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Network inference from temporally dependent grouped observations

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2022年 171卷

作者： Zhao, Yunpeng Arizona State Univ Sch Math & Nat Sci Tempe AZ 85287 USA 4701 W Thunderbird Rd Glendale AZ 85306 USA

In social network analysis, the observed data usually reflect certain social behaviors, such as the formation of groups, rather than an explicit network structure. Zhao and Weko proposed a model-based approach called the hub model to infer implicit networks from grouped observations (Zhao and Weko, 2019). The hub model assumes independence between groups, which sometimes is not valid in practice. The hub model is generalized into the case of grouped observations with temporal dependence. As in the hub model, the group at each time point is gathered under one leader in the new model. Unlike in the hub model, the group leaders are not sampled independently but follow a Markov chain, and other members in adjacent groups can also be correlated. An expectation-maximization (EM) algorithm is developed for this model and a polynomial-time algorithm is proposed for the E-step. The performance of the new model is evaluated under different simulation settings. The proposed model is applied to a data set of the Kibale Chimpanzee Project. (C) 2022 Elsevier B.V. All rights reserved.

关键词： forward-backward algorithm Grouping behavior Social networks

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Hidden Markov Model and multifractal method-based predictive quantization complexity models vis-a-vis the differential prognosis and differentiation of Multiple Sclerosis' subgroups

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KNOWLEDGE-BASED SYSTEMS 2022年 246卷

作者： Karaca, Yeliz Baleanu, Dumitru Karabudak, Rana Univ Massachusetts Med Sch UMASS Worcester MA 01655 USA Cankaya Univ Dept Math TR-1406530 Ankara Turkey Inst Space Sci Bucharest Romania Hacettepe Univ Dept Neurol Ankara Turkey

Hidden Markov Model (HMM) is a stochastic process where implicit or latent stochastic processes can be inferred indirectly through a sequence of observed states. HMM as a mathematical model for uncertain phenomena is applicable for the description and computation of complex dynamical behaviours enabling the mathematical formulation of neural dynamics across spatial and temporal scales. The human brain with its fractal structure demonstrates complex dynamics and fractals in the brain are characterized by irregularity, singularity and self-similarity in terms of form at different observation levels, making detection difficult as observations in real-time occurrences can be time variant, discrete, continuous or noisy. Multiple Sclerosis (MS) is an autoimmune degenerative disease with time and space related dissemination, leading to neuronal apoptosis, coupled with some subtle features that could be overlooked by physicians. This study, through the proposed integrated approach with multi-source complex spatial data, aims to attain accurate prediction, diagnosis and prognosis of MS subgroups by HMM with Viterbi algorithm and forward-backward algorithm as the dynamic and efficient products of knowledge-based and Artificial Intelligence (AI)-based systems within the framework of precision medicine. Multifractal Bayesian method (MFM) accordingly applied to identify and eliminate "insignificant "irregularities while maintaining "significant "singularities. An efficient modelling of HMM is proposed to diagnose and predict the course of MS while using MFM method. Unlike the methods employed in previous studies, our proposed integrated novel method encompasses the subsequent approaches based on reliable MS dataset ((X) over cap) collected: (i) MFM method was applied ((X) over cap) to MS dataset to characterize the irregular, self-similar and significant attributes, thus, attributes with "insignificant " irregularities were eliminated and "significant " singularities were mainta

关键词： Hidden Markov Model Viterbi algorithm forward-backward algorithm Multifractal analysis Nonlinear stochastic processes Computational dynamic complexityanalyses Multiple Sclerosis' subgroups

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Sequential Bayesian inference of transition rates in the hidden Markov model for multi-state systemdegradation

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2021年 214卷 107662-107662页

作者： Zhao, Yunfei Gao, Wei Smidts, Carol Ohio State Univ Dept Mech & Aerosp Engn Nucl Engn Program 201 W 19th Ave Columbus OH 43210 USA

The more easily available system performance data and advances in data analytics have provided us with opportunities to optimize maintenance programs for engineered systems, for example nuclear power plants. One key task in maintenance optimization is to obtain an accurate model for system degradation. In this research, we propose a Bayesian method to address this problem. Noting that systems usually exhibit multiple states and that the actual state of a system usually is not directly observable, in the method we first model the system degradation process and the observation process based on a hidden Markov model. Then we develop a sequential Bayesian inference algorithm based on importance sampling and the forward algorithm to infer the posterior distributions of the transition rates in the hidden Markov model based on available observations. The proposed Bayesian method allows us to take advantage of evidence from multiple sources, and also allows us to perform Bayesian inference sequentially, without the need to use the entire history of observations every time new observations are collected. We demonstrate the proposed method using both synthetic data for a nuclear power plant feedwater pump and realistic data for a nuclear power plant chemistry analytical device.

