A nonparametric Bayesian approach toward robot learning by demonstration

In the past years, many authors have considered application of machine learning methodologies to effect robot learning by demonstration. Gaussian mixture regression (GMR) is one of the most successful methodologies used for this purpose. A major limitation of GMR models concerns automatic selection of the proper number of model states, i.e., the number of model component densities. Existing methods, including likelihood- or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Under this motivation, to resolve the aforementioned issues of GMR-based methods for robot learning by demonstration, in this paper we introduce a nonparametric Bayesian formulation for the GMR model, the Dirichlet process GMR model. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally investigate its efficacy as a robot learning by demonstration methodology, considering a number of demanding robot learning by demonstration scenarios.     

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.     

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.     

Variational Bayesian inference for infinite generalized inverted Dirichlet mixtures with feature selection and its application to clustering

We developed a variational Bayesian learning framework for the infinite generalized Dirichlet mixture model (i.e. a weighted mixture of Dirichlet process priors based on the generalized inverted Dirichlet distribution) that has proven its capability to model complex multidimensional data. We also integrate a “feature selection” approach to highlight the features that are most informative in order to construct an appropriate model in terms of clustering accuracy. Experiments on synthetic data as well as real data generated from visual scenes and handwritten digits datasets illustrate and validate the proposed approach.     

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.     

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.     

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.     

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.     

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.     

Non-Gaussian Data Clustering via Expectation Propagation Learning of Finite Dirichlet Mixture Models and Applications

Learning appropriate statistical models is a fundamental data analysis task which has been the topic of continuing interest. Recently, finite Dirichlet mixture models have proved to be an effective and flexible model learning technique in several machine learning and data mining applications. In this article, the problem of learning and selecting finite Dirichlet mixture models is addressed using an expectation propagation (EP) inference framework. Within the proposed EP learning method, for finite mixture models, all the involved parameters and the model complexity (i.e. the number of mixture components), can be evaluated simultaneously in a single optimization framework. Extensive simulations using synthetic data along with two challenging real-world applications involving automatic image annotation and human action videos categorization demonstrate that our approach is able to achieve better results than comparable techniques.     

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.     

Variational learning of hierarchical infinite generalized Dirichlet mixture models and applications

Data clustering is a fundamental unsupervised learning task in several domains such as data mining, computer vision, information retrieval, and pattern recognition. In this paper, we propose and analyze a new clustering approach based on both hierarchical Dirichlet processes and the generalized Dirichlet distribution, which leads to an interesting statistical framework for data analysis and modelling. Our approach can be viewed as a hierarchical extension of the infinite generalized Dirichlet mixture model previously proposed in Bouguila and Ziou (IEEE Trans Neural Netw 21(1):107–122, 2010). The proposed clustering approach tackles the problem of modelling grouped data where observations are organized into groups that we allow to remain statistically linked by sharing mixture components. The resulting clustering model is learned using a principled variational Bayes inference-based algorithm that we have developed. Extensive experiments and simulations, based on two challenging applications namely images categorization and web service intrusion detection, demonstrate our model usefulness and merits.     

Positive vectors clustering using inverted Dirichlet finite mixture models

In this work we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, which offers a good representation and modeling of positive non-Gaussian data. The proposed approach for estimating the parameters of an inverted Dirichlet mixture is based on the maximum likelihood (ML) using Newton Raphson method. We also develop an approach, based on the minimum message length (MML) criterion, to select the optimal number of clusters to represent the data using such a mixture. Experimental results are presented using artificial histograms and real data sets. The challenging problem of software modules classification is investigated within the proposed statistical framework, also.     

A sparse nonparametric hierarchical Bayesian approach towards inductive transfer for preference modeling

In this paper, we present a novel methodology for preference learning based on the concept of inductive transfer. Specifically, we introduce a nonparametric hierarchical Bayesian multitask learning approach, based on the notion that human subjects may cluster together forming groups of individuals with similar preference rationale (but not identical preferences). Our approach is facilitated by the utilization of a Dirichlet process prior, which allows for the automatic inference of the most appropriate number of subject groups (clusters), as well as the employment of the automatic relevance determination (ARD) mechanism, giving rise to a sparse nature for our model, which significantly enhances its computational efficiency. We explore the efficacy of our novel approach by applying it to both a synthetic experiment and a real-world music recommendation application. As we show, our approach offers a significant enhancement in the effectiveness of knowledge transfer in statistical preference learning applications, being capable of correctly inferring the actual number of human subject groups in a modeled dataset, and limiting knowledge transfer only to subjects belonging to the same group (wherein knowledge transferability is more likely).     

