Recurrent Neural Hidden Markov Model for High-order Transition

We propose a method to pay attention to high-order relations among latent states to improve the conventional HMMs that focus only on the latest latent state, since they assume Markov property. To address the high-order relations, we apply an RNN to each sequence of latent states, because the RNN can represent the information of an arbitrary-length sequence with their cell: a fixed-size vector. However, the simplest way, which provides all latent sequences explicitly for the RNN, is intractable due to the combinatorial explosion of the search space of latent states. Thus, we modify the RNN to represent the history of latent states from the beginning of the sequence to the current state with a fixed number of RNN cells whose number is equal to the number of possible states. We conduct experiments on unsupervised POS tagging and synthetic datasets. Experimental results show that the proposed method achieves better performance than previous methods. In addition, the results on the synthetic dataset indicate that the proposed method can capture the high-order relations.

ANALYSIS OF MULTI-THREADED MARKOV SYSTEMS

Known technologies for analyzing Markov systems use a well-operating mathematical apparatus based on the computational implementation of the fundamental Markov property. Herewith the resulting systems of linear algebraic equations are easily solved numerically. Moreover, when solving lots of practical problems, this numerical solution is insufficient. For instance, both in problems of structural and parametric synthesis of systems, as well as in control problems. These problems require to obtain analytical relations describing the dependences of probability values of states of the analyzed system with the numerical values of its parameters. The complexity of the analytical solution of the related systems of linear algebraic equations increases rapidly along with the increase in the system dimensionality. This very phenomenon manifests itself especially demonstratively when analyzing multi-threaded queuing systems. Accordingly, the objective of this paper is to develop an effective computational method for obtaining analytical relations that allow to analyze high-dimensional Markov systems. To analyze such systems this paper provides for a decomposition method based on the idea of phase enlargement of system states. The proposed and substantiated method allows to obtain analytical relations for calculating the distribution of Markov system states. The method can be effectively applied to solve problems of analysis and management in high-dimensional Markov systems. An example has been considered

Stochastic Processes in Continuous Time

This chapter reviews the theory of continuous-time stochastic processes, covering the concepts of adaptation, Lévy processes, diffusions, martingales, and Markov processes. Brownian motion is studied as the most important case, with properties that include the reflection principle and the strong Markov property. The technique of Skorokhod embedding is introduced, providing novel proofs of the central limit theorem and the law of the iterated logarithm. The family of processes derived from Brownian motion is reviewed and in the final section it is shown that a continuous process having finite variance and independent increments is Brownian motion.

On Cognitive Searching Optimization in Semi-Markov Jump Decision Using Multistep Transition and Mental Rehearsal

Cognitive searching optimization is a subconscious mental phenomenon in decision making. Aroused by exploiting accessible human action, alleviating inefficient decision and shrinking searching space remain challenges for optimizing the solution space. Multiple decision estimation and the jumpy decision transition interval are two of the cross-impact factors resulting in variation of decision paths. To optimize the searching process of decision solution space, we propose a semi-Markov jump cognitive decision method in which a searching contraction index bridges correlation from the time dimension and depth dimension. With the change state and transition interval, the semi-Markov property can obtain the action by limiting the decision solution to the specified range. From the decision depth, bootstrap re-sampling utilizes mental rehearsal iteration to update the transition probability. In addition, dynamical decision boundary by the interaction process limits the admissible decisions. Through the flight simulation, we show that proposed index and reward vary with the transition decision steps and mental rehearsal frequencies. In conclusion, this decision-making method integrates the multistep transition and mental rehearsal on semi-Markov jump decision process, opening a route to the multiple dimension optimization of cognitive interaction.

Deep state-space Gaussian processes

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.