关键词： Sequential Bayesian inference Importance sampling forward-backward algorithm Model parameter inference Hidden Markov model Multi-state system Multi-source evidence Information fusion Nuclear power plant Maintenance optimization

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On the Concatenated Transmission Scheme With the Low-Complexity Symbol-Level Watermark Decoder for Recovering the Synchronization

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IEEE ACCESS 2019年 7卷 160927-160933页

作者： Liu, Yuan Tianjin Normal Univ Coll Elect & Commun Engn Tianjin Key Lab Wireless Mobile Commun & Power Tr Tianjin 300387 Peoples R China

The DaveyMacKay (DM) concatenated code employing the symbol-level watermark decoding algorithm is able to correct a large number of binary insertions, deletions, and substitutions, while it has the high computational complexity for recovering the synchronization. In the DM concatenated scheme, at the large insertion/deletion probability, in order to achieve the reliable output, the watermark decoder needs to perform the forward and backward passes on a very large trellis. In this paper, a threshold is selected to prevent the paths having very low forward and backward quantities from participating in the calculation of log-likelihood ratios from the watermark decoder. Simulation results show that great reduction in the complexity of the decoding algorithm is achieved at a very slight expense of accuracy.

关键词： Decoding Watermarking Synchronization Concatenated codes Reliability Computational complexity DM concatenated scheme forward-backward algorithm binary insertions deletions low complexity

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Explicit-duration Hidden Markov Models for quantum state estimation

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2021年 158卷 107183-107183页

作者： Luati, Alessandra Novelli, Marco Univ Bologna Dept Stat Sci Bologna Italy

An explicit-duration Hidden Markov Model with a nonparametric kernel estimator of the state duration distribution is specified. The motivation comes from the physical problem of extracting the maximum information from an open quantum system subject to an external perturbation, which induces a change in the dynamics of the system. A nonparametric kernel estimator for discrete data is introduced, which is consistent and improves the estimates accuracy in presence of sparse data. To reconstruct the hidden dynamics, a Viterbi algorithm is used, which is robust against the underflow problem. Finite sample properties are investigated through an extensive Monte Carlo study showing that our formulation outperforms the original one both in small and in large samples. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Hidden Markov Models forward-backward algorithm Quantum statistics Kernel estimation Viterbi algorithm

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Direction-of-Arrival Estimation of Virtual Array Signals Based on Doppler Effect

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2015年第10期11卷 1-10页

作者： Zhao, Feng Hao, Xia Chen, Hongbin Guilin Univ Elect Technol Key Lab Cognit Radio & Informat Proc Minist Educ Guilin 541004 Peoples R China

The estimation accuracy of direction-of-departure (DOD) and direction-of-arrival (DOA) is reduced because of Doppler shifts caused by the high-speed moving sources. In this paper, an improved DOA estimation method which combines the forward-backward spatial smoothing (FBSS) technique with the MUSIC algorithm is proposed for virtual MIMO array signals in high mobility scenarios. Theoretical analysis and experiment results demonstrate that the resolution capability can be significantly improved by using the proposed method compared to the MUSIC algorithm for the moving sources with limited array elements, especially the DOA which can still be accurately estimated when the sources are much closely spaced.

关键词： DIRECTION of arrival estimation (Signal processing) DOPPLER effect MULTIPLE Signal Classification MIMO systems forward-backward algorithm SPATIAL analysis (Statistics) SMOOTHING (Numerical analysis)

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De-Interlacing Using Nonlocal Costs and Markov-Chain-Based Estimation of Interpolation Methods

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2013年第4期22卷 1557-1570页

作者： Vedadi, Farhang Shirani, Shahram McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4K1 Canada

A new method of de-interlacing is proposed. De-interlacing is revisited as the problem of assigning a sequence of interpolation methods (interpolators) to a sequence of missing pixels of an interlaced frame (field). With this assumption, our de-interlacing algorithm (de-interlacer), undergoes transitions from one interpolation method to another, as it moves from one missing pixel position to the horizontally adjacent missing pixel position in a missing row of a field. We assume a discrete countable-state Markov-chain model on the sequence of interpolators (Markov-chain states) which are selected from a user-defined set of candidate interpolators. An estimation of the optimum sequence of interpolators with the aforementioned Markov-chain model requires the definition of an efficient cost function as well as a global optimization technique. Our algorithm introduces for the first time using a nonlocal cost (NLC) scheme. The proposed algorithm uses the NLC to not only measure the fitness of an interpolator at a missing pixel position, but also to derive an approximation for transition matrix (TM) of the Markov-chain of interpolators. The TM in our algorithm is a frame-variate matrix, i.e., the algorithm updates the TM for each frame automatically. The algorithm finally uses a Viterbi algorithm to find the global optimum sequence of interpolators given the cost function defined and neighboring original pixels in hand. Next, we introduce a new MAP-based formulation for the estimation of the sequence of interpolators this time not by estimating the best sequence of interpolators but by successive estimations of the best interpolator at each missing pixel using forward-backward algorithm. Simulation results prove that, while competitive with each other on different test sequences, the proposed methods (one using Viterbi and the other forward-backward algorithm) are superior to state-of-the-art de-interlacing algorithms proposed recently. Finally, we propose motion compensat

