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Using Bayesian Dynamical Systems for Motion Template Libraries
"... Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. Recent impressive results range from humanoid robot movement generation to timing models of human motions. The automatic generat ..."
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Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. Recent impressive results range from humanoid robot movement generation to timing models of human motions. The automatic generation of skill libraries containing multiple motion templates is an important step in robot learning. Such a skill learning system needs to cluster similar movements together and represent each resulting motion template as a generative model which is subsequently used for the execution of the behavior by a robot system. In this paper, we show how human trajectories captured as multidimensional timeseries can be clustered using Bayesian mixtures of linear Gaussian statespace models based on the similarity of their dynamics. The appropriate number of templates is automatically determined by enforcing a parsimonious parametrization. As the resulting model is intractable, we introduce a novel approximation method based on variational Bayes, which is especially designed to enable the use of efficient inference algorithms. On recorded human Balero movements, this method is not only capable of finding reasonable motion templates but also yields a generative model which works well in the execution of this complex task on a simulated anthropomorphic SARCOS arm. 1
Okada M: Inferring clusterbased networks from differently stimulated multiple timecourse gene expression data
 Bioinformatics
"... gene expression data ..."
Dirichlet Mixtures of Bayesian Linear Gaussian StateSpace Models: a Variational Approach
, 2007
"... Abstract. We describe two related models to cluster multidimensional timeseries under the assumption of an underlying linear Gaussian dynamical process. In the first model, timesseries are assigned to the same cluster when they show global similarity in their dynamics, while in the second model ti ..."
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Cited by 3 (1 self)
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Abstract. We describe two related models to cluster multidimensional timeseries under the assumption of an underlying linear Gaussian dynamical process. In the first model, timesseries are assigned to the same cluster when they show global similarity in their dynamics, while in the second model timesseries are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian StateSpace models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes. 1
A Bayesian Approach to Switching Linear Gaussian StateSpace Models for Unsupervised TimeSeries Segmentation
"... Timeseries segmentation in the fully unsupervised scenario in which the number of segmenttypes is a priori unknown is a fundamental problem in many applications. We propose a Bayesian approach to a segmentation model based on the switching linear Gaussian statespace model that enforces a sparse p ..."
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Timeseries segmentation in the fully unsupervised scenario in which the number of segmenttypes is a priori unknown is a fundamental problem in many applications. We propose a Bayesian approach to a segmentation model based on the switching linear Gaussian statespace model that enforces a sparse parametrization, such as to use only a small number of a priori available different dynamics to explain the data. This enables us to estimate the number of segmenttypes within the model, in contrast to previous nonBayesian approaches where training and comparing several separate models was required. As the resulting model is computationally intractable, we introduce a variational approximation where a reformulation of the problem enables the use of efficient inference algorithms. 1.
Output Grouping using Dirichlet Mixtures of Linear Gaussian StateSpace Models
"... We consider a model to cluster the components of a vector timeseries. The task is to assign each component of the vector timeseries to a single cluster, basing this assignment on the simultaneous dynamical similarity of the component to other components in the cluster. This is in contrast to the m ..."
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We consider a model to cluster the components of a vector timeseries. The task is to assign each component of the vector timeseries to a single cluster, basing this assignment on the simultaneous dynamical similarity of the component to other components in the cluster. This is in contrast to the more familiar task of clustering a set of timeseries based on global measures of their similarity. The model is based on a Dirichlet Mixture of Linear Gaussian StateSpace models (LGSSMs), in which each LGSSM is treated with a prior to encourage the simplest explanation. The resulting model is approximated using a ‘collapsed ’ variational Bayes implementation. 1
Vancouver General Hospital, The Prostate Cancer Center.
, 2007
"... Time–course microarray data consist of mRNA expression from a common set of genes collected at different time points. Such data are thought to reflect underlying biological processes developing over time. In this paper we propose a method to examine gene network relationships using time course micro ..."
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Time–course microarray data consist of mRNA expression from a common set of genes collected at different time points. Such data are thought to reflect underlying biological processes developing over time. In this paper we propose a method to examine gene network relationships using time course microarray data. We assume that a sample of gene expression profiles is a realization of a process where each profile is modeled as a random functional transformation of a common curve. We propose measures of functional similarity and time order based on estimated time transformation functions. This allows for novel inferences on gene networks, including time–delayed relationships, by taking full account of the timing of the functional features of the gene expression profiles. We discuss the application of our model to simulated data as well as to microarray data in the Shionogi model of progression to androgen independence in prostate cancer. Keywords: Time–course microarray data, gene networks, time transformation, functional similarity, hierarchical model, Shionogi model, Markov Chain Monte Carlo. 2 1
Comparison of Clustering Methods for Time Course Genomic Data: Applications to Aging Effects
, 2014
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Dirichlet Mixtures of Bayesian Linear Gaussian StateSpace Models: a Variational Approach
, 2007
"... We describe two related models to cluster multidimensional timeseries under the assumption of an underlying linear Gaussian dynamical process. In the first model, timesseries are assigned to the same cluster when they show global similarity in their dynamics, while in the second model timesseri ..."
Abstract
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We describe two related models to cluster multidimensional timeseries under the assumption of an underlying linear Gaussian dynamical process. In the first model, timesseries are assigned to the same cluster when they show global similarity in their dynamics, while in the second model timesseries are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian StateSpace models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes.