Control of discrete-time HMM partially observed under fractional Gaussian noises

A discrete-time control problem of a finite-state hidden Markov chain partially observed in a fractional Gaussian process is discussed using filtering. The control problem is then recast as a separated problem with information variables given by the unnormalized conditional probabilities of the whole path of the hidden Markov chain. A dynamic programming result and a minimum principle are obtained.     

Approximate forward-backward algorithm for a switching linear Gaussian model

A hidden Markov model with two hidden layers is considered. The bottom layer is a Markov chain and given this the variables in the second hidden layer are assumed conditionally independent and Gaussian distributed. The observation process is Gaussian with mean values that are linear functions of the second hidden layer. The forward-backward algorithm is not directly feasible for this model as the recursions result in a mixture of Gaussian densities where the number of terms grows exponentially with the length of the Markov chain. By dropping the less important Gaussian terms an approximate forward-backward algorithm is defined. Thereby one gets a computationally feasible algorithm that generates samples from an approximation to the conditional distribution of the unobserved layers given the data. The approximate algorithm is also used as a proposal distribution in a Metropolis-Hastings setting, and this gives high acceptance rates and good convergence and mixing properties. The model considered is related to what is known as switching linear dynamical systems. The proposed algorithm can in principle also be used for these models and the potential use of the algorithm is therefore large. In simulation examples the algorithm is used for the problem of seismic inversion. The simulations demonstrate the effectiveness and quality of the proposed approximate algorithm.     

基于WTFMC算法的递归模糊神经网络结构设计

针对递归模糊神经网络(Recurrent fuzzy neural network, RFNN)的递归量难以自适应的问题, 提出一种基于小波变换–模糊马尔科夫链(Wavelet transform fuzzy Markov chain, WTFMC)算法的RFNN模型.首先, 在时间维度上记录隐含层神经元的模糊隶属度, 并采用小波变换将该时间序列进行分解, 通过模糊马尔科夫链对子序列的未来时段进行预测, 之后将各预测量合并后代入递归函数中得到具有自适应性的递归量.其次, 利用梯度下降算法更新RFNN的参数来保证神经网络的精度.最后, 通过非线性系统建模中几个基准问题和实际污水处理中关键水质参数的预测实验, 证明了该神经网络模型的可行性和有效性.     

Buried Markov models: a graphical-modeling approach to automatic speech recognition

In this work, buried Markov models (BMM) are introduced. In a BMM, a Markov chain state at time t determines the conditional independence patterns that exist between random variables lying within a local time window surrounding t. This model is motivated by and can be fully described by “graphical models”, a general technique to describe families of probability distributions. In the paper, it is shown how information-theoretic criterion functions can be used to induce sparse, discriminative, and class-conditional network structures that yield an optimal approximation to the class posterior probability, and therefore are useful for classification tasks such as speech recognition. Using a new structure learning heuristic, the resulting structurally discriminative models are tested on a medium-vocabulary isolated-word speech recognition task. It is demonstrated that discriminatively structured BMMs, when trained in a maximum likelihood setting using EM, can outperform both hidden Markov models (HMMs) and other dynamic Bayesian networks with a similar number of parameters.     

Review of several stochastic speech unit models

Hidden Markov models are commonly used for speech unit modelling. This type of model is composed of a non-observable or “hidden” process, representing the temporal structure of the speech unit, and an observation process linking the hidden process with the acoustic parameters extracted from the speech signal.Different types of hidden processes (Markov chain, semi-Markov chain, “expanded-state” Markov chain) as well as different types of observation processes (discrete, continuous, semi-continuous—multiple processes) are reviewed, showing their relationships. The maximum likelihood estimation of two-stage stochastic process parameters is presented in an a posteriori probability formalism. An intepretation of the expectation-maximization algorithm is proposed and the practical learning algorithms for hidden Markov models and hidden semi-Markov models are compared in terms of computation structure, probabilistic justification and complexity.This presentation is illustrated by experiments on a multi-speaker 130 isolated word recognition system. The implementation techniques are detailed and the different combinations of state occupancy modelling techniques and observation modelling techniques are studied from a practical point of view.     

Quadratic costs and second moments of jump linear systems with general Markov chain

This paper presents an analytic, systematic approach to handle quadratic functionals associated with Markov jump linear systems with general jumping state. The Markov chain is finite state, but otherwise general, possibly reducible and periodic. We study how the second moment dynamics are affected by the additive noise and the asymptotic behaviour, either oscillatory or invariant, of the Markov chain. The paper comprises a series of evaluations that lead to a tight two-sided bound for quadratic cost functionals. A tight two-sided bound for the norm of the second moment of the system is also obtained. These bounds allow us to show that the long-run average cost is well defined for system that are stable in the mean square sense, in spite of the periodic behaviour of the chain and taking into consideration that it may not be unique, as it may depend on the initial distribution. We also address the important question of approximation of the long-run average cost via adherence of finite horizon costs.     

