contrast function in the Gaussian stationary case that is based on spectral densities and generalizes the contrast function of Pham [22] to richer classes of dependency.
Learning graphical models for stationary time series
 IEEE Transactions on Signal Processing, 52(8):2189 – 2199
, 2004
"... Probabilistic graphical models can be extended to time series by considering probabilistic dependencies between entire time series. For stationary Gaussian time series, the graphical model semantics can be expressed naturally in the frequency domain, leading to interesting families of structured tim ..."
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Cited by 14 (0 self)
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Probabilistic graphical models can be extended to time series by considering probabilistic dependencies between entire time series. For stationary Gaussian time series, the graphical model semantics can be expressed naturally in the frequency domain, leading to interesting families of structured time series models that are complementary to families defined in the time domain. In this paper, we present an algorithm to learn the structure from data for directed graphical models for stationary Gaussian time series. We describe an algorithm for efficient forecasting for stationary Gaussian time series whose spectral densities factorize in a graphical model. We also explore the relationships between graphical model structure and sparsity, comparing and contrasting the notions of sparsity in the time domain and the frequency domain. Finally, we show how to make use of Mercer kernels in this setting, allowing our ideas to be extended to nonlinear models. 1
Graphical Models for Multivariate Time Series from Intensive Care Monitoring
, 2000
"... In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial assoc ..."
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Cited by 13 (3 self)
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In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial associations between the components of multivariate time series. We apply this technique to the hemodynamic system of critically ill patients monitored in intensive care. We appraise the practical value of the procedure by reidentifying known associations between the variables. From separate analyses for different pathophysiological states we conclude that distinct clinical states can be characterised by distinct partial correlation structures.
CrossSpectral Analysis of Tremor Time Series
, 2000
"... We discuss crossspectral analysis and report applications for the investigation of human tremors. For the physiological tremor in healthy subjects, the analysis enables to determine the resonant contribution to the oscillation and allows to test for a contribution of reflexes to this tremor. Compar ..."
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Cited by 9 (3 self)
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We discuss crossspectral analysis and report applications for the investigation of human tremors. For the physiological tremor in healthy subjects, the analysis enables to determine the resonant contribution to the oscillation and allows to test for a contribution of reflexes to this tremor. Comparing the analysis of the relation between the tremor of both hands in normal subjects and subjects with a rare abnormal organization of certain neural pathways proves the involvement of central structures in enhanced physiological tremor. The relation between the left and the right side of the body in pathological tremor shows a specific difference between orthostatic and all other forms of tremor. An investigation of EEG and tremor in patients suffering from Parkinson’s disease reveals the tremorcorrelated cortical activity. Finally, the general issue of interpreting the results of methods designed for the analysis of bivariate processes when applied to multivariate processes is considered. We discuss and apply partial crossspectral analysis in the frame of graphical models as an extention of bivariate crossspectral analysis for the multivariate case.
Online monitoring of highdimensional physiological time series  a casestudy
, 2001
"... In modern statistical process control, intelligent alarm systems have to be constructed which extract the important information from multivariate time series and detect critical "outof control " states of the underlying mechanism quickly and reliably. Regarding highdimensional ti ..."
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Cited by 5 (3 self)
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In modern statistical process control, intelligent alarm systems have to be constructed which extract the important information from multivariate time series and detect critical &quot;outof control &quot; states of the underlying mechanism quickly and reliably. Regarding highdimensional time series, statistical methods for dimension reduction can help to compress the data into a few relevant variables before characteristic patterns in the data are searched for. In this paper we apply graphical models as a preliminary step preceding a factor analysis of the vital signs of critically ill patients in intensive care. Then a procedure for the onlinedetection of change points in univariate time series is applied to the original series and to each of the factors and the results are compared to the judgment of an experienced physician.
Fitting Graphical Interaction Models to Multivariate Time Series
"... Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependenc ..."
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Cited by 4 (0 self)
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Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependencies between the components. Current methods for the identification of the graphical structure are based on nonparametric spectral estimation, which prevents application of common model selection strategies. In this paper, we present a parametric approach for graphical interaction modelling of multivariate stationary time series. The proposed models generalize covariance selection models to the time series setting and are formulated in terms of inverse covariances. We show that these models correspond to vector autoregressive models under conditional independence constraints encoded by undirected graphs. Furthermore, we discuss maximum likelihood estimation based on Whittle’s approximation to the loglikelihood function and propose an iterative method for solving the resulting likelihood equations. The concepts are illustrated by an example.
Assessing Connections in Networks of Biological Neurons
, 1997
"... In this work spike trains of firing times of neurons recorded from various locations in the cat's auditory thalamus are studied. A goal is making inferences concerning connections amongst different regions of the thalamus in both the presence and the absence of a stimulus. Both secondorder mom ..."
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Cited by 3 (1 self)
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In this work spike trains of firing times of neurons recorded from various locations in the cat's auditory thalamus are studied. A goal is making inferences concerning connections amongst different regions of the thalamus in both the presence and the absence of a stimulus. Both secondorder moment (frequency domain) and full likelihood analyses (a threshold crossing model), are carried through. 1 Introduction The sequence of spikes of a neuron, referred to as a "spike train", may carry important information processed by the brain and thus may underlie cognitive functions and sensory perception [1]. The data studied are recorded stretches of point processes corresponding to the firing times of Statistics Department, University of California, Berkeley y Institute of Physiology, University of Lausanne, Switzerland Pars dorsalis (D) Pars lateralis (PL) Pars magnocellularis (M) Auditory Cortex RE Input Figure 1: A block diagram of the auditory regions of the cat's brain. neurons mea...
Grangercausality graphs for multivariate time series
"... In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Grangercausality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Grangercausalit ..."
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Cited by 2 (1 self)
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In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Grangercausality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Grangercausality relations between the variables whereas lines correspond to contemporaneous conditional association. We show that the concept of Grangercausality graphs provides a framework for the derivation of general noncausality relations relative to reduced information sets by performing sequences of simple operations on the graphs. We briefly discuss the implications for the identification of causal relationships. Finally we provide an extension of the linear concept to strong Grangercausality. JEL classification: C320 Keywords: Grangercausality, graphical models, spurious causality, multivariate