Results 1  10
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325
Variational learning for switching statespace models
 Neural Computation
, 1998
"... We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Ma ..."
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Cited by 170 (5 self)
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We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Markov models and linear dynamical systems  and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forwardbackward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching statespace models.
Surrogate time series
 PHYSICA D
, 2000
"... Before we apply nonlinear techniques, e.g. those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified by the data. While many processes in nature seem very unlikely a priori to be linear, the possible n ..."
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Cited by 161 (0 self)
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Before we apply nonlinear techniques, e.g. those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified by the data. While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in
Efficiently Supporting Ad Hoc Queries in Large Datasets of Time Sequences
, 1997
"... Ad hoc querying is difficult on very large datasets, since it is usually not possible to have the entire dataset on disk. While compression can be used to decrease the size of the dataset, compressed data is notoriously difficult to index or access. In this paper we consider a very large dataaet com ..."
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Cited by 125 (17 self)
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Ad hoc querying is difficult on very large datasets, since it is usually not possible to have the entire dataset on disk. While compression can be used to decrease the size of the dataset, compressed data is notoriously difficult to index or access. In this paper we consider a very large dataaet comprising multiple distinct time sequences. Each point in the sequence is a numerical value. We show how to compress such a dataset into a format that supports ad hoc querying, provided that a small error can be tolerated when the data is uncompressed. Experiments on large, real world datasets (AT&T customer calling patterns) show that the proposed method achieves an average of less thau 5% error in any data value after compressing to a mere 2.5% of the original space (i. e., a 40:1 compression ratio), with these numbers not very sensitive to dataset size. Experiments on aggregate queries achieved a 0.5% reconstruction error with a space requirement under 2%.
On the OutofSample Importance of Skewness and Asymmetric Dependence for Asset Allocation
 Journal of Financial Econometrics
, 2004
"... Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear t ..."
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Cited by 104 (5 self)
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Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear to be more highly correlated during market downturns than during market upturns. In this article we examine the economic and statistical significance of these asymmetries for asset allocation decisions in an outofsample setting. We consider the problem of a constant relative risk aversion (CRRA) investor allocating wealth between the riskfree asset, a smallcap portfolio, and a largecap portfolio. We use models that can capture timevarying moments up to the fourth order, and we use copula theory to construct models of the timevarying dependence structure that allow for different dependence during bear markets than bull markets. The importance of these two asymmetries for asset allocation is assessed by comparing the performance of a portfolio based on a normal distribution model with a portfolio based on a more flexible distribution model. For investors with no shortsales constraints, we find that knowledge of higher moments and asymmetric dependence leads to gains that are economically significant and statistically significant in some cases. For short salesconstrained investors the gains are limited.
NeuroAnimator: Fast Neural Network Emulation and Control of PhysicsBased Models
, 1998
"... Animation through the numerical simulation of physicsbased graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, finding controllers that enable physicsbased models to produce desired animations usually entails formidable computational cost. This paper de ..."
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Cited by 100 (4 self)
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Animation through the numerical simulation of physicsbased graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, finding controllers that enable physicsbased models to produce desired animations usually entails formidable computational cost. This paper demonstrates the possibility of replacing the numerical simulation and control of model dynamics with a dramatically more efficient alternative. In particular, we propose the NeuroAnimator, a novel approach to creating physically realistic animation that exploits neural networks. NeuroAnimators are automatically trained offline to emulate physical dynamics through the observation of physicsbased models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAnimator, we introduce a fast algorithm for learning controllers that enables either physicsbased models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for passive and active (actuated) rigid body, articulated, and deformable physicsbased models.
Interdisciplinary application of nonlinear time series methods
 Phys. Reports
, 1998
"... This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situatio ..."
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Cited by 84 (4 self)
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This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.
Annealed Competition of Experts for a Segmentation and Classification of Switching Dynamics
, 1996
"... We present a method for the unsupervised segmentation of data streams originating from different unknown sources which alternate in time. We use an architecture consisting of competing neural networks. Memory is included in order to resolve ambiguities of inputoutput relations. In order to obtain m ..."
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Cited by 74 (22 self)
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We present a method for the unsupervised segmentation of data streams originating from different unknown sources which alternate in time. We use an architecture consisting of competing neural networks. Memory is included in order to resolve ambiguities of inputoutput relations. In order to obtain maximal specialization, the competition is adiabatically increased during training. Our method achieves almost perfect identification and segmentation in the case of switching chaotic dynamics where input manifolds overlap and inputoutput relations are ambiguous. Only a small dataset is needed for the training proceedure. Applications to time series from complex systems demonstrate the potential relevance of our approach for time series analysis and shortterm prediction. 1 Introduction Neural networks provide frameworks for the representation of relations present in data. Especially in the fields of classification and time series prediction, neural networks Corresponding author, email:k...
Online Data Mining for CoEvolving Time Sequences
 In Proceedings of the 16th International Conference on Data Engineering
, 2000
"... In many applications, the data of interest comprises multiple sequences that evolve over time. Examples include currency exchange rates, network traffic data. We develop a fast method to analyze such coevolving time sequences jointly to allow (a) estimation/forecasting of missing /delayed/future v ..."
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Cited by 71 (5 self)
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In many applications, the data of interest comprises multiple sequences that evolve over time. Examples include currency exchange rates, network traffic data. We develop a fast method to analyze such coevolving time sequences jointly to allow (a) estimation/forecasting of missing /delayed/future values, (b) quantitative data mining,and (c) outlier detection. Our method, MUSCLES, adapts to changing correlations among time sequences. It can handle indefinitely long sequences efficiently using an incremental algorithm and requires only small amount of storage and less I/O operations. To make it scale for a large number of sequences, we present a variation, the Selective MUSCLES method and propose an efficient algorithm to reduce the problem size. Experiments on real datasets show that MUSCLES outperforms popular competitors in prediction accuracy up to 10 times, and discovers interesting correlations. Moreover, Selective MUSCLES scales up very well for large numbers of sequences, reducing response time up to 110 times over MUSCLES, and sometimes even improves the prediction quality.
New Results on Recurrent Network Training: Unifying the Algorithms and Accelerating Convergence
 IEEE TRANS. NEURAL NETWORKS
, 2000
"... How to efficiently train recurrent networks remains a challenging and active research topic. Most of the proposed training approaches are based on computational ways to efficiently obtain the gradient of the error function, and can be generally grouped into five major groups. In this study we presen ..."
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Cited by 62 (3 self)
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How to efficiently train recurrent networks remains a challenging and active research topic. Most of the proposed training approaches are based on computational ways to efficiently obtain the gradient of the error function, and can be generally grouped into five major groups. In this study we present a derivation that unifies these approaches. We demonstrate that the approaches are only five different ways of solving a particular matrix equation. The second goal of this paper is develop a new algorithm based on the insights gained from the novel formulation. The new algorithm, which is based on approximating the error gradient, has lower computational complexity in computing the weight update than the competing techniques for most typical problems. In addition, it reaches the error minimum in a much smaller number of iterations. A desirable characteristic of recurrent network training algorithms is to be able to update the weights in an online fashion. We have also developed an online version of the proposed algorithm, that is based on updating the error gradient approximation in a recursive manner.