Variational learning for Dirichlet process mixtures of Dirichlet distributions and applications

In this paper, we propose a Bayesian nonparametric approach for modeling and selection based on a mixture of Dirichlet processes with Dirichlet distributions, which can also be seen as an infinite Dirichlet mixture model. The proposed model uses a stick-breaking representation and is learned by a variational inference method. Due to the nature of Bayesian nonparametric approach, the problems of overfitting and underfitting are prevented. Moreover, the obstacle of estimating the correct number of clusters is sidestepped by assuming an infinite number of clusters. Compared to other approximation techniques, such as Markov chain Monte Carlo (MCMC), which require high computational cost and whose convergence is difficult to diagnose, the whole inference process in the proposed variational learning framework is analytically tractable with closed-form solutions. Additionally, the proposed infinite Dirichlet mixture model with variational learning requires only a modest amount of computational power which makes it suitable to large applications. The effectiveness of our model is experimentally investigated through both synthetic data sets and challenging real-life multimedia applications namely image spam filtering and human action videos categorization.     

Dirichlet 过程及其在自然语言处理中的应用

Dirichlet过程是一种典型的变参数贝叶斯模型,其优点是参数的个数和性质灵活可变,可通过模型和数据来自主地计算,近年来它已成为机器学习和自然语言处理研究领域中的一个研究热点。该文较为系统的介绍了Dirichlet过程的产生、发展,并重点介绍了其模型计算,同时结合自然语言处理中的具体应用问题进行了详细分析。最后讨论了Dirichlet过程未来的研究方向和发展趋势。     

分层Dirichlet过程及其应用综述

Dirichlet过程是一种应用于非参数贝叶斯模型中的随机过程, 特别是作为先验分布应用在概率图模型中. 与传统的参数模型相比, Dirichlet过程的应用更加广泛且模型更加灵活, 特别是应用于聚类问题时, 该过程能够自动确定聚类数目和生成聚类中心的分布参数. 因此, 近年来, 在理论和应用上均得到了迅速的发展, 引起越来越多的关注. 本文首先介绍Dirichlet过程, 而后描述了以Dirichlet过程为先验分布的Dirichlet过程混合模型及其应用, 接着概述分层Dirichlet过程及其在相关算法构造中的应用, 最后对分层Dirichlet过程的理论和应用进行了总结, 并对未来的发展方向作了探讨.     

A countably infinite mixture model for clustering and feature selection

Mixture modeling is one of the most useful tools in machine learning and data mining applications. An important challenge when applying finite mixture models is the selection of the number of clusters which best describes the data. Recent developments have shown that this problem can be handled by the application of non-parametric Bayesian techniques to mixture modeling. Another important crucial preprocessing step to mixture learning is the selection of the most relevant features. The main approach in this paper, to tackle these problems, consists on storing the knowledge in a generalized Dirichlet mixture model by applying non-parametric Bayesian estimation and inference techniques. Specifically, we extend finite generalized Dirichlet mixture models to the infinite case in which the number of components and relevant features do not need to be known a priori. This extension provides a natural representation of uncertainty regarding the challenging problem of model selection. We propose a Markov Chain Monte Carlo algorithm to learn the resulted infinite mixture. Through applications involving text and image categorization, we show that infinite mixture models offer a more powerful and robust performance than classic finite mixtures for both clustering and feature selection.     

Bayesian learning of inverted Dirichlet mixtures for SVM kernels generation

We describe approaches for positive data modeling and classification using both finite inverted Dirichlet mixture models and support vector machines (SVMs). Inverted Dirichlet mixture models are used to tackle an outstanding challenge in SVMs namely the generation of accurate kernels. The kernels generation approaches, grounded on ideas from information theory that we consider, allow the incorporation of data structure and its structural constraints. Inverted Dirichlet mixture models are learned within a principled Bayesian framework using both Gibbs sampler and Metropolis-Hastings for parameter estimation and Bayes factor for model selection (i.e., determining the number of mixture’s components). Our Bayesian learning approach uses priors, which we derive by showing that the inverted Dirichlet distribution belongs to the family of exponential distributions, over the model parameters, and then combines these priors with information from the data to build posterior distributions. We illustrate the merits and the effectiveness of the proposed method with two real-world challenging applications namely object detection and visual scenes analysis and classification.     

