Expectation Maximization Technique Research Articles

On the metric-based approximate minimization of Markov Chains

In this paper we address the approximate minimization problem of Markov Chains (MCs) from a behavioral metric-based perspective. Specifically, given a finite MC and a positive integer k, we are looking for an MC with at most k states having minimal distance to the original. The metric considered in this work is the bisimilarity distance of Desharnais et al. For this metric we show that (1) optimal approximations always exist; (2) the problem has a bilinear program characterization; and (3) prove that its threshold problem is in PSPACE and NP-hard.In addition to the bilinear program solution, we present an approach inspired by expectation maximization techniques for computing suboptimal solutions to the problem. Experiments suggest that our method gives a practical approach that outperforms the bilinear program implementation run on state-of-the-art bilinear solvers.

Danish translation, cultural adaption and initial psychometric evaluation of the patient feedback form

AimNo suitable Danish questionnaire exists to evaluate patient satisfaction with various patient reported outcome measures. Thus, the aim of this research project was to conduct a study on the translation and cultural adaption of an American patient reported experience measures questionnaire, “Patient Feedback Form”, among Danish patients, and to examine selected psychometric properties within reliability.Material and methodsIn the first phase of the study, the Patient Feedback Form was forward and backward translated following the methodology of existing guidelines. Subsequently, cognitive interviewing was performed with seven cancer patients and seven healthy persons (19–86 years old/6 men and 8 women) to ensure that questions were easy to understand and made sense to Danish interviewees.In the second phase, phone interviews were carried out with 95 prostate cancer patients after they had responded to the same Patient Feedback Form. Missing data was imputed using the Expectation-Maximization technique. To examine the structure of the questionnaire, an exploratory factor analysis was conducted. Cronbach’s alpha was calculated to investigate internal consistency.ResultsThere were only minor disagreements in the translation process, and the reconciliation went smoothly (phase 1). With regard to one item, however, it was difficult to reach a consensus. Through the qualitative validation process, the right solution was found. The results from the psychometric testing (phase 2) showed that four factors had an Eigen value > 1, but only one factor was extracted as the Scree plot had a clear “elbow”, showing a one factor structure that explained 46.1% of the variance. The internal consistency was high as Cronbach’s alpha was 0.89.ConclusionThe translated, culturally adapted, and validated version of the Patient Feedback Form seems to be suitable for measuring satisfaction with patient reported outcome measures in a Danish setting. While the results should be treated with caution due to the small sample size, psychometric testing indicates that the questionnaire is a valid instrument. However, additional psychometric testing such as hypotheses testing, responsiveness, and test-retest on a larger and more diverse sample size is required to further verify the validity of the instrument.

A quantum framework for likelihood ratios

The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantum mechanical expression.

Estimating fluorescence lifetimes using the expectation‐maximisation algorithm

The expectation-maximisation (EM) algorithm uses incomplete data to get the estimation of the probabilistic model parameter, and it has been widely used in machine learning. EM techniques are applied to estimate fluorescence lifetimes in time-correlated single-photon counting based fluorescence lifetime imaging experiments without measuring the instrument response functions. The results of Monte Carlo simulations indicate that the proposed approach can obtain better or comparable accuracy and precision performances than the previously reported method.

Affinely Parametrized State-space Models: Ways to Maximize the Likelihood Function

Using Maximum Likelihood (or Prediction Error) methods to identify linear state space model is a prime technique. The likelihood function is a nonconvex function and care must be exercised in the numerical maximization. Here the focus will be on affine parameterizations which allow some special techniques and algorithms. Three approaches to formulate and perform the maximization are described in this contribution: (1) The standard and well known Gauss-Newton iterative search, (2) a scheme based on the EM (expectation-maximization) technique, which becomes especially simple in the affine parameterization case, and (3) a new approach based on lifting the problem to a higher dimension in the parameter space and introducing rank constraints.

A Grayscale Segmentation Approach Using the Firefly Algorithm and the Gaussian Mixture Model

In this article, the author proposes an unsupervised grayscale image segmentation method based on a combination of the Firefly Algorithm and the Gaussian Mixture Model. Firstly, the Firefly Algorithm has been applied in a histogram-based research of cluster centroids. The Firefly Algorithm is a stochastic global optimization technique, centred on the flashing characteristics of fireflies. In this histogram-based segmentation approach, it is employed to determine the number of clusters and to select the gray levels for grouping pixels into homogeneous regions. Successively these gray values are used in the initialization step for the parameter estimation of a Gaussian Mixture Model. The parametric probability density function of a Gaussian Mixture Model is represented as a weighted sum of Gaussian components, whose parameters are evaluated applying the iterative Expectation-Maximization technique. The coefficients of the linear super-position of Gaussians can be thought as prior probabilities of each component. Applying the Bayes rule, the posterior probabilities of the grayscale intensities have been evaluated, therefore their maxima are used to assign each pixel to the clusters, according to their gray levels.

Sketching for large-scale learning of mixture models

AbstractLearning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a ‘compressive learning’ framework, where we estimate model parameters from a sketch of the training data. This sketch is a collection of generalized moments of the underlying probability distribution of the data. It can be computed in a single pass on the training set and is easily computable on streams or distributed datasets. The proposed framework shares similarities with compressive sensing, which aims at drastically reducing the dimension of high-dimensional signals while preserving the ability to reconstruct them. To perform the estimation task, we derive an iterative algorithm analogous to sparse reconstruction algorithms in the context of linear inverse problems. We exemplify our framework with the compressive estimation of a Gaussian mixture model (GMM), providing heuristics on the choice of the sketching procedure and theoretical guarantees of reconstruction. We experimentally show on synthetic data that the proposed algorithm yields results comparable to the classical expectation-maximization technique while requiring significantly less memory and fewer computations when the number of database elements is large. We further demonstrate the potential of the approach on real large-scale data (over $10^{8}$ training samples) for the task of model-based speaker verification. Finally, we draw some connections between the proposed framework and approximate Hilbert space embedding of probability distributions using random features. We show that the proposed sketching operator can be seen as an innovative method to design translation-invariant kernels adapted to the analysis of GMMs. We also use this theoretical framework to derive preliminary information preservation guarantees, in the spirit of infinite-dimensional compressive sensing.

Maximum likelihood principle and moving horizon estimation based adaptive unscented Kalman filter

The classical unscented Kalman filter (UKF) requires prior knowledge on statistical characteristics of system noises for state estimation of a nonlinear dynamic system. If the statistical characteristics of system noises are unknown or inaccurate, the UKF solution will be deteriorated or even divergent. This paper presents a novel adaptive UKF by combining the maximum likelihood principle (MLP) and moving horizon estimation (MHE) to overcome this limitation. This method constructs an optimization based estimation of system noise statistics according to MLP. Subsequently, it further establishes a moving horizon strategy to improve the computational efficiency of the MLP based optimization estimation. Based on above, a new expectation maximization technique is developed to iteratively compute the MLP and MHE based noise statistic estimation by replacing complex smoothed estimates with filtering estimates for further improvement of the computational efficiency. The proposed method can achieve the online estimation of system noise statistic and enhance the robustness of the classical UKF. The efficacy of the proposed adaptive UKF is demonstrated through simulations and practical experiments in the INS/GPS integrated navigation.

