Reproducing Gaussian densities and linear Gaussian detection

It is shown that the expected value of a Gaussian density function of a Gaussian random variable is another Gaussian density function. This is used to determine which of M partially observed Gaussian linear systems is the most likely, given the observations.     

On Minimax Detection of Gaussian Stochastic Sequences and Gaussian Stationary Signals

Problems of Information Transmission - We consider the detection problem for Gaussian stochastic sequences (signals) with unknown covariance matrices in white Gaussian noise. For a given false...     

Approximation problems with the divergence criterion for Gaussian variables and Gaussian processes

System identification for stationary Gaussian processes includes an approximation problem. Currently, the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation. There is no proof that this algorithm is the optimal solution to an approximation problem with a specific criterion. In this paper it is shown that the optimal solution to an approximation problem for Gaussian random variables with the divergence criterion is identical to the main step of the subspace algorithm. An approximation problem for stationary Gaussian processes with the divergence criterion is formulated.     

Gaussian processes and neuronal modeling

This work is a contribution towards the understanding of certain features of mathematical models of single neurons. Emphasis is set on neuronal firing, for which the first passage time (FPT) problem bears a fundamental relevance. We focus the attention on modeling the change of the neuron membrane potential between two consecutive spikes by Gaussian stochastic processes, both of Markov and of non-Markov types. Methods to solve the FPT problems, both of a theoretical and of a computational nature, are sketched, including the case of random initial values. Significant similarities or diversities between computational and theoretical results are pointed out, disclosing the role played by the correlation time that has been used to characterize the neuronal activity. It is highlighted that any conclusion on this matter is strongly model-dependent. In conclusion, an outline of the asymptotic behavior of FPT densities is provided, which is particularly useful to discuss neuronal firing under certain slow activity conditions.     

Hybrid model based on SVM with Gaussian loss function and adaptive Gaussian PSO

In view of the bad capability of the standard support vector machine (SVM) in field of white noise of input series, a new v-SVM with Gaussian loss function which is call g-SVM is put forward to handle white noises. To seek the unknown parameters of g-SVM, an adaptive normal Gaussian particle swarm optimization (ANPSO) is also proposed. The results of applications show that the hybrid forecasting model based on the g-SVM and ANPSO is feasible and effective, the comparison between the method proposed in this paper and other ones is also given which proves this method is better than v-SVM and other traditional methods.     

用于图像分割的多分类高斯混合模型和基于邻域信息的高斯混合模型

高斯混合模型是一种简单有效且被广泛使用的图像分割工具。然而,传统的高斯混合模型在混合成分个数确定时的拟合结果不够精确;此外,由于没有考虑像素间的空间关系,导致分割结果易受噪声干扰,且分割精度不高。为弥补传统高斯混合模型的缺陷,文中提出多分类高斯混合模型和基于邻域信息的高斯混合模型用于图像分割。多分类高斯混合模型对传统混合模型进行二重分解:传统混合模型由M个分布加权混合得到,多分类混合模型进一步将M个分布中的每一个分布分解成R个分布。即多分类高斯混合模型由M个高斯分布混合组成,而这M个分布分别由R个不同的分布混合得到,提高了模型的拟合精度。基于邻域信息的高斯混合模型通过对模型中的先验概率和后验概率添加空间信息约束,增强了像素间的信息关联和抗噪性。采用结构相似性、误分率和峰值信噪比等指标来评价分割结果。通过实验发现:与现有的混合模型分割方法相比,文中方法大幅提高了分割精度,且有效地抑制了噪声干扰。     

Scale-Covariant and Scale-Invariant Gaussian Derivative Networks

Journal of Mathematical Imaging and Vision - This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling...     

Gaussian processes and limiting linear models

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the Gaussian processes which encode the linear model either have probability of nearly zero or are otherwise unattainable without the explicit construction of a prior with the limiting linear model in mind. We develop such a prior, and show that its practical benefits extend well beyond the computational and conceptual simplicity of the linear model. For example, linearity can be extracted on a per-dimension basis, or can be combined with treed partition models to yield a highly efficient nonstationary model. Our approach is demonstrated on synthetic and real datasets of varying linearity and dimensionality.     

Gaussian processes and limiting linear models

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the Gaussian processes which encode the linear model either have probability of nearly zero or are otherwise unattainable without the explicit construction of a prior with the limiting linear model in mind. We develop such a prior, and show that its practical benefits extend well beyond the computational and conceptual simplicity of the linear model. For example, linearity can be extracted on a per-dimension basis, or can be combined with treed partition models to yield a highly efficient nonstationary model. Our approach is demonstrated on synthetic and real datasets of varying linearity and dimensionality.     

