Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We m...
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Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-varying stimuli and the neurons' own spike histories to drive both the spiking behavior in each state and the transitioning behavior between states. We employ an appropriately modified expectation-maximization algorithm to estimate the model parameters. The expectation step is solved by the standard forward-backward algorithm for HMMs. The maximization step reduces to a set of separable concave optimization problems if the model is restricted slightly. We first test our algorithm on simulated data and are able to fully recover the parameters used to generate the data and accurately recapitulate the sequence of hidden states. We then apply our algorithm to a recently published data set in which the observed neuronal ensembles displayed multistate behavior and show that inclusion of spike history information significantly improves the fit of the model. Additionally, we show that a simple reformulation of the state space of the underlying Markov chain allows us to implement a hybrid half-multistate, half-histogram model that may be more appropriate for capturing the complexity of certain data sets than either a simple HMM or a simple peristimulus time histogram model alone.
A degradation model is presented in this paper for the prediction of the residual life using an adapted Brownian motion-based approach with a drifting parameter. This model differs from other Brownian motion-based app...
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A degradation model is presented in this paper for the prediction of the residual life using an adapted Brownian motion-based approach with a drifting parameter. This model differs from other Brownian motion-based approaches in that the drifting parameter of the degradation process is adapted to the history of monitored information. This adaptation is performed by Kalman filtering. We also use a threshold distribution instead of the usual single threshold line which is sometime difficult to obtain in practice. We demonstrate the model using some examples and show that the model performs reasonably well and has a better prediction ability than the standard Brownian motion-based model. The model is then fitted to the data generated from a simulator using the expectation-maximization algorithm. We also fit a standard Brownian motion-based model to the same data to compare the difference and performance. The result shows that the adapted model performs better in terms of certain test statistics and the total mean square errors. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper we present an efficient implementation of the EM algorithm for estimating multivariate gaussian mixture model parameters in the context of local-neighborhood image texture analysis. We illustrate its app...
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ISBN:
(纸本)9781457705700
In this paper we present an efficient implementation of the EM algorithm for estimating multivariate gaussian mixture model parameters in the context of local-neighborhood image texture analysis. We illustrate its application in a study case of mass detection in mammography, providing a detailed description of a feasible and efficient implementation. Our proposed method overcomes numerical variable underflow problems by means of logarithmic and exponential manipulations and saves computational time using a look up table approach. We reduced computation time to 57.14% with respect to direct computation, achieving numerical conditions for convergence.
In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian den...
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In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace scale mixtures can subserve a Bayesian framework for sparse learning with nonconvex penalization. The densities of EP-GIG can be explicitly expressed. Moreover, the corresponding posterior distribution also follows a generalized inverse Gaussian distribution. We exploit these properties to develop EM algorithms for sparse empirical Bayesian learning. We also show that these algorithms bear an interesting resemblance to iteratively reweighted l 2 or l 1 methods. Finally, we present two extensions for grouped variable selection and logistic regression.
In this paper we present a novel method for automatic threshold handling and tracking of sensor data at drilling rigs. A hybrid system for automated drilling operation classification is extended by the expectation Max...
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In this paper we present a novel method for automatic threshold handling and tracking of sensor data at drilling rigs. A hybrid system for automated drilling operation classification is extended by the expectationmaximization algorithm in combination with the Bayes' theorem to find automatically threshold values required by a rule based system used in an automated drilling operations classification system. The streaming data from the rig site is gathered and analyzed, the main clusters in the sensor data are identified and monitored as in a real life case. The first part of the suggested method is based on the expectationmaximization algorithm which is used to decompose Gaussian mixture models in the sensor data set. Bayes' theorem is used as a subsequent part to calculate optimal threshold values. The threshold values calculation concept is heavily depending on the likelihood probabilities of each data cluster. The work in this paper not only suggests a solution and analytical method for tracking this kind of thresholds in the sensor data but also verifies how to compute such reliable thresholds in real-time.
This paper surveys a short study about using and applying symbolic processing to direct execution of the expectation-maximization algorithm. Formulas are derived in the manner defined by the expectation-maximization a...
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This paper surveys a short study about using and applying symbolic processing to direct execution of the expectation-maximization algorithm. Formulas are derived in the manner defined by the expectation-maximization algorithm and how there are applied. Symbolic processing uses the set of equations on the same way that describe expectationmaximization algorithm without any adaptation and loops of computation as usually done. The methodology of processing is described step-by-step for direct execution of expectation-maximization algorithm. Some of the advantages of symbolic processing are described in regard to numerical processing. Finally, numerical data are applied on the complete model and results are displayed.
Model-based clustering using a family of Gaussian mixture models, with parsimonious factor analysis like covariance structure, is described and an efficient algorithm for its implementation is presented. This algorith...
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Model-based clustering using a family of Gaussian mixture models, with parsimonious factor analysis like covariance structure, is described and an efficient algorithm for its implementation is presented. This algorithm uses the alternating expectation-conditional maximization (AECM) variant of the expectation-maximization (EM) algorithm. Two central issues around the implementation of this family of models, namely model selection and convergence criteria, are discussed. These central issues also have implications for other model-based clustering techniques and for the implementation of techniques like the EM algorithm, in general. The Bayesian information criterion (BIC) is used for model selection and Aitken's acceleration, which is shown to outperform the lack of progress criterion, is used to determine convergence. A brief introduction to parallel computing is then given before the implementation of this algorithm in parallel is facilitated within the master-slave paradigm. A simulation study is then carried out to confirm the effectiveness of this parallelization. The resulting software is applied to two datasets to demonstrate its effectiveness when compared to existing software. (C) 2009 Elsevier B.V. All rights reserved.
EM-type algorithms are popular tools for modal estimation and the most widely used parameter estimation procedures in statistical modeling. However, they are often criticized for their slow convergence. Despite the ap...
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EM-type algorithms are popular tools for modal estimation and the most widely used parameter estimation procedures in statistical modeling. However, they are often criticized for their slow convergence. Despite the appearance of numerous acceleration techniques along the last decades, their use has been limited because they are either difficult to implement or not general. In the present paper, a new generation of fast, general and simple maximum likelihood estimation (MLE) algorithms is presented. In these cyclic iterative algorithms, extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. Some new complementary strategies like cycling, squaring and alternating are added to that processes. The presented schemes generally exhibit either fast-linear or superlinear convergence. Numerical illustrations allow us to compare a selection of its variants and generally confirm that this category is extremely simple as well as fast. (C) 2008 Elsevier B.V. All rights reserved.
The task of obtaining an optimal set of parameters to fit a mixture model has many applications in science and engineering domains and is a computationally challenging problem. A novel algorithm using a convolution ba...
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The task of obtaining an optimal set of parameters to fit a mixture model has many applications in science and engineering domains and is a computationally challenging problem. A novel algorithm using a convolution based smoothing approach to construct a hierarchy (or family) of smoothed log-likelihood surfaces is proposed. This approach smooths the likelihood function and applies the EM algorithm to obtain a promising solution on the smoothed surface. Using the most promising solutions as initial guesses, the EM algorithm is applied again on the original likelihood. Though the results are demonstrated using only two levels, the method can potentially be applied to any number of levels in the hierarchy. A theoretical insight demonstrates that the smoothing approach indeed reduces the overall gradient of a modified version of the likelihood surface. This optimization procedure effectively eliminates extensive searching in non-promising regions of the parameter space. Results on some benchmark datasets demonstrate significant improvements of the proposed algorithm compared to other approaches. Empirical results on the reduction in the number of local maxima and improvements in the initialization procedures are provided. Published by Elsevier B.V.
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