Computationally Efficient Wide-Band DOA Estimation Methods Based on Sparse Bayesian Framework

For practical wide-band direction-of-arrival (DOA) estimation problems, the sparse Bayesian algorithms, implemented by expectation maximization or variational Bayesian inference techniques, generally require prohibitive computational complexity. In this paper, computationally efficient wide-band DOA estimation is considered within a sparse Bayesian framework. In particular, two computationally efficient wide-band DOA estimation methods are proposed, i.e., single and multiple observations sparse Bayesian multitask learning methods, denoted as SO-SBMTL and MO-SBMTL. The proposed methods can independently and jointly process the signals to obtain the DOA estimates, respectively, with significantly reduced computational complexity. In addition, the off-the-grid problem in wide-band DOA estimation is also considered within this framework. The remarkable feature of our proposed methods is that the off-the-grid parameter can be desirably obtained with a closed-form solution, so that numerical searching procedure is appropriately avoided and the computational complexity is substantially reduced. Experimental results have demonstrated that the proposed algorithms can achieve desirable performance with substantially reduced computational complexities. The MO-SBMTL achieves better performance than the SO-SBMTL in the scenarios of static or slow time-varying moving sources, and the off-the-grid algorithm can also efficiently estimate the true DOAs of the sources.

Machine Vision-Based Positioning and Inspection Using Expectation–Maximization Technique

Precision positioning is very important for automatic assembly and inspection in the electronic manufacturing process. In this paper, we propose a fast image alignment method using the expectation–maximization (E–M) technique. The proposed algorithm is especially applied to positioning and defect inspection of printed circuit boards (PCBs). It can well handle deformed or incomplete object shapes with translation, rotation, and scale changes. The Canny edge detector is used to generate the edge maps of images. The E-step of the E–M procedure finds mutual edge points in both compared images by assigning weights to individual edge points. The mutual edge points give larger weights, while the foreign edge points in two images have smaller weights. The M-step then calculates the geometric transformation parameters using the weighted edge points in individual images. For an edge point in one image, a fast spiral search is proposed to find its corresponding edge point with the shortest distance in the other image. The spiral search is carried out by a predetermined lookup table, and no computation is involved in the search process. The weight of each edge point is inversely proportional to the neighboring distance. Experimental results indicate that the proposed E–M positioning method can achieve a translation error less than 1 pixel and a rotation error smaller than 1° for PCB positioning.

Acoustic source localization in strong reverberant environment by parametric Bayesian dictionary learning

Sparse representation techniques have become increasingly promising for localizing the sound source in reverberant environment, where the multipath channel effects can be accurately characterized by the image model. In this paper, a dictionary is constructed by discretizing the inner space of the enclosure, which is parameterized by the unknown energy reflective ratio. More specifically, each atom of the dictionary can characterize a specific source-to-microphone multipath channel. Subsequently, source localization can be reformulated as a joint sparse signal recovery and parametric dictionary learning problem. In particular, a sparse Bayesian framework is utilized for modeling, where its solution can be obtained by variational Bayesian expectation maximization technique. Moreover, the joint sparsity in frequency domain is exploited to improve the dictionary learning performances. A remarkably advantage of this approach is that no laborious parameter tuning procedure is required and statistical information can be provided. Numerical simulation results have shown that the proposed algorithm achieves high source localization accuracy, low sidelobes and high robustness for multiple sources with low computational complexity in strong reverberant environments, compared with other state-of-the-art methods.

An unsupervised learning algorithm for multiscale neural activity.

Technological advances have enabled the simultaneous recording of multiscale neural activity consisting of spikes, local field potential (LFP), and electrocorticogram (ECoG). Developing models that describe the encoding of behavior within multiscale activity is essential both for understanding neural mechanisms and for various neurotechnologies such as brain-machine interfaces (BMI). Multiscale recordings consist of signals with different statistical profiles and time-scales. While encoding models have been developed for each scale of activity alone, developing statistical models that simultaneously characterize discrete spike and continuous LFP/ECoG recordings and their various time-scales is a major challenge. To address this challenge, we have recently proposed a multiscale state-space encoding model for combined spike/LFP/ECoG recordings. However, methods to learn these state-space models from data are still lacking. Here, we develop an unsupervised learning algorithm for multiscale state-space models. Given a multiscale dataset, our algorithm finds the maximum-likelihood estimate of the state-space model parameters using a new expectation-maximization (EM) technique. We show that the new algorithm can learn the encoding model accurately from simulated multiscale data. We also show that the learned model can be used to decode arm movement trajectories from simulated multiscale activity. These multiscale models have the potential to improve the performance and robustness of various neurotechnologies.

快时变衰落信道下OFDM系统的SAGE检测算法研究

OFDM技术可以有效地抑制多径效应的影响，从而被广泛地应用到无线通信系统中。快时变衰落信道下的OFDM系统将产生严重的子载波间干扰(ICI)，从而影响系统性能。本文对快时变OFDM系统，提出一种基于空间交替广义期望最大化算法(SAGE)的信号检测算法。理论分析的实验仿真结果表明，所提SAGE算法是有效的。 Orthogonal frequency division multiplexing (OFDM) technology can effectively suppress the im-pact of multipath effects, which is widely used in wireless communication systems. However, OFDM systems will lead to severe inter carrier interference (ICI) under fast time-varying fading channels, which will determine system performance. In this paper, an efficient data detection al-gorithm is proposed based on the space alternating generalized expectation maximization (SAGE) technique for OFDM systems under fast fading channels. Simulation results show that the pro-posed algorithm is effective for improving the performance of OFDM systems under fast time- varying fading channels.

A Hidden Markov Model inference approach to testing the Random Walk Hypothesis: Empirical evidence from the Nigerian Stock Market

The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and taking estimation into account via the Sequential Monte Carlo Expectation Maximisation (SMCEM) technique, this study finds no support of randomness. In conclusion, the stock price movements of the NSE do not follow the random walk process.

A Novel Hybridization of Expectation-Maximization and K-Means Algorithms for Better Clustering Performance

Expectation Maximization (EM) is a widely employed mixture model-based data clustering algorithm and produces exceptionally good results. However, many researchers reported that the EM algorithm requires huge computational efforts than other clustering algorithms. This paper presents an algorithm for the novel hybridization of EM and K-Means techniques for achieving better clustering performance (NovHbEMKM). This algorithm first performs K-Means and then using these results it performs EM and K-Means in the alternative iterations. Along with the NovHbEMKM, experiments are carried out with the algorithms for EM, EM using the results of K-Means and Cluster package of Purdue University. Experiments are carried out with datasets from UCI ML repository and synthetic datasets. Execution time, Clustering Fitness and Sum of Squared Errors (SSE) are computed as performance criteria. In all the experiments the proposed NovHbEMKM algorithm is taking less execution time by producing results with higher clustering fitness and lesser SSE than other algorithms including the Cluster package.

Hybridization of Expectation-Maximization and K-Means Algorithms for Better Clustering Performance

Abstract The present work proposes hybridization of Expectation-Maximization (EM) and K-means techniques as an attempt to speed-up the clustering process. Even though both the K-means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with the proposed algorithm for hybridization, the present work also experiments with the Standard EM algorithm. Six different datasets, three of which synthetic datasets, are used for the experiments. Clustering fitness and Sum of Squared Errors (SSE) are computed for measuring the clustering performance. In all the experiments it is observed that the proposed algorithm for hybridization of EM and K-means techniques is consistently taking less execution time with acceptable Clustering Fitness value and less SSE than the standard EM algorithm. It is also observed that the proposed algorithm is producing better clustering results than the Cluster package of Purdue University.

Expectation–Maximization Based Image Fusion Algorithm for Detection of Underwater Targets from SONAR Images

With the advancement of technology, the imaging sonars have become the reality and their usage has been extensive in the area of obstacle avoidance in respect of Autonomous Underwater Vehicle (AUV). The underwater environment being heterogeneous, the sonar images have a very complex background, low contrast, and deteriorative edges. To locate and identify the underwater objects from the Sonar images, the initial step needs to be undertaken is the segmentation. Several general purpose algorithms have been developed for segmentation of various images. In this paper the various existing image processing techniques in respect of the sonar images are reviewed. As there is no general solution to the image segmentation problem, making use of the available techniques two new algorithms for processing the underwater Sonar images are proposed. In first algorithm segmented images are combined to a single image called image fusion which performs better than the existing methods with PSNR of 38.006. But in this method also edges of the target are missing. Hence another algorithm is proposed in combination with Expectation maximization technique whose PSNR is 41.2634. Therefore, the proposed algorithm is best suitable to the underwater scenario and is also useful for navigation and guidance of underwater vehicles.

