The Experts below are selected from a list of 122286 Experts worldwide ranked by ideXlab platform
Djallel Bouneffouf - One of the best experts on this subject based on the ideXlab platform.
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Computing the Dirichlet-Multinomial Log-Likelihood Function.
arXiv: Machine Learning, 2020Co-Authors: Djallel BouneffoufAbstract:Dirichlet-multinomial (DMN) distribution is commonly used to model over-dispersion in count data. Precise and fast numerical computation of the DMN log-Likelihood Function is important for performing statistical inference using this distribution, and remains a challenge. To address this, we use mathematical properties of the gamma Function to derive a closed form expression for the DMN log-Likelihood Function. Compared to existing methods, calculation of the closed form has a lower computational complexity, hence is much faster without comprimising computational accuracy.
Ta-wei Soong - One of the best experts on this subject based on the ideXlab platform.
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A log-Likelihood Function-based algorithm for QAM signal classification
Signal Processing, 1998Co-Authors: Yawpo Yang, Ching-hwa Liu, Ta-wei SoongAbstract:Abstract In this paper we derive a log-Likelihood Function-based classification algorithm for classifying quadrature amplitude modulation (QAM) signals buried in additive white Gaussian noise. We derive the amplitude density Functions of received QAM signals first, then develop the required statistics for signal classification based on the maximum a posteriori probability criterion and demonstrate a schematic structure of classifier for M -ary QAM signals. The resultant structure of this proposed classifier is shown to be flexible and easy to expand. Both the theoretical approach and the numerical approach are employed to evaluate the performance that is expressed in terms of the probability of successful classification. We also provide an example to show the capabilities of the developed classifier. It is illustrated that two approaches have consistent results and the successful classification rate reaches 100% for SNR⩾12 dB.
Yunpeng Zhao - One of the best experts on this subject based on the ideXlab platform.
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A note on new Bernstein-type inequalities for the log-Likelihood Function of Bernoulli variables
Statistics & Probability Letters, 2020Co-Authors: Yunpeng ZhaoAbstract:Abstract We prove a new Bernstein-type inequality for the log-Likelihood Function of Bernoulli variables. In contrast to classical Bernstein’s inequality and Hoeffding’s inequality when applied to this log-Likelihood, the new bound is independent of the parameters of the Bernoulli variables and therefore does not blow up as the parameters approach 0 or 1. The new inequality strengthens certain theoretical results on Likelihood-based methods for community detection in networks and can be applied to other Likelihood-based methods for binary data.
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A Note on New Bernstein-type Inequalities for the Log-Likelihood Function of Bernoulli Variables
arXiv: Probability, 2019Co-Authors: Yunpeng ZhaoAbstract:We prove a new Bernstein-type inequality for the log-Likelihood Function of Bernoulli variables. In contrast to classical Bernstein's inequality and Hoeffding's inequality when applied to the log-Likelihood, the new bound is independent of the parameters of the Bernoulli variables and therefore does not blow up as the parameters approach 0 or 1. The new inequality strengthens certain theoretical results on Likelihood-based methods for community detection in networks and can be applied to other Likelihood-based methods for binary data.
Alfred O. Hero - One of the best experts on this subject based on the ideXlab platform.
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On Tests for Global Maximum of the Log-Likelihood Function
IEEE Transactions on Information Theory, 2007Co-Authors: D. Blatt, Alfred O. HeroAbstract:Given the location of a relative maximum of the log-Likelihood Function, how to assess whether it is the global maximum? This paper investigates an existing statistical tool, which, based on asymptotic analysis, answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool for performance prediction and a measure for comparison between tests. The sensitivity of the tests to model mismatch is analyzed in terms of the Renyi divergence and the Kullback-Leibler divergence between the true underlying distribution and the assumed parametric class and tests that are insensitive to small deviations from the model are derived thereby overcoming a fundamental weakness of existing tests. The tests are illustrated for three applications: passive localization or direction finding using an array of sensors, estimating the parameters of a Gaussian mixture model, and estimation of superimposed exponentials in noise-problems that are known to suffer from local maxima.
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tests for global maximum of the Likelihood Function
International Conference on Acoustics Speech and Signal Processing, 2005Co-Authors: D. Blatt, Alfred O. HeroAbstract:Given a relative maximum of the log-Likelihood Function, how to assess whether it is the global maximum? This paper investigates a statistical tool, which answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for the global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool for performance prediction and a measure for comparison between tests. The tests are illustrated for two applications: estimating the parameters of a Gaussian mixture model and direction finding using an array of sensors - practical problems that are known to suffer from local maxima.
Yawpo Yang - One of the best experts on this subject based on the ideXlab platform.
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Maximum Log-Likelihood Function-Based QAM Signal Classification over Fading Channels
Wireless Personal Communications, 2004Co-Authors: Yawpo Yang, Jen-ning Chang, Ji-chyun Liu, Ching-hwa LiuAbstract:In this paper, we propose a modulation classification algorithm for M-ary QAM signals in Rician and Rayleigh fading channels. The developed algorithms are based on the maximum log-Likelihood Functions, which are derived from received signals. First of all, we derived the amplitude PDF of M-ary QAM signal over flat and slowly Rayleigh and Rician fading channel, then we developed the log-Likelihood Functions and then the decision Functions for classification. To demonstrate the performance of the proposed classifier, we give an example to classify the 16/32 QAM signals. Results indicate that the performance of classifier is heavily dependent on the severity of channel fading. When channel is AWGN, which means that there exists only one path (may be specular path) between transmitter and receiver, and the Rician factor k, approaches infinity in this case, henceforth, the performance is the best. The performance, however, is degraded with the decrease of k, and finally the classifier performs worst when channel becomes Rayleigh. Further performance improvement can be achieved by increasing the length of record.
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A log-Likelihood Function-based algorithm for QAM signal classification
Signal Processing, 1998Co-Authors: Yawpo Yang, Ching-hwa Liu, Ta-wei SoongAbstract:Abstract In this paper we derive a log-Likelihood Function-based classification algorithm for classifying quadrature amplitude modulation (QAM) signals buried in additive white Gaussian noise. We derive the amplitude density Functions of received QAM signals first, then develop the required statistics for signal classification based on the maximum a posteriori probability criterion and demonstrate a schematic structure of classifier for M -ary QAM signals. The resultant structure of this proposed classifier is shown to be flexible and easy to expand. Both the theoretical approach and the numerical approach are employed to evaluate the performance that is expressed in terms of the probability of successful classification. We also provide an example to show the capabilities of the developed classifier. It is illustrated that two approaches have consistent results and the successful classification rate reaches 100% for SNR⩾12 dB.