关键词： De-interlacing forward-backward algorithm Markov-chain nonlocal cost Viterbi algorithm

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Convergence of proximal gradient algorithm in the presence of adjoint mismatch *

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INVERSE PROBLEMS 2021年第6期37卷

作者： Chouzenoux, Emilie Pesquet, Jean-Christophe Riddell, Cyril Savanier, Marion Trousset, Yves Univ Paris Saclay CentraleSupelec CVN Inria Gif Sur Yvette France GE Healthcare Buc France

We consider the proximal gradient algorithm for solving penalized least-squares minimization problems arising in data science. This first-order algorithm is attractive due to its flexibility and minimal memory requirements allowing to tackle large-scale minimization problems involving non-smooth penalties. However, for problems such as x-ray computed tomography, the applicability of the algorithm is dominated by the cost of applying the forward linear operator and its adjoint at each iteration. In practice, the adjoint operator is thus often replaced by an alternative operator with the aim to reduce the overall computation burden and potentially improve conditioning issues. In this paper, we propose to analyze the effect of such an adjoint mismatch on the convergence of the proximal gradient algorithm in an infinite-dimensional setting, thus generalizing the existing results on PGA. We derive conditions on the step-size and on the gradient of the smooth part of the objective function under which convergence of the algorithm to a fixed point is guaranteed. We also derive bounds on the error between this point and the solution to the original minimization problem. We illustrate our theoretical findings with two image reconstruction tasks in computed tomography.

关键词： adjoint mismatch convex optimization convergence analysis fixed point methods image reconstruction computed tomography forward-backward algorithm

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Periodic group-sparse method via generalized minimax-concave penalty for machinery fault diagnosis

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MEASUREMENT SCIENCE AND TECHNOLOGY 2024年第9期35卷

作者： He, Wangpeng Wen, Zhihui Liu, Xuan Guo, Xiaoya Zhu, Juanjuan Chen, Weisheng Xidian Univ Sch Aerosp Sci & Technol Xian 710071 Peoples R China Xidian Univ Guangzhou Inst Technol Xian 510555 Guangdong Peoples R China

Diagnosing faults in large mechanical equipment poses challenges due to strong background noise interference, wherein extracting weak fault features with periodic group-sparse property is the most critical step for machinery intelligent maintenance. To address this problem, a periodic group-sparse method based on a generalized minimax-concave penalty function is proposed in this paper. This method uses periodic group sparse techniques to capture the periodic clustering trends of fault impact signals. To further enhance the sparsity of the results and preserve the high amplitude of the impact signals, non-convex optimization techniques are integrated. The overall convexity of the optimization problem is maintained through the introduction of a non-convex controllable parameter, and an appropriate optimization algorithm is derived. The effectiveness of this method has been demonstrated through experiments with simulated signals and mechanical fault signals.

关键词： non-convex penalty periodic group-sparse method forward-backward algorithm fault diagnosis

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A strongly convergent Krasnosel' skil-Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021年 395卷 113589-113589页

作者： Bot, Radu Ioan Meier, Dennis Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

In this article, we propose a Krasnosel'skil-Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators (T-n)(n >= 0) in Hilbert spaces. We formulate an asymptotic property which the family (T-n)(n >= 0) has to fulfill such that the sequence generated by the algorithm converges strongly to the element in boolean AND(n >= 0) Fix T-n with minimum norm. Based on this, we derive a forward-backward algorithm that allows variable step sizes and generates a sequence of iterates that converge strongly to the zero with minimum norm of the sum of a maximally monotone operator and a cocoercive one. We demonstrate the superiority of the forward-backward algorithm with variable step sizes over the one with constant step size by means of numerical experiments on variational image reconstruction and split feasibility problems in infinite dimensional Hilbert spaces. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Fixed points of families of nonexpansive mappings Tikhonov regularization Splitting methods forward-backward algorithm

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