A spatially-constrained normalized Gamma process prior

In this work, we propose a novel nonparametric Bayesian method for clustering of data with spatial interdependencies. Specifically, we devise a novel normalized Gamma process, regulated by a simplified (pointwise) Markov random field (Gibbsian) distribution with a countably infinite number of states. As a result of its construction, the proposed model allows for introducing spatial dependencies in the clustering mechanics of the normalized Gamma process, thus yielding a novel nonparametric Bayesian method for spatial data clustering. We derive an efficient truncated variational Bayesian algorithm for model inference. We examine the efficacy of our approach by considering an image segmentation application using a real-world dataset. We show that our approach outperforms related methods from the field of Bayesian nonparametrics, including the infinite hidden Markov random field model, and the Dirichlet process prior.     

Nonparametric Bayesian Image Segmentation

Image segmentation algorithms partition the set of pixels of an image into a specific number of different, spatially homogeneous groups. We propose a nonparametric Bayesian model for histogram clustering which automatically determines the number of segments when spatial smoothness constraints on the class assignments are enforced by a Markov Random Field. A Dirichlet process prior controls the level of resolution which corresponds to the number of clusters in data with a unique cluster structure. The resulting posterior is efficiently sampled by a variant of a conjugate-case sampling algorithm for Dirichlet process mixture models. Experimental results are provided for real-world gray value images, synthetic aperture radar images and magnetic resonance imaging data.     

A Digital Twin approach based on nonparametric Bayesian network for complex system health monitoring

This paper proposes a Digital Twin approach for health monitoring. In this approach, a Digital Twin model based on nonparametric Bayesian network is constructed to denote the dynamic degradation process of health state and the propagation of epistemic uncertainty. Then, a real-time model updating strategy based on improved Gaussian particle filter (GPF) and Dirichlet process mixture model (DPMM) is presented to enhance the model adaptability. On one hand, for those parameters in the nonparametric Bayesian network with prior models, the improved GPF is used to update them in real time. On the other hand, for parameters lacking a prior model, DPMM is proposed to learn hidden variables, which adaptively update the model structure and greatly reduce uncertainty. Experiments on the electro-optical system are conducted to validate the feasibility of the Digital Twin approach and verify the effectiveness of the nonparametric Bayesian network. The results of comparative experiments prove that the Digital Twin approach based on nonparametric Bayesian Network has a good model self-learning ability, which improves the accuracy of health monitoring.     

Data-efficient learning of robotic clothing assistance using Bayesian Gaussian process latent variable model

ABSTRACT

Motor-skill learning for complex robotic tasks is a challenging problem due to the high task variability. Robotic clothing assistance is one such challenging problem that can greatly improve the quality-of-life for the elderly and disabled. In this study, we propose a data-efficient representation to encode task-specific motor-skills of the robot using Bayesian nonparametric latent variable models. The effectivity of the proposed motor-skill representation is demonstrated in two ways: (1) through a real-time controller that can be used as a tool for learning from demonstration to impart novel skills to the robot and (2) by demonstrating that policy search reinforcement learning in such a task-specific latent space outperforms learning in the high-dimensional joint configuration space of the robot. We implement our proposed framework in a practical setting with a dual-arm robot performing clothing assistance tasks.     

