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Identification of errors-in-variables models using the em algorithm

IFAC Proceedings Volumes 2008年第2期41卷 1378-1383页

作者： Jaafar ALMutawa Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals

This paper advocates a new subspace system identification algorithm for the errors-in-variables (EIV) state space model via the em algorithm. To initialize the em algorithm an initial estimate is obtained by the errors-in-variables subspace system identification method: EIV-MOESP (Chou et al. [1997]) and EIV-N4SID (Gustafsson [2001]). The em algorithm is an algorithm to compute the maximum value for the likelihood function that is consists of two steps; namely the E- and M-steps. The E- and M-steps in the em algorithm are calculated by computing the conditional expectation under the assumption that the input-output data is completely observed. Numerical example shows that the em algorithm can monotonically improve the initial estimates obtained by subspace identification methods.

关键词： Subspace system identification errors-in-variables model em-algorithm

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Parametric estimation and robust inference for current status data with Lindley lifetimes

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2025年

作者： Castilla, Elena Rey Juan Carlos Univ Dept Matemat Aplicada Mostoles Campus Madrid 28933 Spain

Current status data appear in many biomedical studies when we only know if an event of interest occurs before or after a specific time point. In this paper, we develop statistical inference for the estimation of parameters from current status data under the Lindley lifetime distribution, which is seen to work better than the exponential distribution in some lifetime contexts. We first develop an em algorithm for Maximum Likelihood (ML) estimation and derive the asymptotic confidence intervals for model parameters. Then, we address the problem of model misspecification and define a new family of robust divergence-based estimators as a robust alternative to ML. Finally, we illustrate these methods through a simulation study as well as a numerical example.

关键词： Current status data Confidence intervals em-algorithm Lindley distribution Model misspecification Robustness

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Statistical separation of mixtures in the problem of reconstructing the coefficients of an Itô stochastic process-type model of the interplanetary magnetic flux density: ℓ2-distance minimization vs likelihood maximization

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RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHemATICAL MODELLING 2025年第1期40卷 17-31页

作者： Karpov, Kirill Korolev, Victor Sukhareva, Natalia Moscow State Univ Fac Computat Math & Cybernet Moscow 119991 Russia Moscow Ctr Fundamental & Appl Math Moscow 119991 Russia Russian Acad Sci Fed Res Ctr Comp Sci & Control Moscow 119333 Russia Hangzhou Dianzi Univ Sch Math Hangzhou 310018 Peoples R China Moscow State Univ Fac Phys Moscow 119991 Russia

Two approaches to the problem of statistical separation of finite mixtures of probability distributions are discussed. The first of them consists in finding maximum likelihood estimates of the parameters of the mixture by the em-algorithm, whereas the second approach consists in finding the values of the parameters that deliver minimum to the distance between the theoretical and empirical distribution functions. It is demonstrated that the second approach is preferable at least in the problem of statistical reconstruction of the coefficients of an It & ocirc;stochastic process that requires dynamic separation of finite normal mixtures in the moving window mode. For this problem, the performance of the numerical procedures is critical. A combination of numerical procedures is described that provides (almost) the same value of the likelihood function for the second approach that is attained by the em-algorithm, but ensures multiple decrease of the & ell;2-distance between the theoretical mixture and the empirical distribution function while demonstrating better performance. A kind of 'metric' regularization of the problem of likelihood maximization is proposed. The proposed techniques are illustrated by adjusting the It & ocirc;process model to the time series of the interplanetary magnetic field (magnetic flux density) registered by the Global Geospace Science (GGS) Wind apparatus (the spacecraft placed in the Lagrange point between the Earth and the Sun).

