The Experts below are selected from a list of 100449 Experts worldwide ranked by ideXlab platform
Reiichiro Kawai - One of the best experts on this subject based on the ideXlab platform.
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Numerical inverse Lévy measure method for infinite shot noise Series Representation
Journal of Computational and Applied Mathematics, 2013Co-Authors: Junichi Imai, Reiichiro KawaiAbstract:Infinitely divisible random vectors without Gaussian component admit Representations with shot noise Series. We analyze four known methods of deriving kernels of the Series and reveal the superiority of the inverse Levy measure method over the other three methods for simulation use. We propose a numerical approach to the inverse Levy measure method, which in most cases provides no explicit kernel. We also propose to apply the quasi-Monte Carlo procedure to the inverse Levy measure method to enhance the numerical efficiency. It is known that the efficiency of the quasi-Monte Carlo could be enhanced by sensible alignment of low discrepancy sequence. In this paper we apply this idea to exponential interarrival times in the shot noise Series Representation. The proposed method paves the way for simulation use of shot noise Series Representation for any infinite Levy measure and enables one to simulate entire approximate trajectory of stochastic differential equations with jumps based on infinite shot noise Series Representation. Although implementation of the proposed method requires a small amount of initial work, it is applicable to general Levy measures and has the potential to yield substantial improvements in simulation time and estimator efficiency. Numerical results are provided to support our theoretical analysis and confirm the effectiveness of the proposed method for practical use.
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On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws
Monte Carlo and Quasi-Monte Carlo Methods 2010, 2012Co-Authors: Reiichiro Kawai, Junichi ImaiAbstract:Infinitely divisible random vectors and Levy processes without Gaussian component admit Representations with shot noise Series. To enhance efficiency of the Series Representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise Series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the Series Representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the Series Representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.
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On finite truncation of infinite shot noise Series Representation of tempered stable laws
Physica A-statistical Mechanics and Its Applications, 2011Co-Authors: Junichi Imai, Reiichiro KawaiAbstract:Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise Series Representation is the only exact simulation method for the tempered stable process and has recently attracted attention for simulation use with ever improved computational speed. In this paper, we derive Series Representations for the tempered stable laws of increasing practical interest through the thinning, rejection, and inverse Levy measure methods. We make a rigorous comparison among those Representations, including the existing one due to Imai and Kawai [29] and Rosinski (2007) [3], in terms of the tail mass of Levy measures which can be simulated under a common finite truncation scheme. The tail mass are derived in closed form for some Representations thanks to various structural properties of the tempered stable laws. We prove that the Representation via the inverse Levy measure method achieves a much faster convergence in truncation to the infinite sum than all the other Representations. Numerical results are presented to support our theoretical analysis.
Heggere S Ranganath - One of the best experts on this subject based on the ideXlab platform.
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an analysis of time Series Representation methods data mining applications perspective
ACM Southeast Regional Conference, 2014Co-Authors: Vineetha Bettaiah, Heggere S RanganathAbstract:Because of high dimensionality, proven data mining and pattern recognition methods are not suitable for processing time Series data. As a result, several time Series Representations capable of achieving significant reduction in dimensionality without losing important features have been developed. Each Representation has its own advantages and disadvantages. In this paper, based on the requirements of key data mining applications, such as clustering, classification and query by content, characteristics desired in an ideal time Series Representation are identified. Using the identified characteristics as metrics, widely known time Series Representation methods are evaluated to determine the extent to which the Representations satisfy the requirements.
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ACM Southeast Regional Conference - An analysis of time Series Representation methods: data mining applications perspective
Proceedings of the 2014 ACM Southeast Regional Conference on - ACM SE '14, 2014Co-Authors: Vineetha Bettaiah, Heggere S RanganathAbstract:Because of high dimensionality, proven data mining and pattern recognition methods are not suitable for processing time Series data. As a result, several time Series Representations capable of achieving significant reduction in dimensionality without losing important features have been developed. Each Representation has its own advantages and disadvantages. In this paper, based on the requirements of key data mining applications, such as clustering, classification and query by content, characteristics desired in an ideal time Series Representation are identified. Using the identified characteristics as metrics, widely known time Series Representation methods are evaluated to determine the extent to which the Representations satisfy the requirements.
Junichi Imai - One of the best experts on this subject based on the ideXlab platform.