Knowledge-based target detection in compound Gaussian clutter with inverse Gaussian texture

This paper addresses the problem of adaptive detection of radar targets embedded in heterogeneous compound-Gaussian clutter environments. Based on the Bayesian theory, a priori knowledge of clutter is utilized to improve detection performance. The clutter texture is modeled by the inverse Gaussian distribution to describe the heavy-tailed clutter. Furthermore, clutter's heterogeneity results in insufficient secondary data, and the inverse complex Wishart distribution is exploited to model the speckle covariance matrix. Based on a priori distributions of clutter, a novel detector without using secondary data is derived via the generalized likelihood ratio test (GLRT). Monte Carlo experiments are performed to evaluate the detection performance of the proposed detector. Experimental results illustrate that the proposed detector outperforms its competitors in scenarios with limited secondary data.     

Quantum correlations in Gaussian states via Gaussian channels: steering,entanglement, and discord

Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein–Podolsky–Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.     

Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields

This article discusses the following problem, often encountered when analyzing spatial lattice data. How can one construct a Gaussian Markov random field (GMRF), on a lattice, that reflects well the spatial-covariance properties present either in data or in prior knowledge? The Markov property on a spatial lattice implies spatial dependence expressed conditionally, which allows intuitively appealing site-by-site model building. There are also cases, such as in biological network analysis, where the Markov property has a deep scientific significance. Moreover, the model is often important for computational efficiency of Markov chain Monte Carlo algorithms. In this article, we introduce a new criterion to fit a GMRF to a given Gaussian field, where the Gaussian field is characterized by its spatial covariances. We establish that this criterion is computationally appealing, it can be used on both regular and irregular lattices, and both stationary and nonstationary fields can be fitted.     

约束高斯分类网研究

针对基于一元高斯函数估计属性边缘密度的朴素贝叶斯分类器不能有效利 用属性之间的依赖信息和使用多元高斯函数估计属性联合密度的完全贝叶斯分类器 易于导致对数据的过度拟合而且高阶协方差矩阵的计算也非常困难等情况,在建立 属性联合密度分解与组合定理和属性条件密度计算定理的基础上,将朴素贝叶斯分类 器的属性选择、分类准确性标准和属性父结点的贪婪选择相结合,进行约束高斯 分类网学习与优化,并依据贝叶斯网络理论,对贝叶斯衍生分类器中属性为类提供 的信息构成进行分析.使用UCI数据库中连续属性分类数据进行实验,结果显示,经过 优化的约束高斯分类网具有良好的分类准确性.     

Fixed-structure Gaussian process model

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.     

Large-margin multi-view Gaussian process

Multimedia Systems - In image classification, the goal was to decide whether an image belongs to a certain category or not. Multiple features are usually employed to comprehend the contents of...     

Antialiasing by Gaussian integration

The antialiasing method presented is based on Gaussian integration rather than Fourier spectrum analysis; it views aliasing as a general integral approximating a sampled function instead of a signal reconstruction problem. In this way, we can use classical numerical analysis to study the problem     

高斯渐进贝叶斯滤波器

渐进贝叶斯方法将先验分布到后验分布的演化描述为一阶动态系统,通过在伪时间上连续地引入观测信息实现后验状态估计.该方法的一般形式解,即动态系统的时间导数,是难以得到的.本文提出一种高斯型渐进贝叶斯滤波器.首先在线性高斯条件下推导了时间导数的解析解;然后证明了在该条件下,由该解析解确定的一阶动态系统与常量状态估计的Kalman-Bucy滤波器是一致的,且由此导出的高斯渐进贝叶斯滤波器与卡尔曼滤波器是一致的.最后利用一阶Taylor展开推导了滤波器在非线性高斯条件下的近似解表达式,并采用Monte Carlo方法给出了具体实现方法.通过若干仿真算例表明,新滤波器具有较高的精度,且在一定精度条件下的时间复杂度低于一般粒子滤波器.     

Fuzzy Gaussian Mixture Models

In this paper, in order to improve both the performance and the efficiency of the conventional Gaussian Mixture Models (GMMs), generalized GMMs are firstly introduced by integrating the conventional GMMs and the active curve axis GMMs for fitting non-linear datasets, and then two types of Fuzzy Gaussian Mixture Models (FGMMs) with a faster convergence process are proposed based on the generalized GMMs, inspired from the mechanism of Fuzzy C-means (FCMs) which introduces the degree of fuzziness on the dissimilarity function based on distances. One is named as probability based FGMMs defining the dissimilarity as the multiplicative inverse of probability density function, and the other is distance based FGMMs which define the dissimilarity function focusing the degree of fuzziness only on the distances between points and component centres. Different from FCMs, both of the proposed dissimilarity functions are based on the exponential function of the distance. The FGMMs are compared with the conventional GMMs and the generalized GMMs in terms of the fitting degree and convergence speed. The experimental results show that the proposed FGMMs not only possess the non-linearity to fit datasets with curve manifolds but also have a much faster convergence process saving more than half computational cost than GMMs'.     

Variational Gaussian process classifiers

Gaussian processes are a promising nonlinear regression tool, but it is not straightforward to solve classification problems with them. In the paper the variational methods of Jaakkola and Jordan (2000) are applied to Gaussian processes to produce an efficient Bayesian binary classifier.