关键词： Time series It & ocirc stochastic process finite normal mixture statistical separation of mixtures em-algorithm sequential quadratic programming algorithm ill-posed problem interplanetary magnetic field

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em-estimation and modeling of heavy-tailed processes with the multivariate normal inverse Gaussian distribution

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SIGNAL PROCESSING 2005年第8期85卷 1655-1673页

作者： Oigård, TA Hanssen, A Hansen, RE Godtliebsen, F Univ Tromso Dept Stat NO-9037 Tromso Norway Univ Tromso Dept Phys NO-9037 Tromso Norway Norwegian Def Res Estab NO-2027 Kjeller Norway

The heavy-tailed multivariate normal inverse Gaussian (MNIG) distribution is a recent variance-mean mixture of a multivariate Gaussian with a univariate inverse Gaussian distribution. Due to the complexity of the likelihood function, parameter estimation by direct maximization is exceedingly difficult. To overcome this problem, we propose a fast and accurate multivariate expectation-maximization (em) algorithm for maximum likelihood estimation of the scalar, vector, and matrix parameters of the MNIG distribution. Important fundamental and attractive properties of the MNIG as a modeling tool for multivariate heavy-tailed processes are discussed. The modeling strength of the MNIG, and the feasibility of the proposed em parameter estimation algorithm, are demonstrated by fitting the MNIG to real world hydrophone data, to wideband synthetic aperture sonar data, and to multichannel radar sea clutter data. (c) 2005 Elsevier B.V. All rights reserved.

关键词： heavy tails em-algorithm multivariate estimation

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em-based channel estimation algorithms for OFDM

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EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2004年第10期2004卷 1460-1477页

作者： Ma, XQ Kobayashi, H Schwartz, SC Princeton Univ Sch Engn & Appl Sci Dept Elect Engn Princeton NJ 08544 USA

Estimating a channel that is subject to frequency-selective Rayleigh fading is a challenging problem in an orthogonal frequency division multiplexing (OFDM) system. We propose three em-based algorithms to efficiently estimate the channel impulse response (CIR) or channel frequency response of such a system operating on a channel with multipath fading and additive white Gaussian noise (AWGN). These algorithms are capable of improving the channel estimate by making use of a modest number of pilot tones or using the channel estimate of the previous frame to obtain the initial estimate for the iterative procedure. Simulation results show that the bit error rate (BER) as well as the mean square error (MSE) of the channel can be significantly reduced by these algorithms. We present simulation results to compare these algorithms on the basis of their performance and rate of convergence. We also derive Cramer-Rao-like lower bounds for the unbiased channel estimate, which can be achieved via these em-based algorithms. It is shown that the convergence rate of two of the algorithms is independent of the length of the multipath spread. One of them also converges most rapidly and has the smallest overall computational burden.

关键词： OFDM em-algorithm channel estimation Cramer-Rao lower bound

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em-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ

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STATISTICS AND COMPUTING 2004年第1期14卷 67-77页

作者： Protassov, RS Harvard Univ Dept Stat Ctr Sci Cambridge MA 02138 USA FleetBoston Financial Capital Markets Anal Boston MA 02110 USA

Generalized Hyperbolic distribution (Barndorff-Nielsen 1977) is a variance-mean mixture of a normal distribution with the Generalized Inverse Gaussian distribution. Recently subclasses of these distributions (e.g., the hyperbolic distribution and the Normal Inverse Gaussian distribution) have been applied to construct stochastic processes in turbulence and particularly in finance, where multidimensional problems are of special interest. Parameter estimation for these distributions based on an i.i.d. sample is a difficult task even for a specified one-dimensional subclass (subclass being uniquely defined by.) and relies on numerical methods. For the hyperbolic subclass (lambda = 1), computer program 'hyp' (Blaesild and Sorensen 1992) estimates parameters via ML when the dimensionality is less than or equal to three. To the best of the author's knowledge, no successful attempts have been made to fit any given subclass when the dimensionality is greater than three. This article proposes a simple em-based ( Dempster, Laird and Rubin 1977) ML estimation procedure to estimate parameters of the distribution when the subclass is known regardless of the dimensionality. Our method relies on the ability to numerically evaluate modified Bessel functions of the third kind and their logarithms, which is made possible by currently available software. The method is applied to fit the five dimensional Normal Inverse Gaussian distribution to a series of returns on foreign exchange rates.

