Hidden Markov Models and Dynamical Systems

Fraser, Andrew M.

doi:10.1137/1.9780898717747

Cited by 71 publications

(47 citation statements)

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“…The random process is memoryless where future states depend only on the present state [80,81]. In Markov models, the states are visible to the observer; however, in the hidden Markov model (HMM), some states are hidden or not explicitly visible [82].…”

Section: Markov Modelmentioning

confidence: 99%

Recent advances on artificial intelligence and learning techniques in cognitive radio networks

Abbas

Nasser

Ahmad

2015

J Wireless Com Network

122

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Cognitive radios are expected to play a major role towards meeting the exploding traffic demand over wireless systems. A cognitive radio node senses the environment, analyzes the outdoor parameters, and then makes decisions for dynamic time-frequency-space resource allocation and management to improve the utilization of the radio spectrum. For efficient real-time process, the cognitive radio is usually combined with artificial intelligence and machine-learning techniques so that an adaptive and intelligent allocation is achieved. This paper firstly presents the cognitive radio networks, resources, objectives, constraints, and challenges. Then, it introduces artificial intelligence and machine-learning techniques and emphasizes the role of learning in cognitive radios. Then, a survey on the state-of-the-art of machine-learning techniques in cognitive radios is presented. The literature survey is organized based on different artificial intelligence techniques such as fuzzy logic, genetic algorithms, neural networks, game theory, reinforcement learning, support vector machine, case-based reasoning, entropy, Bayesian, Markov model, multi-agent systems, and artificial bee colony algorithm. This paper also discusses the cognitive radio implementation and the learning challenges foreseen in cognitive radio applications. IntroductionAccording to Cisco Visual Networking Index, the global IP traffic will reach 168 exabytes per month by 2019 [1], and the number of devices will be three times the global population. In addition, the resources in terms of power and bandwidth are scarce. Therefore, novel solutions are needed to minimize energy consumption and optimize resource allocation. Cognitive radio (CR) was introduced by Joseph Mitola III and Gerald Q. Maguire in 1999 for a flexible spectrum access [2]. Basically, they defined cognitive radio as the integration of model-based reasoning with software radio technologies [3]. In 2005, Simon Haykin had given a review of the cognitive radio concept and had treated it as brain-empowered wireless communications [4]. Cognitive radio is a radio or system that senses the environment, analyzes its transmission parameters, *Correspondence: nfa23@aub.edu.lb Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon and then makes decisions for dynamic time-frequencyspace resource allocation and management to improve the utilization of the radio electromagnetic spectrum.Generally, radio resource management aims at optimizing the utilization of various radio resources such that the performance of the radio system is improved. For instance, the authors in [5] proposed an optimal resource (power and bandwidth) allocation in cognitive radio networks (CRNs), specifically in the scenario of spectrum underlay, while taking into consideration the limitations of interference temperature limits. The optimization formulations provide optimal solutions for resources allocation at, sometimes, the detriment of global convergence, computation time, and...

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Section: Markov Modelmentioning

confidence: 99%

Recent advances on artificial intelligence and learning techniques in cognitive radio networks

Abbas

Nasser

Ahmad

2015

J Wireless Com Network

122

View full text Add to dashboard Cite

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“…Although filtering and smoothing distributions for z t are within this framework, they are only tractable for either a discrete state space (forward(-backward) algorithm) or for linear functions f, g and additive Gaussian noise (Kalman filter/smoother) [14]. Efficient and exact solutions for the general nonlinear and/or non-Gaussian cases do not exist [8].…”

Section: Dynamic Bayesian Networkmentioning

confidence: 99%

“…We assume that long-range dependencies are negligible. Whereas we do not model interactions beyond order K, Hidden Markov Models do have a long-term memory due to the Markov process on the hidden state sequence, thereby rendering the observation sequence non-Markov ( [14], Section 1.3.3).…”

Section: Latent Space View and Comparison To Hidden Markov Modelsmentioning

confidence: 99%

Efficient Nonlinear Markov Models for Human Motion

Lehrmann

Gehler

Nowozin

2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

152

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Dynamic Bayesian networks such as Hidden Markov Models (HMMs) are successfully used as probabilistic models for human motion. The use of hidden variables makes them expressive models, but inference is only approximate and requires procedures such as particle filters or Markov chain Monte Carlo methods. In this work we propose to instead use simple Markov models that only model observed quantities. We retain a highly expressive dynamic model by using interactions that are nonlinear and non-parametric. A presentation of our approach in terms of latent variables shows logarithmic growth for the computation of exact loglikelihoods in the number of latent states. We validate our model on human motion capture data and demonstrate state-of-the-art performance on action recognition and motion completion tasks.

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“…According to [24], due to the fact that at a time t, the current state of a dynamical system provides all of the information necessary to calculate future states, the sequence of states of a dynamical system satisfies the Markov condition. Nonetheless, considering that in several real-time series there is a combination of both deterministic and stochastic components, it cannot be completely modeled by means of a Markov chain.…”

Section: Hmm-based Entropy Measuresmentioning

confidence: 99%

“…The advantage of using the entropy estimations in Equations (15) and (17) or their combination, instead of the ApEn-based measures mentioned before, is that the imposed MC characterizes the divergence of the trajectories and the directions into the state space in terms of the transitions between regions provided by the MC states, whilst the HMP quantifies the instability of the trajectories in terms of the noise level or scatter in every state of the process [10,24].…”

Section: Hmm-based Entropy Measuresmentioning

confidence: 99%

Entropies from Markov Models as Complexity Measures of Embedded Attractors

Arias-Londoño

Godino-Llorente

2015

Entropy

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This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the "profile trajectory", that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.

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Hidden Markov Models and Dynamical Systems

Cited by 71 publications

References 0 publications

Recent advances on artificial intelligence and learning techniques in cognitive radio networks

Recent advances on artificial intelligence and learning techniques in cognitive radio networks

Efficient Nonlinear Markov Models for Human Motion

Entropies from Markov Models as Complexity Measures of Embedded Attractors

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