Dynamical System

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Mari Ostendorf - One of the best experts on this subject based on the ideXlab platform.

  • a Dynamical System model for generating fundamental frequency for speech synthesis
    IEEE Transactions on Speech and Audio Processing, 1999
    Co-Authors: Kenneth N Ross, Mari Ostendorf
    Abstract:

    Higher quality speech synthesis is required for widespread use of text to-speech (TTS) technology, and prosody is one component of synthesis technology with the greatest need for improvement. This paper describes a new approach to generation of two important cues to prosodic patterns-fundamental frequency (F/sub 0/) and energy contours-given symbolic prosodic labels and text. Specifically, the approach represents vectors of F/sub 0/ and energy with a Dynamical System model, which allows automatic estimation of parameters from labeled speech. Parameters at different time scales in the model are structured to capture segment, syllable, phrase and discourse level effects based on linguistic research. F/sub 0/ generation experiments with the Dynamical System model show improved synthetic speech quality over the hybrid target/filter approach.

  • a Dynamical System approach to continuous speech recognition
    International Conference on Acoustics Speech and Signal Processing, 1991
    Co-Authors: Vassilios Digalakis, J R Rohlicek, Mari Ostendorf
    Abstract:

    An Dynamical System model is proposed for better representing the spectral dynamics of speech for recognition. It is assumed that the observed feature vectors of a phone segment are the output of a stochastic linear Dynamical System, and two alternative assumptions regarding the relationship of the segment length and the evolution of the dynamics are considered. Training is equivalent to the identification of a stochastic linear System, and a nontraditional approach based on the estimate-maximize algorithm is followed. This model is evaluated on a phoneme classification task using the TIMIT database. It is shown that the classification performance obtained using the proposed model is significantly better than that obtained using either an independent-frame or a Gauss-Markov assumption on the observed frames. >

Geoffrey J Gordon - One of the best experts on this subject based on the ideXlab platform.

  • supervised learning for Dynamical System learning
    arXiv: Machine Learning, 2015
    Co-Authors: Ahmed Hefny, Carlton Downey, Geoffrey J Gordon
    Abstract:

    Recently there has been substantial interest in spectral methods for learning Dynamical Systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of Dynamical System learning: we show how to learn Dynamical Systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.

  • A New View of Predictive State Methods for Dynamical System Learning.
    2015
    Co-Authors: Ahmed Hefny, Carlton Downey, Geoffrey J Gordon
    Abstract:

    Recently there has been substantial interest in predictive state methods for learning Dynamical Systems: these algorithms are popular since they often offer a good tradeoff between computational speed and statistical efficiency. Despite their desirable properties, though, predictive state methods can sometimes be difficult to use in practice. E.g., in contrast to the rich literature on supervised learning methods, which allows us to choose from an extensive menu of models and algorithms to suit the prior beliefs we have about properties of the function to be learned, predictive state Dynamical System learning methods are comparatively inflexible: it is as if we were restricted to use only linear regression instead of being allowed to choose decision trees, nonparametric regression, or the lasso. To address this problem, we propose a new view of predictive state methods in terms of instrumentalvariable regression. This view allows us to construct a wide variety of Dynamical System learners simply by swapping in different supervised learning methods. We demonstrate the effectiveness of our proposed methods by experimenting with non-linear regression to learn a hidden Markov model, showing that the resulting algorithm outperforms its linear counterpart; the correctness of this algorithm follows directly from our general analysis.

Kishor G Bhat - One of the best experts on this subject based on the ideXlab platform.

  • arithmetic coding as a non linear Dynamical System
    Communications in Nonlinear Science and Numerical Simulation, 2009
    Co-Authors: Nithin Nagaraj, Prabhakar G Vaidya, Kishor G Bhat
    Abstract:

    Abstract In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear Dynamical System known as Generalized Luroth Series (GLS). GLS achieves Shannon’s entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.

Ahmed Hefny - One of the best experts on this subject based on the ideXlab platform.

  • supervised learning for Dynamical System learning
    arXiv: Machine Learning, 2015
    Co-Authors: Ahmed Hefny, Carlton Downey, Geoffrey J Gordon
    Abstract:

    Recently there has been substantial interest in spectral methods for learning Dynamical Systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of Dynamical System learning: we show how to learn Dynamical Systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.

  • A New View of Predictive State Methods for Dynamical System Learning.
    2015
    Co-Authors: Ahmed Hefny, Carlton Downey, Geoffrey J Gordon
    Abstract:

    Recently there has been substantial interest in predictive state methods for learning Dynamical Systems: these algorithms are popular since they often offer a good tradeoff between computational speed and statistical efficiency. Despite their desirable properties, though, predictive state methods can sometimes be difficult to use in practice. E.g., in contrast to the rich literature on supervised learning methods, which allows us to choose from an extensive menu of models and algorithms to suit the prior beliefs we have about properties of the function to be learned, predictive state Dynamical System learning methods are comparatively inflexible: it is as if we were restricted to use only linear regression instead of being allowed to choose decision trees, nonparametric regression, or the lasso. To address this problem, we propose a new view of predictive state methods in terms of instrumentalvariable regression. This view allows us to construct a wide variety of Dynamical System learners simply by swapping in different supervised learning methods. We demonstrate the effectiveness of our proposed methods by experimenting with non-linear regression to learn a hidden Markov model, showing that the resulting algorithm outperforms its linear counterpart; the correctness of this algorithm follows directly from our general analysis.

Cheinshan Liu - One of the best experts on this subject based on the ideXlab platform.

  • cone of non linear Dynamical System and group preserving schemes
    International Journal of Non-linear Mechanics, 2001
    Co-Authors: Cheinshan Liu
    Abstract:

    Abstract The first step in investigating the dynamics of a continuous time System described by a set of ordinary differential equations is to integrate to obtain trajectories. In this paper, we convert the non-linear Dynamical System x = f ( x ,t), x ∈ R n , into an augmented Dynamical System of Lie type X = A ( X ,t) X , X ∈ M n+1 , A ∈ so (n, 1) locally. In doing so, the inherent symmetry group and the (null) cone structure of the non-linear Dynamical System are brought out; then the Cayley transformation and the Pade approximants are utilized to develop group preserving schemes in the augmented space. The schemes are capable of updating the augmented state point to locate automatically on the cone at the end of each time increment. By projection we thus obtain the numerical schemes on state space x , which have the form similar to the Euler scheme but with stepsize adaptive. Furthermore, the schemes are shown to have the same asymptotic behavior as the original continuous System and do not induce spurious solutions or ghost fixed points. Some examples are used to test the performance of the schemes. Because the numerical implementations are easy and parsimonious and also have high computational efficiency and accuracy, these schemes are recommended for use in the physical calculations.