In Advances in Neural Information Processing Systems 23, pages: 388-396, (Editors: Lafferty, J. , C. K.I. Williams, J. Shawe-Taylor, R. S. Zemel, A. Culotta), Curran, Red Hook, NY, USA, Twenty-Fourth Annual Conference on Neural Information Processing Systems (NIPS), 2010 (inproceedings)
Many time-series such as human movement data consist of a sequence of basic actions, e.g., forehands and backhands in tennis. Automatically extracting and characterizing such actions is an important problem for a variety of different applications. In this paper, we present a probabilistic segmentation approach in which an observed time-series is modeled as a concatenation of segments corresponding
to different basic actions. Each segment is generated through a noisy transformation of one of a few hidden trajectories representing different types of movement,
with possible time re-scaling. We analyze three different approximation methods for dealing with model intractability, and demonstrate how the proposed approach
can successfully segment table tennis movements recorded using a robot arm as haptic input device.
In SIAM International Conference on Data Mining, pages: 295-304, (Editors: Park, H. , S. Parthasarathy, H. Liu), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, SDM, May 2009 (inproceedings)
Many real-world applications with graph data require
the efficient solution of a given regression task as well as the
identification of the subgraphs which are relevant for the task. In these cases graphs
are commonly represented as binary vectors of indicators of subgraphs, giving rise to an intractable input dimensionality.
An efficient solution to this problem was recently proposed by a Lasso-type
method where the objective function optimization over an intractable
number of variables is reformulated as a dual mathematical programming problem
over a small number of variables but a large number of constraints. The
dual problem is then solved by column generation where the subgraphs corresponding
to the most violated constraints are found by weighted subgraph mining.
This paper proposes an extension of this method to a fully Bayesian approach which
defines a prior distribution on the parameters and integrate them out from the model, thus providing a posterior distribution on the target variable as
opposed to a single estimate. The advantage of this approach is that
the extra information given by the target posterior distribution can be used for improving
the model in several ways. In this paper, we use the target posterior variance as a measure of uncertainty in the
prediction and show that, by rejecting unconfident predictions, we can improve state-of-the-art
performance on several molecular graph datasets.
In Advances in neural information processing systems 21, pages: 297-304, (Editors: Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou), Curran, Red Hook, NY, USA, Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS), June 2009 (inproceedings)
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 time-series can be clustered using Bayesian mixtures of linear Gaussian state-space 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.
(171), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, June 2008 (techreport)
Unsupervised time-series segmentation in the general scenario in which the number of segment-types
and segment boundaries are a priori unknown is a fundamental problem in many applications and requires an accurate segmentation model as well as a way of determining an appropriate number of segment-types.
In most approaches, segmentation and determination of number of segment-types are addressed
in two separate steps, since the segmentation model assumes a predefined number of segment-types.
The determination of number of segment-types is thus achieved by training and comparing several separate models. In this paper, we take a Bayesian approach to a segmentation model based on linear Gaussian state-space models to achieve structure selection within the model. An appropriate prior distribution on the parameters is used to enforce a sparse parametrization, such that the model automatically selects the smallest number of underlying dynamical systems that explain the data well and a parsimonious structure for each dynamical system. As the resulting model is computationally intractable, we introduce a variational approximation, in which a reformulation of the problem enables to use an efficient inference algorithm.
In ICMLA 2008, pages: 3-9, (Editors: Wani, M. A., X.-W. Chen, D. Casasent, L. Kurgan, T. Hu, K. Hafeez), IEEE Computer Society, Los Alamitos, CA, USA, 7th International Conference on Machine Learning and Applications, December 2008 (inproceedings)
Time-series segmentation in the fully unsupervised scenario in which the number of segment-types 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 state-space 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 segment-types within the model, in contrast to previous non-Bayesian 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.
In ISPA 2007, pages: 446-451, IEEE Computer Society, Los Alamitos, CA, USA, 5th International Symposium on Image and Signal Processing and Analysis, September 2007 (inproceedings)
We consider a model to cluster the components of a vector
time-series. The task is to assign each component of the
vector time-series 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 time-series based on
global measures of their similarity. The model is based on
a Dirichlet Mixture of Linear Gaussian State-Space 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.
(161), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, March 2007 (techreport)
We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian State-Space 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.
Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems