从高斯过程到高斯过程混合模型:研究与展望

高斯过程（GP）模型是核学习方法与贝叶斯推理相结合的典范,现已成为机器学习领域的一个研究热点。作为对GP模型的拓展,高斯过程混合（MGP）模型具有更强大的学习能力和适应性。然而,目前关于GP和MGP模型的研究较为零散,尚缺少系统的分析与总结。本文首先对于GP模型的基本原理及其研究进展进行了深入地分析和讨论;然后将GP模型拓展至MGP模型,从多方面对MGP模型的研究现状和进展进行了深入地分析和讨论,并指出未来值得探索的研究方向和应用问题。      

基于高斯过程混合模型的国债收益率预测

债券分析的核心问题是发现偿还期限与到期收益率之间的关系,即利率期限结构,而实际上国债利率期限结构是最为重要和基本的模式。目前人们对于利率期限结构的分析主要采用经济理论模型和数量模型进行,但是这两种方法都难于对国债收益率进行有效的预测。基于高斯过程混合模型强大的数据拟合和分析能力,本文将其应用于国债收益率的建模和预测。本文采用国债收益率数据作为输出变量,筛选出对国债收益率影响最强的一组作用因子作为驱动或输入变量,然后利用高斯过程混合模型对数据进行学习和建模,并依此对国债收益率进行建模和分析。实验结果表明高斯过程混合模型能够更好的描述国债利率期限结构。相比于其他机器学习模型和算法,高斯过程混合模型在国债收益率的测试数据上获得了更好准确的预测结果。      

基于高斯过程混合模型的瓦斯安全状态分类研究

针对目前瓦斯浓度预测与瓦斯安全状态分类方法中主观性较强、超参数难以选取、解释性差、无法有效地利用样本之间时序信息等问题,本文提出了基于高斯过程混合模型的瓦斯浓度预测与安全状态分类方法。高斯过程是机器学习领域中解决非线性回归问题的典型方法,能够有效地利用数据之间的相关性,常用于时间序列的建模与预测。然而,单个高斯过程存在着一定的局限性,难于对非平稳、多模态的数据进行有效地建模和回归分析。在高斯过程的基础上引入其混合模型,则可增强模型的表达能力,能够对有复杂结构的数据进行建模。我们将瓦斯安全状态根据风险由高至低分成红橙黄蓝四个等级,在每个风险等级上瓦斯浓度数据采用单个高斯过程进行建模。由于一般瓦斯浓度数据包含着各个风险等级的数据,高斯过程混合模型则可用于对整体数据进行建模和回归分析。根据对数据的参数学习结果,高斯过程混合模型便可自适应地得到每个时刻对应的风险等级,并在预测瓦斯浓度时对各个高斯过程分量的预测进行加权,得到更为鲁棒的预测结果。实验结果表明,基于高斯过程混合模型的方法可有效地预测瓦斯浓度、评估安全状态。      

基于局部层次化混合高斯模型的视频序列运动目标检测

在视频分析的过程中,背景建模和运动目标提取是一个非常重要的问题.混合高斯模型是进行背景建模常用的模型之一.但是单纯运用混合高斯模型进行运动目标提取的效果并不是非常理想.本文提出了一种自上而下的局部层次化混合高斯模型,该算法首先确定更新区域,然后在区域中运用分块的混合高斯模型和点像素混合高斯模型进行背景建模和目标提取.实验表明该方法具有较好的处理效果,同时也提高了处理的时间效率.     

基于改进高斯混合模型的运动图像目标检测算法

运动图像目标检测指的是从序列图像中将变化的目标从背景中分离出来,高斯混合模型可以对视频序列图像的前景和背景进行分类,再利用背景减除实现运动目标的检测。提出一种基于改进高斯混合模型的优化背景建模方法,该方法首先利用3×3模板对序列图像帧中的像素进行类似卷积的均值计算,然后利用相邻均值的差提取均差因子自适应更新图像的均值。在此基础上,设计了自适应学习率和学习速率,利用改进高斯混合模型实现序列图像的背景建模。改进模型不仅能有效减少数据计算量,同时可以降低在相似区域像素计算的时长,大大加快背景建模速度。实验结果表明,改进模型在目标检测、算法执行速率等性能指标上都有更好的表现,能满足实时检测要求。     

高斯过程混合模型在含噪输入预测策略下的煤矿瓦斯浓度柔性预测

高斯过程回归是机器学习中解决非线性回归的一种典型回归方法。然而,单一的高斯过程难以拟合非平稳、多模态的时序数据。另外,在实际应用中需要预测的输入数据会受到噪声的干扰。为了克服这些问题,本文提出了含噪输入预测策略下的高斯过程混合回归预测方法（niMGP）,并针对煤矿瓦斯浓度数据进行了参数学习和柔性预测。与其它传统回归方法相比,这种柔性预测方法是在测试输入数据具有噪声干扰的情况下进行预测,使其结果更为鲁棒和准确。本文首先通过模拟实验验证了在具有固定信噪比的测试输入数据上,高斯过程混合模型在含噪输入预测策略下的回归结果在稳定性上优于其传统预测策略下的回归结果。本文进一步选取松藻煤矿中打通一矿的333944号传感器获取的实际瓦斯浓度数据片段,对其进行了适当的数据增强之后,通过实际数据的实验进一步表明,高斯过程混合模型采用含噪输入预测策略在数据回归分析的预测上相比传统预测策略具有更好的稳定性。实际中还可以通过调节测试输入数据中噪声分布的方差来调节预测的灵敏度,达到分级预警的效果。      

双麦克风噪声消除的高斯混合模型法

为了解决基于相位差滤波器（PBF）双麦克风方法残留噪声较多的问题,本文在PBF方法基础上提出一种基于高斯混合模型的双麦克风噪声消除方法。该方法首先采用高斯混合模型（GMM）对目标语音存在(λ1)与目标语音不存(λ0)在这两种情况进行建模。其次,在实时增强阶段,根据贝叶斯分类器计算每帧的目标语音存在概率(TSPP),随后根据噪声抑制最大化准则修正PBF的增益函数并得到改进的相位差滤波器（IPBF）,最后将TSPP与 IPBF的增益函数相结合,进而得到一种用于双麦克风噪声消除的掩蔽滤波器。实验结果表明:本文提出算法可有效抑制残留噪声,尤其是在目标语音不存在的时间段      

基于改进GPR模型的发酵过程软测量建模

针对生物反应过程中许多关键参量难以在线检测的难题,提出了一种改进的高斯过程回归建模方法。由于传统高斯过程的均值函数不易确定,从而简单预置为零,导致模型对数据的解释性不够完全的缺点。改进的方法是利用一种组合基函数来确定高斯过程回归模型的一个非零均值函数,基函数的选取是通过高斯过程建立多项式回归噪声模型的方式推导而出,最后进行软测量模型的预测输出。基于氨基酸类典型菌种L-赖氨酸反应过程关键生物量参数预测的试验研究表明：与传统的高斯过程回归模型和支持向量机相比,改进的高斯过程回归模型具有更好的预测精度和泛化能力,能很好的跟踪预测值的变化趋势。     

高斯混合模型在海面运动目标检测中的应用

针对海面背景图像的特点,利用高斯混合模型参数估计方法,建立了象素点背景模型并用于海面运动目标的检测。提出的基于变化检测的高斯混合模型参数估计方法与EM算法估计的模型参数极为相似,但前者大大节省了建立背景模型所需的内存空间,建模速度大约是后者的两倍。视频流实验验证了算法的有效性。     

混合高斯模型的熵惩罚最大似然估计与自动模型选择

有限高斯混合模型是一种重要的概率模型,并在聚类分析,模式识别和信号处理等方面有着广泛的应用.在高斯(即正态)分量个数K未知时,仅仅根据样本数据来确定K是一个非常困难的问题.这实际上是一个模型选择问题,直接影响着应用的效果.为了解决这一模型选择问题,本文在一维混合高斯模型下提出了基于熵惩罚最大似然估计的梯度算法.实验表明这种算法能够在参数估计过程中自动实现模型选择,使得多余高斯分量的混合比例系数衰减为零.     

New autoregressive (AR) order selection criteria based on the prediction error estimation

The most important problem in data modeling using the AR model is the order selection. Some AR order selection criteria estimate the prediction error and choose the order that minimizes this estimated prediction error. All of these criteria use the same formula for estimating the prediction error from the residual variance for all AR models. However, experimental results show that the relationship between the prediction error and the residual variance depends on the AR model. In this paper, we introduce new formulas for estimating the prediction error using the residual variance. These formulas depend on the AR model, and are obtained through assuming a white Gaussian noise as the input noise to the AR model and assuming that the least-squares-forward (LSF) method is used for estimating the AR coefficients. The performance of the new order selection criteria introduced in this paper is compared with other AR order selection criteria using simulated data. Results show that the new criteria have good performance in estimating the prediction error and in selecting an appropriate order for the AR model.     

Generalized Gaussian mixture models as a nonparametric Bayesian approach for clustering using class-specific visual features

Recently, there has been a growing interest in the problem of learning mixture models from data. The reasons and motivations behind this interest are clear, since finite mixture models offer a formal approach to the important problems of clustering and data modeling. In this paper, we address the problem of modeling non-Gaussian data which are largely present, and occur naturally, in several computer vision and image processing applications via the learning of a generative infinite generalized Gaussian mixture model. The proposed model, which can be viewed as a Dirichlet process mixture of generalized Gaussian distributions, takes into account the feature selection problem, also, by determining a set of relevant features for each data cluster which provides better interpretability and generalization capabilities. We propose then an efficient algorithm to learn this infinite model parameters by estimating its posterior distributions using Markov Chain Monte Carlo (MCMC) simulations. We show how the model can be used, while comparing it with other models popular in the literature, in several challenging applications involving photographic and painting images categorization, image and video segmentation, and infrared facial expression recognition.     

Iterative learning algorithms for linear Gaussian observation models

In this paper, we consider a signal/parameter estimation problem that is based on a linear model structure and a given setting of statistical models with unknown hyperparameters. We consider several combinations of Gaussian and Laplacian models. We develop iterative algorithms based on two typical machine learning methods - the evidence-based method and the integration-based method - to deal with the hyperparameters. We have applied the proposed algorithms to adaptive prediction and wavelet denoising. In linear prediction, we show that the proposed algorithms are efficient tools for tackling a difficult problem of adapting simultaneously the order and the coefficients of the predictor. In wavelet denoising, we show that by using the proposed algorithms, the noisy wavelet coefficients are subject to shrinkage and thresholding.     

Link quality prediction model based on Gaussian process regression

Link quality is an important factor of reliable communication and the foundation of upper protocol design for wireless sensor network.Based on this,a link quality prediction model based on Gaussian process regression was proposed.It employed grey correlation algorithm to analyze correlation between link quality parameters and packet receive rate.The mean of the link quality indication and the mean of the signal-to-noise were selected as input parameters so as to reduce the computational complexity.The above parameters and packet receive rate were taken to build Gaussian process regression model with combination of covariance function,so that link quality could be predicted.In the stable and unstable scenarios,the experimental results show that the proposed model has better prediction accuracy than the one of dynamic Bayesian network prediction model.     

A New Approach to Variable Selection Using the TLS Approach

The problem of variable selection is one of the most important model selection problems in statistical applications. It is also known as the subset selection problem and arises when one wants to explain the observations or data adequately by a subset of possible explanatory variables. The objective is to identify factors of importance and to include only variables that contribute significantly to the reduction of the prediction error. Numerous selection procedures have been proposed in the classical multiple linear regression model. We extend one of the most popular methods developed in this context, the backward selection procedure, to a more general class of models. In the basic linear regression model, errors are present on the observations only, if errors are present on the regressors as well, one gets the errors-in-variables model which for Gaussian noise becomes the total-least-squares (TLS) model, this is the context considered here     

基于EK算法改进的多目标跟踪技术

在随机有限集理论框架下,传统的3种基于高斯混合实现的滤波算法仅适用于线性高斯系统中的目标跟踪。为了将算法的使用范围扩展到非线性高斯系统,文中提出了传统3种滤波器基于扩展卡尔曼（EK）改进后的算法,通过泰勒级数展开将非线性问题转化为线性问题近似处理,并对比分析了3种新算法对于匀速转弯目标的跟踪性能。仿真结果表明,3种新算法均能实现对于非线性高斯系统中目标的有效跟踪。