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Alexander Gasnikov - One of the best experts on this subject based on the ideXlab platform.

  • An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
    European Journal of Operational Research, 1
    Co-Authors: Pavel Dvurechensky, Eduard Gorbunov, Alexander Gasnikov
    Abstract:

    Abstract We consider smooth stochastic convex optimization problems in the context of algorithms which are based on Directional Derivatives of the objective function. This context can be considered as an intermediate one between Derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the Directional Derivative of the objective function at this point and in this direction is available with some additive noise. The noise is assumed to be of an unknown nature, but bounded in the absolute value. We underline that we consider Directional Derivatives in any direction, as opposed to coordinate descent methods which use only Derivatives in coordinate directions. For this setting, we propose a non-accelerated and an accelerated Directional Derivative method and provide their complexity bounds. Our non-accelerated algorithm has a complexity bound which is similar to the gradient-based algorithm, that is, without any dimension-dependent factor. Our accelerated algorithm has a complexity bound which coincides with the complexity bound of the accelerated gradient-based algorithm up to a factor of square root of the problem dimension. We extend these results to strongly convex problems.

Pavel Dvurechensky - One of the best experts on this subject based on the ideXlab platform.

  • An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
    European Journal of Operational Research, 1
    Co-Authors: Pavel Dvurechensky, Eduard Gorbunov, Alexander Gasnikov
    Abstract:

    Abstract We consider smooth stochastic convex optimization problems in the context of algorithms which are based on Directional Derivatives of the objective function. This context can be considered as an intermediate one between Derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the Directional Derivative of the objective function at this point and in this direction is available with some additive noise. The noise is assumed to be of an unknown nature, but bounded in the absolute value. We underline that we consider Directional Derivatives in any direction, as opposed to coordinate descent methods which use only Derivatives in coordinate directions. For this setting, we propose a non-accelerated and an accelerated Directional Derivative method and provide their complexity bounds. Our non-accelerated algorithm has a complexity bound which is similar to the gradient-based algorithm, that is, without any dimension-dependent factor. Our accelerated algorithm has a complexity bound which coincides with the complexity bound of the accelerated gradient-based algorithm up to a factor of square root of the problem dimension. We extend these results to strongly convex problems.

Eduard Gorbunov - One of the best experts on this subject based on the ideXlab platform.

  • An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
    European Journal of Operational Research, 1
    Co-Authors: Pavel Dvurechensky, Eduard Gorbunov, Alexander Gasnikov
    Abstract:

    Abstract We consider smooth stochastic convex optimization problems in the context of algorithms which are based on Directional Derivatives of the objective function. This context can be considered as an intermediate one between Derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the Directional Derivative of the objective function at this point and in this direction is available with some additive noise. The noise is assumed to be of an unknown nature, but bounded in the absolute value. We underline that we consider Directional Derivatives in any direction, as opposed to coordinate descent methods which use only Derivatives in coordinate directions. For this setting, we propose a non-accelerated and an accelerated Directional Derivative method and provide their complexity bounds. Our non-accelerated algorithm has a complexity bound which is similar to the gradient-based algorithm, that is, without any dimension-dependent factor. Our accelerated algorithm has a complexity bound which coincides with the complexity bound of the accelerated gradient-based algorithm up to a factor of square root of the problem dimension. We extend these results to strongly convex problems.

Johan De Vriendt - One of the best experts on this subject based on the ideXlab platform.

  • Effect of sampling, quantization and noise on the performance of the second Directional Derivative edge detector
    Multidimensional Systems and Signal Processing, 1995
    Co-Authors: Johan De Vriendt
    Abstract:

    Berzins [2] and De Vriendt [14] studied the processes that influence the performance of the Laplacian and the second Directional Derivative edge detector in the continuous domain. In this paper the influence of sampling, quantization and noise is studied in the discrete domain for the second Directional Derivative edge detector. The results are compared with those for the Laplacian edge detector. The smoothing and Derivative operations are implemented by FIR digital filters. Two sampling processes are considered: a square aperture and a Gaussian smoothing process. The influence of sampling can be limited by increasing the spread σ of the smoothing filter. Though, σ should not be chosen too large because of the influence of nearby edges. The quantization of the intensity function introduces an uncertainty in the edge location. The uncertainty is larger than the error due to sampling if the step height is small. We also prove that the second Directional Derivative is less sensitive to noise than the Laplacian. An increase of σ slightly reduces the variation of the edge location.