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。     

A Bayesian nonparametric study of a dynamic nonlinear model

A Bayesian nonparametric approach to modeling a nonlinear dynamic model is presented. New techniques for sampling infinite mixture models are used. The inference procedure specifically in the case of the logistic model and when the nonparametric component is applied to the additive errors is demonstrated.     

Predictive performance of Dirichlet process shrinkage methods in linear regression

An obvious Bayesian nonparametric generalization of ridge regression assumes that coefficients are exchangeable, from a prior distribution of unknown form, which is given a Dirichlet process prior with a normal base measure. The purpose of this paper is to explore predictive performance of this generalization, which does not seem to have received any detailed attention, despite related applications of the Dirichlet process for shrinkage estimation in multivariate normal means, analysis of randomized block experiments and nonparametric extensions of random effects models in longitudinal data analysis. We consider issues of prior specification and computation, as well as applications in penalized spline smoothing. With a normal base measure in the Dirichlet process and letting the precision parameter approach infinity the procedure is equivalent to ridge regression, whereas for finite values of the precision parameter the discreteness of the Dirichlet process means that some predictors can be estimated as having the same coefficient. Estimating the precision parameter from the data gives a flexible method for shrinkage estimation of mean parameters which can work well when ridge regression does, but also adapts well to sparse situations. We compare our approach with ridge regression, the lasso and the recently proposed elastic net in simulation studies and also consider applications to penalized spline smoothing.     

Unsupervised selection of a finite Dirichlet mixture model: an MML-based approach

This paper proposes an unsupervised algorithm for learning a finite Dirichlet mixture model. An important part of the unsupervised learning problem is determining the number of clusters which best describe the data. We extend the minimum message length (MML) principle to determine the number of clusters in the case of Dirichlet mixtures. Parameter estimation is done by the expectation-maximization algorithm. The resulting method is validated for one-dimensional and multidimensional data. For the one-dimensional data, the experiments concern artificial and real SAP image histograms. The validation for multidimensional data involves synthetic data and two real applications: shadow detection in images and summarization of texture image databases for efficient retrieval. A comparison with results obtained for other selection criteria is provided.     

The infinite Student's t-factor mixture analyzer for robust clustering and classification

Recently, the Student's t-factor mixture analyzer (tFMA) has been proposed. Compared with the mixture of Student's t-factor analyzers (MtFA), the tFMA has better performance when processing high-dimensional data. Moreover, the factors estimated by the tFMA can be visualized in a low-dimensional latent space, which is not shared by the MtFA. However, as the tFMA belongs to finite mixtures and the related parameter estimation method is based on the maximum likelihood criterion, it could not automatically determine the appropriate model complexity according to the observed data, leading to overfitting. In this paper, we propose an infinite Student's t-factor mixture analyzer (itFMA) to handle this issue. The itFMA is based on the nonparametric Bayesian statistics which assumes infinite number of mixing components in advance, and automatically determines the proper number of components after observing the high-dimensional data. Moreover, we derive an efficient variational inference algorithm for the itFMA. The proposed itFMA and the related variational inference algorithm are used to cluster and classify high-dimensional data. Experimental results of some applications show that the itFMA has good generalization capacity, offering a more robust and powerful performance than other competing approaches.     

基于狄利克雷过程混合模型的内外先验融合

近年来,使用高斯混合模型作为块先验的贝叶斯方法取得了优秀的图像复原性能,针对这类模型分量固定及主要依赖外部学习的缺点,提出了一种新的基于狄利克雷过程混合模型的图像先验模型。该模型从干净图像数据库中学习外部通用先验,从退化图像中学习内部先验,借助模型中统计量的可累加性自然实现内外部先验融合。通过聚类的新增及归并机制,模型的复杂度随着数据的增大或缩小而自适应地变化,可以学习到可解释及紧凑的模型。为了求解所有隐变量的变分后验分布,提出了一种结合新增及归并机制的批次更新可扩展变分算法,解决了传统坐标上升算法在大数据集下效率较低、容易陷入局部最优解的问题。在图像去噪及填充实验中,相比传统方法,所提模型无论在客观质量评价还是视觉观感上都更有优势,验证了该模型的有效性。