针对PM2.5单时间序列数据的动态调整预测模型

针对细颗粒物PM2.5的浓度预测,本文提出了基于单时间序列数据的动态调整模型.在动态指数平滑算法中,指数平滑次数与参数基于样本数据并借助二分查找进行调整.在动态马尔科夫模型中,马尔科夫链的残差状态数、隐马尔科夫模型的隐状态数、连续样本数和阈值参数都通过训练数据加以调整.动态调整模型将指数平滑法和马尔科夫模型有效结合起来,指数平滑法得到的预测值由马尔科夫模型进行校正,从而提高预测准确度.基于大量实际PM2.5数据进行测试,验证了算法的有效性.并与其他现有的灰色模型、人工神经网络、自回归滑动平均模型、支持向量机等方法进行了对比,表明所提模型能够得到精度更高的预测结果.本文模型不局限于PM2.5数据,还可应用于其他类型的数据预测.     

Bayesian multiscale feature detection of log-spectral densities

A fully-automatic Bayesian visualization tool to identify periodic components of evenly sampled stationary time series, is presented. The given method applies the multiscale ideas of the SiZer-methodology to the log-spectral density of a given series. The idea is to detect significant peaks in the true underlying curve viewed at different resolutions or scales. The results are displayed in significance maps, illustrating for which scales and for which frequencies, peaks in the log-spectral density are detected as significant. The inference involved in producing the significance maps is performed using the recently developed simplified Laplace approximation. This is a Bayesian deterministic approach used to get accurate estimates of posterior marginals for latent Gaussian Markov random fields at a low computational cost, avoiding the use of Markov chain Monte Carlo techniques. Application of the given exploratory tool is illustrated analyzing both synthetic and real time series.     

Bayesian posterior mean estimates for Poisson hidden Markov models

This paper focuses on the Bayesian posterior mean estimates (or Bayes’ estimate) of the parameter set of Poisson hidden Markov models in which the observation sequence is generated by a Poisson distribution whose parameter depends on the underlining discrete-time time-homogeneous Markov chain. Although the most commonly used procedures for obtaining parameter estimates for hidden Markov models are versions of the expectation maximization and Markov chain Monte Carlo approaches, this paper exhibits an algorithm for calculating the exact posterior mean estimates which, although still cumbersome, has polynomial rather than exponential complexity, and is a feasible alternative for use with small scale models and data sets. This paper also shows simulation results, comparing the posterior mean estimates obtained by this algorithm and the maximum likelihood estimates obtained by expectation maximization approach.     

Robust Sequential Data Modeling Using an Outlier Tolerant Hidden Markov Model

Hidden Markov (chain) models using finite Gaussian mixture models as their hidden state distributions have been successfully applied in sequential data modeling and classification applications. Nevertheless, Gaussian mixture models are well known to be highly intolerant to the presence of untypical data within the fitting data sets used for their estimation. Finite Student's t-mixture models have recently emerged as a heavier-tailed, robust alternative to Gaussian mixture models, overcoming these hurdles. To exploit these merits of Student's t-mixture models in the context of a sequential data modeling setting, we introduce, in this paper, a novel hidden Markov model where the hidden state distributions are considered to be finite mixtures of multivariate Student's t-densities. We derive an algorithm for the model parameters estimation under a maximum likelihood framework, assuming full, diagonal, and factor-analyzed covariance matrices. The advantages of the proposed model over conventional approaches are experimentally demonstrated through a series of sequential data modeling applications.     

基于小波的搜索量聚类及在变量选择中的应用

针对使用网络购物搜索量数据建立预测模型时的变量选择问题,提出一种基于连续小波变换(CWT)及其逆变换的聚类方法。算法充分考虑了搜索量的数据特征,将原始序列分解成为不同时间尺度下的周期成分,并重构为输入向量。在此基础上通过加权模糊C均值(FCM)方法进行聚类。变量选择是根据聚类后每个分类中的关键词隶属度函数值确定的,选择效果通过我国居民消费价格指数(CPI)的预测模型进行验证。结果表明,搜索量序列具有不同长度的周期成分,聚类后同组关键词具有明显的商品类型一致性。与其他变量选择方法相比,基于小波重构序列聚类的预测模型具有更高的预测精度,单步和三步预测相对误差仅为0.3891%和0.5437%,预测变量也具有清晰的经济含义,因此特别适用于解决大数据背景下高维预测模型的变量选择问题。     

Pairwise Markov chains

We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like maximum a posteriori (MAP), or maximal posterior mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model.     