关键词： em-algorithm Generalized Hyperbolic distribution Normal Inverse Gaussian distribution multivariate modeling parameter estimation

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Exercises in em

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AMERICAN STATISTICIAN 2000年第3期54卷 207-209页

作者： Flury, B Zoppè, A Univ Neuchatel Grp Stat CH-2000 Neuchatel Switzerland Univ Trento Dept Management & Comp Sci I-38100 Trento Italy

Suppose survival times follow an exponential distribution, and some observations are right-censored: in this situation the em algorithm gives a straightforward solution to the problem of maximum likelihood estimation. But what happens if survival times are also left-censored, or if they follow a uniform distribution? The em algorithm is a generic device useful in a variety of problems with incomplete data, and it appears more and more often in statistical textbooks. This article presents two exercises, which are extensions of a well-known example used in introductions to the em algorithm. They focus on two points: the applicability of the algorithm and its self-consistency property.

关键词： em-algorithm exponential distribution incomplete data maximum likelihood estimation uniform distribution

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Data Streams Fast em-Fuzzy Clustering based on Kohonen's Self-Learning 1

Data Streams Fast EM-Fuzzy Clustering based on Kohonen's Sel...

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1st IEEE International Conference on Data Stream Mining and Processing (DSMP)

作者： Bodyanskiy, Yevgeniy V. Deineko, Anastasiia O. Kutsenko, Yana V. Zayika, Oleksandr O. Kharkiv Natl Univ Radio Elect 14 Nauky Ave UA-61166 Kharkov Ukraine

In the paper soft probabilistic clustering algorithm of multidimensional data sets that are sequentially fed to processing in on-line mode is investigated. The proposed system solves the tasks of Data Stream Mining wh... 详细信息

ISBN: (纸本)9781509037360

关键词： data stream mining big data very large databases (VLDB) computational intelligence fuzzy clustering em-algorithm Kohonen's self-learning

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EnAli: entity alignment across multiple heterogeneous data sources

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计算机科学前沿 2019年第1期13卷 157-169页

作者： Chao KONG Ming GAO Chen XU Yunbin FU Weining QIAN Aoying ZHOU School of Data Science and Engineering East China Normal University Shanghai 200062 China Technische Universit(a)t Berlin Berlin 10623 Germany

Entity alignment is the problem of identifying which entities in a data source refer to the same real-world entity in the *** entities across heterogeneous data sources is paramount to many research fields,such as data cleaning,data integration,information retrieval and machine *** aligning process is not only overwhelmingly expensive for large data sources since it involves all tuples from two or more data sources,but also need to handle heterogeneous entity *** this paper,we propose an unsupervised approach,called EnAli,to match entities across two or more heterogeneous data *** employs a generative probabilistic model to incorporate the heterogeneous entity attributes via employing exponential family,handle missing values,and also utilize the locality sensitive hashing schema to reduce the candidate tuples and speed up the aligning *** is highly accurate and efficient even without any ground-truth *** illustrate the performance of EnAli on re-identifying entities from the same data source,as well as aligning entities across three real data *** experimental results manifest that our proposed approach outperforms the comparable baseline.

关键词： entity alignment exponential family locality sensitive hashing em-algorithm

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Inference of discontinuity trace length distributions using statistical graphical models

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INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES 2006年第6期43卷 877-893页

作者： Jimenez-Rodriguez, R. Sitar, N. Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

The characterization of discontinuities within rock masses is often accomplished using stochastic discontinuity network models, in which the stochastic nature of the discontinuity network is represented by means of statistical distributions. We present a flexible methodology for maximum likelihood inference of the distribution of discontinuity trace lengths based oil observations at rock Outcrops. The inference problem is formulated using statistical graphical models and target distributions with several Gaussian mixture components. We use the Expectation-Maximization algorithm to exploit the relations of conditional independence between variables in the maximum likelihood estimation problem. Initial results using artificially generated discontinuity traces show that the method has good inference capabilities, and inferred trace length distributions closely reproduce those used for generation. In addition, the convergence of the algorithm is shown to be fast. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： em-algorithm fracture network discontinuitu size maximum likelihood

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