  • Accuracy of the zero crossings of the second Directional Derivative as an edge detector
    Multidimensional Systems and Signal Processing, 1993
    Co-Authors: Johan De Vriendt
    Abstract:

    In this paper the accuracy of the second Directional Derivative edge detector is analyzed, based on a number of idealized edge models. The results are compared with those for the Laplacian edge detector. Errors are shown to be small under a number of conditions. These conditions are less severe for the second Directional Derivative than for the Laplacian edge detector. Spurious or phantom edges can be removed by checking the sign of the third Directional Derivative, though this is not enough to remove all large errors. Indeed, it is also shown that large errors will be obtained if no threshold is set on the magnitude of a third order Derivative.

  • Derivation of the third-order Directional Derivative
    Pattern Recognition Letters, 1993
    Co-Authors: Johan De Vriendt
    Abstract:

    Abstract We give an easy derivation of the third order Directional Derivative in the direction of the gradient of the intensity function. The obtained formula is a correction of the formula found by Clark (1989).

Shrikanth S. Narayanan - One of the best experts on this subject based on the ideXlab platform.

  • INTERSPEECH - Spectro-Temporal Directional Derivative Features for Automatic Speech Recognition
    2013
    Co-Authors: James Gibson, Maarten Van Segbroeck, Antonio Ortega, Panayiotis G. Georgiou, Shrikanth S. Narayanan
    Abstract:

    We introduce a novel spectro-temporal representation of speech by applying Directional Derivative filters to the Melspectrogram, with the aim of improving the robustness of automatic speech recognition. Previous studies have shown that two-dimensional wavelet functions, when tuned to appropriate spectral scales and temporal rates, are able to accurately capture the acoustic modulations of speech, even in high noise conditions. Therefore, spectro-temporal features extracted from the wavelet transformation of the spectrogram, offer additional noise robustness to important signal processing tasks, such as voice activity detection and speech recognition. In this paper, we explore the use of the steerable pyramid, a Directional wavelet transform that is common in image processing, to derive a spectro-temporal feature representation of speech that can serve as an alternative to cepstral Derivatives and Gabor filterbank features. We discuss their application for the task of robust automatic speech recognition. Experiments conducted on the Aurora-2 database demonstrate their competitive robustness to other state-of-the-art speech features, especially in low signalto-noise ratio conditions. Index Terms: spectro-temporal features, automatic speech recognition, Directional wavelet transforms

  • spectro temporal Directional Derivative features for automatic speech recognition
    Conference of the International Speech Communication Association, 2013
    Co-Authors: James Gibson, Maarten Van Segbroeck, Antonio Ortega, Panayiotis G. Georgiou, Shrikanth S. Narayanan
    Abstract:

    We introduce a novel spectro-temporal representation of speech by applying Directional Derivative filters to the Melspectrogram, with the aim of improving the robustness of automatic speech recognition. Previous studies have shown that two-dimensional wavelet functions, when tuned to appropriate spectral scales and temporal rates, are able to accurately capture the acoustic modulations of speech, even in high noise conditions. Therefore, spectro-temporal features extracted from the wavelet transformation of the spectrogram, offer additional noise robustness to important signal processing tasks, such as voice activity detection and speech recognition. In this paper, we explore the use of the steerable pyramid, a Directional wavelet transform that is common in image processing, to derive a spectro-temporal feature representation of speech that can serve as an alternative to cepstral Derivatives and Gabor filterbank features. We discuss their application for the task of robust automatic speech recognition. Experiments conducted on the Aurora-2 database demonstrate their competitive robustness to other state-of-the-art speech features, especially in low signalto-noise ratio conditions. Index Terms: spectro-temporal features, automatic speech recognition, Directional wavelet transforms