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Numerical inverse Lévy measure method for infinite shot noise Series Representation
Journal of Computational and Applied Mathematics, 2013Co-Authors: Junichi Imai, Reiichiro KawaiAbstract:Infinitely divisible random vectors without Gaussian component admit Representations with shot noise Series. We analyze four known methods of deriving kernels of the Series and reveal the superiority of the inverse Levy measure method over the other three methods for simulation use. We propose a numerical approach to the inverse Levy measure method, which in most cases provides no explicit kernel. We also propose to apply the quasi-Monte Carlo procedure to the inverse Levy measure method to enhance the numerical efficiency. It is known that the efficiency of the quasi-Monte Carlo could be enhanced by sensible alignment of low discrepancy sequence. In this paper we apply this idea to exponential interarrival times in the shot noise Series Representation. The proposed method paves the way for simulation use of shot noise Series Representation for any infinite Levy measure and enables one to simulate entire approximate trajectory of stochastic differential equations with jumps based on infinite shot noise Series Representation. Although implementation of the proposed method requires a small amount of initial work, it is applicable to general Levy measures and has the potential to yield substantial improvements in simulation time and estimator efficiency. Numerical results are provided to support our theoretical analysis and confirm the effectiveness of the proposed method for practical use.
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On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws
Monte Carlo and Quasi-Monte Carlo Methods 2010, 2012Co-Authors: Reiichiro Kawai, Junichi ImaiAbstract:Infinitely divisible random vectors and Levy processes without Gaussian component admit Representations with shot noise Series. To enhance efficiency of the Series Representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise Series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the Series Representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the Series Representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.
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On finite truncation of infinite shot noise Series Representation of tempered stable laws
Physica A-statistical Mechanics and Its Applications, 2011Co-Authors: Junichi Imai, Reiichiro KawaiAbstract:Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise Series Representation is the only exact simulation method for the tempered stable process and has recently attracted attention for simulation use with ever improved computational speed. In this paper, we derive Series Representations for the tempered stable laws of increasing practical interest through the thinning, rejection, and inverse Levy measure methods. We make a rigorous comparison among those Representations, including the existing one due to Imai and Kawai [29] and Rosinski (2007) [3], in terms of the tail mass of Levy measures which can be simulated under a common finite truncation scheme. The tail mass are derived in closed form for some Representations thanks to various structural properties of the tempered stable laws. We prove that the Representation via the inverse Levy measure method achieves a much faster convergence in truncation to the infinite sum than all the other Representations. Numerical results are presented to support our theoretical analysis.
Yihong Mauro - One of the best experts on this subject based on the ideXlab platform.
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On the Prony Series Representation of Stretched Exponential Relaxation
arXiv: Soft Condensed Matter, 2018Co-Authors: John C. Mauro, Yihong MauroAbstract:Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony Series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony Series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of the exponent. The fitting quality of the Prony Series is analyzed as a function of the number of terms in the Series. With a sufficient number of terms, the Prony Series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony Series Representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.
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On the Prony Series Representation of stretched exponential relaxation
Physica A: Statistical Mechanics and its Applications, 2018Co-Authors: John C. Mauro, Yihong MauroAbstract:Abstract Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β . In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony Series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony Series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β . The fitting quality of the Prony Series is analyzed as a function of the number of terms in the Series. With a sufficient number of terms, the Prony Series can accurately capture the time evolution of the stretched exponential function, including its “fat tail” at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony Series Representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.
Vineetha Bettaiah - One of the best experts on this subject based on the ideXlab platform.
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an analysis of time Series Representation methods data mining applications perspective
ACM Southeast Regional Conference, 2014Co-Authors: Vineetha Bettaiah, Heggere S RanganathAbstract:Because of high dimensionality, proven data mining and pattern recognition methods are not suitable for processing time Series data. As a result, several time Series Representations capable of achieving significant reduction in dimensionality without losing important features have been developed. Each Representation has its own advantages and disadvantages. In this paper, based on the requirements of key data mining applications, such as clustering, classification and query by content, characteristics desired in an ideal time Series Representation are identified. Using the identified characteristics as metrics, widely known time Series Representation methods are evaluated to determine the extent to which the Representations satisfy the requirements.
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ACM Southeast Regional Conference - An analysis of time Series Representation methods: data mining applications perspective
Proceedings of the 2014 ACM Southeast Regional Conference on - ACM SE '14, 2014Co-Authors: Vineetha Bettaiah, Heggere S RanganathAbstract:Because of high dimensionality, proven data mining and pattern recognition methods are not suitable for processing time Series data. As a result, several time Series Representations capable of achieving significant reduction in dimensionality without losing important features have been developed. Each Representation has its own advantages and disadvantages. In this paper, based on the requirements of key data mining applications, such as clustering, classification and query by content, characteristics desired in an ideal time Series Representation are identified. Using the identified characteristics as metrics, widely known time Series Representation methods are evaluated to determine the extent to which the Representations satisfy the requirements.