Remaining useful life estimation based on the joint use of an observer and a hidden Markov model

We propose an approach for failure prognosis based on the estimation of the Remaining Useful Life (RUL) of a system in a situation in which monitoring signals providing information about its degradation evolution are not measured and no operating model of the system is available. These conditions are of practical interest for industrial applications such as mechanical (e.g. rolling bearing) or electrical (e.g. wind turbine) devices or equipment-critical components (e.g. batteries) in which the addition of sensors to the system is not feasible (e.g. space limitations for sensors, cost, etc.). The approach is based on an estimation of the system degradation using residual generation (where the difference between the system and the observer outputs is processed) and Hidden Markov Models with discrete observations. The prediction of the system RUL is given by the Markov property concerning the mean time before absorption. The approach comprises two phases: a training phase to model the degradation behavior and an “on-line” use phase to estimate the remaining life of the system. Two case studies were conducted for RUL prediction to verify the effectiveness of the proposed approach.

Mutual information superadditivity and unitarity bounds

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

Finite-time and spectral-finite methods of optimal filtering of discrete signals

На основе содержания теоремы ортогонального проецирования излагаются методы оптимальных, линейных рекуррентных оценок, в общем случае, не марковских, сигналов, на фоне произвольных помех. Предлагаемые алгоритмы оптимальной обработки дискретных сигналов являются альтернативными методу фильтрации Калмана, не отличающимися заметно от них по точности обработки и являющимися более универсальными и простыми при их реализации. Универсальность исследуемых методов определяется применимостью их к широкому классу моделей сигналов, не требующих марковского свойства оцениваемого сигнала и изменения структуры алгоритма оценки в зависимости от моделей помех измерения в виде случайного коррелированного процесса или белого шума. Более простые структуры алгоритмов рассматриваемых методов по отношению к фильтрации Калмана объясняются отсутствием необходимости представления модели в пространстве состояний и требования решать нелинейное уравнение Риккати для реализации алгоритма. Спектрально-финитный алгоритм оптимальной оценки сигнала осуществляет сжатие информации в спектральном аспекте на основе использования метода нахождения собственных чисел и векторов и позволяет осуществить понижение размерности векторов результатов измерений вплоть до скалярных величин без заметной потери точности оценки. В качестве исходной информации необходимо знание корреляционной функции и математического ожидания оцениваемого дискретного сигнала и дисперсии и математического ожидания дискретной помехи. Based on the content of the orthogonal projection theorem, methods of optimal, linear recurrent estimates of, in general, non-Markov signals, against the background of arbitrary interference, are presented. The proposed algorithms for optimal processing of discrete signals are alternative to the Kalman filtering method, which do not differ significantly from them in terms of processing accuracy and are more universal and simple to implement. The universality of the studied methods is determined by their applicability to a wide class of signal models that do not require the Markov property of the estimated signal and changes in the structure of the estimation algorithm depending on the measurement interference models in the form of a random correlated process or white noise. The simpler structures of the algorithms of the methods under consideration in relation to Kalman filtering are explained by the absence of the need to represent the model in the state space and the requirement to solve the nonlinear Riccati equation for the implementation of the algorithm.

Delay Propagation in Large Railway Networks with Data-Driven Bayesian Modeling

Reliability and punctuality are the key evaluation criteria in railway service for both passengers and operators. Delays spanning over spatial and temporal dimensions significantly affect the reliability and punctuality level of train operation. The optimization of capacity utilization and timetable design requires the prediction of the reliability and punctuality level of train operations, which is determined by train delays and delay propagation. To predict the punctuality level of train operations, the distributions of arrival and departure delays must be estimated as realistically as possible by taking into account the complex railway network structure and different types of delays caused by route conflict and connected trips. This paper aims to predict the propagation of delays on the railway network in the Greater Sydney area by developing a conditional Bayesian model. In the model, the propagation satisfies the Markov property if one can predict future delay propagation in the network based solely on its present state just as well as one could knowing the process’s full history, so that it is independent of such historical procedures. Meanwhile, we consider the throughput estimation for the cases of delay caused by interchange line conflicts and train connection in this model. To the best of the authors’ knowledge, this is the first work of data-driven delay propagation modeling that examines both spatial and temporal dimensions under four different scenarios for railway networks. Implementation on real-world railway network operation data shows the feasibility and accuracy of the proposed model compared with traditional probability models.