基于函数型数据时间序列建模的单传感器日常行为识别

在基于惯性传感器的人体行为识别中,传统算法常忽略行为的周期性与时序性,对提取特征的滑动窗口大小也有相应要求.文中基于单个腰部传感器分析人体日常行为,提出面向周期行为的函数型数据分析方法和隐马尔可夫模型结合的行为识别算法.首先,使用函数型数据分析方法,拟合周期性日常行为的动作捕捉数据,提取拟合后的单个周期数据.然后基于此周期时间序列数据建立描述各个日常行为过程的隐马尔可夫模型.最后,使用最大似然估计判别行为,得到识别结果.该算法通过单个腰部传感器即可快速有效地识别8种日常行为,在基于用户依赖策略和用户独立策略时识别率较高.     

Adaptive signal processing of asset price dynamics with predictability analysis

In this paper we illustrate the optimal filtering of log returns of commodity prices in which both the mean and volatility are modulated by a hidden Markov chain with finite state space. The optimal estimate of the Markov chain and the parameters of the price model are given in terms of discrete-time recursive filters. We provide an application on a set of high frequency gold price data for the period 1973-2006 and analyse the h-step ahead price predictions against the Diebold-Kilian metric. Within the modelling framework where the mean and volatility are switching regimes, our findings suggest that a two-state hidden Markov model is sufficient to describe the dynamics of the data and the gold price is predictable up to a certain extent in the short term but almost impossible to predict in the long term. The proposed model is also benchmarked with ARCH and GARCH models with respect to price predictability and forecasting errors.     

Stabilization of stochastic systems with hidden Markovian jumps

This paper considers the adaptive control of discrete-time hybrid stochastic systems with unknown randomly jumping parameters described by a finite-state hidden Markov chain. An intuitive yet longstanding conjecture in this area is that such hybrid systems can be adaptively stabilized whenever the rate of transition of the hidden Markov chain is small enough. This paper provides a rigorous positive answer to this conjecture by establishing the global stability of a gradient-algorithm-based adaptive linear-quadratic control.     

An M-ary detection approach for asset allocation

We develop a continuous-time asset allocation model which incorporates both model uncertainty and structural changes in economic conditions. A “dynamic” M-ary detection framework for a continuous-time hidden Markov chain partially observed in a Gaussian process is used to model the price dynamics of the risky asset and the hidden states of an economy. The goal of an investor is to select an optimal asset portfolio mix so as to maximize the expected utility of terminal wealth. Filtering theory is used first to turn the problem into one with complete observations and then to derive M-ary detection filters for the hidden system. The Hamilton-Jacobi-Bellman dynamic programming approach is used to solve the asset allocation problem with complete observations. An explicit solution is obtained for the power utility case.     

Statistical downscaling of rainfall data using sparse variable selection methods

In many statistical downscaling methods, atmospheric variables are chosen by using a combination of expert knowledge with empirical measures such as correlations and partial correlations. In this short communication, we describe the use of a fast, sparse variable selection method, known as RaVE, for selecting atmospheric predictors, and illustrate its use on rainfall occurrence at stations in South Australia. We show that RaVE generates parsimonious models that are both sensible and interpretable, and whose results compare favourably to those obtained by a non-homogeneous hidden Markov model (Hughes et al., 1999).     

基于免疫聚类与HMM的时序信息系统决策

本文针对时间序列数据的符号化问题，提出采用免疫聚类算法处理多维时间序列的符号化，利用克隆选择原理，生成能充分反映数据真实分布的记忆抗体作为符号集合. 时间序列信息系统中的决策问题的关键是有效地挖掘历史数据中包含的时序信息. 本文提出了一种改进的隐马尔科夫模型，运用最大熵原理对模型进行训练，求取熵最大化的概率分布，并将其应用于时序信息系统的决策. 通过实验验证了其有效性．     

Optimal sensor scheduling for hidden Markov model state estimation

Consider the Hidden Markov model where the realization of a single Markov chain is observed by a number of noisy sensors. The sensor scheduling problem for the resulting hidden Markov model is as follows: design an optimal algorithm for selecting at each time instant, one of the many sensors to provide the next measurement. Each measurement has an associated measurement cost. The problem is to select an optimal measurement scheduling policy, so as to minimize a cost function of estimation errors and measurement costs. The problem of determining the optimal measurement policy is solved via stochastic dynamic programming. Numerical results are presented.     

非线性模拟电路软故障诊断方法

针对非线性模拟电路故障诊断中软故障诊断的难题,提出了Volterra级数结合隐马尔科夫模型（HMM）进行故障诊断的方法。首先利用梯度搜索算法求解Volterra级数并提取出故障特征,然后利用提取出来的故障特征构造出观察变量对隐马尔科夫模型进行训练,最后用训练好的隐马尔科夫模型完成故障诊断。实验结果表明,该方法能有效提取故障特征,提高故障诊断效果。