Sparse Channel Estimation and Equalization for OFDM-Based Underwater Cooperative Systems With Amplify-and-Forward Relaying

This paper is concerned with a challenging problem of channel estimation and equalization for amplify-and-forward cooperative relay based orthogonal frequency division multiplexing (OFDM) systems in sparse underwater acoustic (UWA) channels. The sparseness of the channel impulse response and prior information for the non-Gaussian channel gains, modeled by an exact continuous Gaussian mixture (CGM), are exploited to improve the performance of the channel estimation algorithm. The resulting novel algorithm initially estimates the overall sparse complex-valued channel taps from the source to the destination as well as their locations using the matching pursuit (MP) approach. The effective time-domain non-Gaussian noise is approximated well as a Gaussian noise in the frequency-domain, where the estimation takes place. An efficient and low complexity algorithm is developed based on a combination of the MP and the maximum a posteriori probability (MAP) based space-alternating generalized expectation-maximization technique, to improve the estimates of the channel taps and their locations in an iterative manner. Computer simulations show that the UWA channel is estimated very effectively and the proposed algorithm exhibits excellent symbol error rate and channel estimation performance.

Using Expectation Maximization and Resource Overlap Techniques to Classify Species According to Their Niche Similarities in Mutualistic Networks

Mutualistic networks in nature are widespread and play a key role in generating the diversity of life on Earth. They constitute an interdisciplinary field where physicists, biologists and computer scientists work together. Plant-pollinator mutualisms in particular form complex networks of interdependence between often hundreds of species. Understanding the architecture of these networks is of paramount importance for assessing the robustness of the corresponding communities to global change and management strategies. Advances in this problem are currently limited mainly due to the lack of methodological tools to deal with the intrinsic complexity of mutualisms, as well as the scarcity and incompleteness of available empirical data. One way to uncover the structure underlying complex networks is to employ information theoretical statistical inference methods, such as the expectation maximization (EM) algorithm. In particular, such an approach can be used to cluster the nodes of a network based on the similarity of their node neighborhoods. Here, we show how to connect network theory with the classical ecological niche theory for mutualistic plant-pollinator webs by using the EM algorithm. We apply EM to classify the nodes of an extensive collection of mutualistic plant-pollinator networks according to their connection similarity. We find that EM recovers largely the same clustering of the species as an alternative recently proposed method based on resource overlap, where one considers each party as a consuming resource for the other party (plants providing food to animals, while animals assist the reproduction of plants). Furthermore, using the EM algorithm, we can obtain a sequence of successfully-refined classifications that enables us to identify the fine-structure of the ecological network and understand better the niche distribution both for plants and animals. This is an example of how information theoretical methods help to systematize and unify work in ecology.

Optimal stimulus scheduling for active estimation of evoked brain networks

Objective. We consider the problem of optimal probing to learn connections in an evoked dynamic network. Such a network, in which each edge measures an input–output relationship between sites in sensor/actuator-space, is relevant to emerging applications in neural mapping and neural connectivity estimation. Approach. We show that the problem of scheduling nodes to a probe (i.e., stimulate) amounts to a problem of optimal sensor scheduling. Main results. By formulating the evoked network in state-space, we show that the solution to the greedy probing strategy has a convenient form and, under certain conditions, is optimal over a finite horizon. We adopt an expectation maximization technique to update the state-space parameters in an online fashion and demonstrate the efficacy of the overall approach in a series of detailed numerical examples. Significance. The proposed method provides a principled means to actively probe time-varying connections in neuronal networks. The overall method can be implemented in real time and is particularly well-suited to applications in stimulation-based cortical mapping in which the underlying network dynamics are changing over time.