基于改进动态系统稳定估计器的机器人技能学习方法

提出一种基于改进动态系统稳定估计器的机器人技能学习方法. 现有的动态系统稳定估计器方法可以通过非线性优化来确保学习系统的全局稳定性, 但是存在确定高斯混合分量个数困难以及稳定性和精度无法兼顾的问题. 因此, 根据贝叶斯非参数模型可以自动确定合适分量个数的特性, 采用狄利克雷过程高斯混合模型对演示进行初始拟合. 随后利用参数化二次李雅普诺夫函数重新推导新的稳定性约束, 有效地解决了动态系统稳定估计器方法中稳定性和精度难以兼顾的问题. 最后, 在LASA数据库和Franka-panda机器人上的实验验证了新方法的有效性和优越性.     

Bayesian learning of finite generalized inverted Dirichlet mixtures: Application to object classification and forgery detection

The advent of mixture models has opened the possibility of flexible models which are practical to work with. A common assumption is that practitioners typically expect that data are generated from a Gaussian mixture. The inverted Dirichlet mixture has been shown to be a better alternative to the Gaussian mixture and to be of significant value in a variety of applications involving positive data. The inverted Dirichlet is, however, usually undesirable, since it forces an assumption of positive correlation. Our focus here is to develop a Bayesian alternative to both the Gaussian and the inverted Dirichlet mixtures when dealing with positive data. The alternative that we propose is based on the generalized inverted Dirichlet distribution which offers high flexibility and ease of use, as we show in this paper. Moreover, it has a more general covariance structure than the inverted Dirichlet. The proposed mixture model is subjected to a fully Bayesian analysis based on Markov Chain Monte Carlo (MCMC) simulation methods namely Gibbs sampling and Metropolis–Hastings used to compute the posterior distribution of the parameters, and on Bayesian information criterion (BIC) used for model selection. The adoption of this purely Bayesian learning choice is motivated by the fact that Bayesian inference allows to deal with uncertainty in a unified and consistent manner. We evaluate our approach on the basis of two challenging applications concerning object classification and forgery detection.     

基于多源信息融合的协作机器人演示编程及优化方法

为解决现有机器人装配学习过程复杂且对编程技术要求高等问题,提出一种基于前臂表面肌电信号和惯性多源信息融合的隐式交互方式来实现机器人演示编程.在通过演示学习获得演示人的装配经验的基础上,为提高对装配对象和环境变化的自适应能力,提出了一种多工深度确定性策略梯度算法（M-DDPG）来修正装配参数,在演示编程的基础上,进行强化学习确保机器人稳定执行任务.在演示编程实验中,提出一种改进的PCNN（并行卷积神经网络）,称作1维PCNN（1D-PCNN）,即通过1维的卷积与池化过程自动提取惯性信息与肌电信息特征,增强了手势识别的泛化性和准确率;在演示再现实验中,采用高斯混合模型（GMM）对演示数据进行统计编码,利用高斯混合回归（GMR）方法实现机器人轨迹动作再现,消除噪声点.最后,基于Primesense Carmine摄像机采用帧差法与多特征图核相关滤波算法（MKCF）的融合跟踪算法分别获取X轴与Y轴方向的环境变化,采用2个相同的网络结构并行进行连续过程的深度强化学习.在轴孔相对位置变化的情况下,机械臂能根据强化学习得到的泛化策略模型自动对机械臂末端位置进行调整,实现轴孔装配的演示学习.     

子空间聚类的非参数模型及变分贝叶斯学习

子空间聚类的目标是在不同的特征子集上对给定的一组数据归类.此非监督学习方法试图发现数据"在不同表达下的相似"模式,并且引起了相关领域大量的关注和研究.首先扩展Hoff提出的"均值与方差平移"模型为一个新的基于特征子集的非参数聚类模型,其优点是能应用变分贝叶斯方法学习模型参数.此模型结合Dirichlet过程混合模型和选择特征子集的非参数模型,能自动选择聚类个数和进行子空间聚类.然后给出基于马尔可夫链蒙特卡罗的参数后验推断算法.出于计算速度上的考虑,提出应用变分贝叶斯方法学习模型参数.在仿真数据上的实验结果及在人脸聚类问题上的应用均表明了此模型能同时选择相关特征和在这些特征上具有相似模式的数据点.在UCI"多特征数据库"上应用无需抽样的变分贝叶斯方法,其实验结果说明此方法能快速推断模型参数.     

Monte-Carlo tree search for Bayesian reinforcement learning

Bayesian model-based reinforcement learning can be formulated as a partially observable Markov decision process (POMDP) to provide a principled framework for optimally balancing exploitation and exploration. Then, a POMDP solver can be used to solve the problem. If the prior distribution over the environment’s dynamics is a product of Dirichlet distributions, the POMDP’s optimal value function can be represented using a set of multivariate polynomials. Unfortunately, the size of the polynomials grows exponentially with the problem horizon. In this paper, we examine the use of an online Monte-Carlo tree search (MCTS) algorithm for large POMDPs, to solve the Bayesian reinforcement learning problem online. We will show that such an algorithm successfully searches for a near-optimal policy. In addition, we examine the use of a parameter tying method to keep the model search space small, and propose the use of nested mixture of tied models to increase robustness of the method when our prior information does not allow us to specify the structure of tied models exactly. Experiments show that the proposed methods substantially improve scalability of current Bayesian reinforcement learning methods.     

基于模仿学习的双曲率曲面零件复合材料织物机器人铺放

针对双曲率曲面零件的复合材料织物铺放,手工铺放效率低、质量均一性差,机器人铺放的相关研究未能准确地描述手工铺放技能。为此,本文提出基于模仿学习的铺放技能采集、描述与重现的相关方法。首先,利用拖动示教获取织物铺放的轨迹信息,以压力阈值为分割依据进行有监督的轨迹分割,再采用高斯混合模型（Gaussian mixture m...     

Dirichlet Process Gaussian Mixture Models: Choice of the Base Distribution

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the “correct” number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.     

Bayesian mixture of autoregressive models

An infinite mixture of autoregressive models is developed. The unknown parameters in the mixture autoregressive model follow a mixture distribution, which is governed by a Dirichlet process prior. One main feature of our approach is the generalization of a finite mixture model by having the number of components unspecified. A Bayesian sampling scheme based on a weighted Chinese restaurant process is proposed to generate partitions of observations. Using the partitions, Bayesian prediction, while accounting for possible model uncertainty, determining the most probable number of mixture components, clustering of time series and outlier detection in time series, can be done. Numerical results from simulated and real data are presented to illustrate the methodology.     

Bayesian mixture of autoregressive models

An infinite mixture of autoregressive models is developed. The unknown parameters in the mixture autoregressive model follow a mixture distribution, which is governed by a Dirichlet process prior. One main feature of our approach is the generalization of a finite mixture model by having the number of components unspecified. A Bayesian sampling scheme based on a weighted Chinese restaurant process is proposed to generate partitions of observations. Using the partitions, Bayesian prediction, while accounting for possible model uncertainty, determining the most probable number of mixture components, clustering of time series and outlier detection in time series, can be done. Numerical results from simulated and real data are presented to illustrate the methodology.     

基于数据关联狄利克雷混合模型的电网净负荷不确定性表征研究EI北大核心CSCD

针对电网净负荷时序数据关联的特点,提出基于数据关联的狄利克雷混合模型(Data-relevance Dirichlet process mixture model,DDPMM)来表征净负荷的不确定性.首先,使用狄利克雷混合模型对净负荷的观测数据与预测数据进行拟合,得到其混合概率模型;然后,提出考虑数据关联的变分贝叶斯推断方法,改进后验分布对该混合概率模型进行求解,从而得到混合模型的最优参数;最后,根据净负荷预测值的大小得到其对应的预测误差边缘概率分布,实现不确定性表征.本文基于比利时电网的净负荷数据进行检验,算例结果表明:与传统的狄利克雷混合模型和高斯混合模型(Gaussian mixture model,GMM)等方法相比,所提出的基于数据关联狄利克雷混合模型可以更为有效地表征净负荷的不确定性.