Learning mixture models with the regularized latent maximum entropy principle

This paper presents a new approach to estimating mixture models based on a recent inference principle we have proposed: the latent maximum entropy principle (LME). LME is different from Jaynes' maximum entropy principle, standard maximum likelihood, and maximum a posteriori probability estimation. We demonstrate the LME principle by deriving new algorithms for mixture model estimation, and show how robust new variants of the expectation maximization (EM) algorithm can be developed. We show that a regularized version of LME (RLME), is effective at estimating mixture models. It generally yields better results than plain LME, which in turn is often better than maximum likelihood and maximum a posterior estimation, particularly when inferring latent variable models from small amounts of data.     

Latent Classification Models

One of the simplest, and yet most consistently well-performing set of classifiers is the Naïve Bayes models. These models rely on two assumptions: (i) All the attributes used to describe an instance are conditionally independent given the class of that instance, and (ii) all attributes follow a specific parametric family of distributions. In this paper we propose a new set of models for classification in continuous domains, termed latent classification models. The latent classification model can roughly be seen as combining the Naïve Bayes model with a mixture of factor analyzers, thereby relaxing the assumptions of the Naïve Bayes classifier. In the proposed model the continuous attributes are described by a mixture of multivariate Gaussians, where the conditional dependencies among the attributes are encoded using latent variables. We present algorithms for learning both the parameters and the structure of a latent classification model, and we demonstrate empirically that the accuracy of the proposed model is significantly higher than the accuracy of other probabilistic classifiers.Editors: Pedro Larrañaga, Jose A. Lozano, Jose M. Peña and Iñaki Inza     

Learning flexible features for conditional random fields

Extending traditional models for discriminative labeling of structured data to include higher-order structure in the labels results in an undesirable exponential increase in model complexity. In this paper, we present a model that is capable of learning such structures using a random field of parameterized features. These features can be functions of arbitrary combinations of observations, labels and auxiliary hidden variables. We also present a simple induction scheme to learn these features, which can automatically determine the complexity needed for a given data set. We apply the model to two real-world tasks, information extraction and image labeling, and compare our results to several other methods for discriminative labeling.     

多尺度空间判别性概率潜在语义分析的场景分类

传统潜在语义分析(Latent Semantic Analysis, LSA)方法无法获得场景目标空间分布信息和潜在主题的判别信息。针对这一问题提出了一种基于多尺度空间判别性概率潜在语义分析(Probabilistic Latent Semantic Analysis, PLSA)的场景分类方法。首先通过空间金字塔方法对图像进行空间多尺度划分获得图像空间信息,结合PLSA模型获得每个局部块的潜在语义信息;然后串接每个特定局部块中的语义信息得到图像多尺度空间潜在语义信息;最后结合提出的权值学习方法来学习不同图像主题间的判别信息,从而得到图像的多尺度空间判别性潜在语义信息,并将学习到的权值信息嵌入支持向量基(Support Vector Machine, SVM)分类器中完成图像的场景分类。在常用的三个场景图像库(Scene-13、Scene-15和Caltech-101)上的实验表明,该方法平均分类精度比现有许多state-of-art方法均优。验证了其有效性和鲁棒性。     

Recognizing handwritten digits using hierarchical products ofexperts

The product of experts learning procedure can discover a set of stochastic binary features that constitute a nonlinear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, a hierarchy of separate models can be learned, for each digit class. Each model in the hierarchy learns a layer of binary feature detectors that model the probability distribution of vectors of activity of feature detectors in the layer below. The models in the hierarchy are trained sequentially and each model uses a layer of binary feature detectors to learn a generative model of the patterns of feature activities in the preceding layer. After training, each layer of feature detectors produces a separate, unnormalized log probability score. With three layers of feature detectors for each of the 10 digit classes, a test image produces 30 scores which can be used as inputs to a supervised, logistic classification network that is trained on separate data     

Confidence- and margin-based MMI/MPE discriminative training for off-line handwriting recognition

We present a novel confidence- and margin-based discriminative training approach for model adaptation of a hidden Markov model (HMM)-based handwriting recognition system to handle different handwriting styles and their variations. Most current approaches are maximum-likelihood (ML) trained HMM systems and try to adapt their models to different writing styles using writer adaptive training, unsupervised clustering, or additional writer-specific data. Here, discriminative training based on the maximum mutual information (MMI) and minimum phone error (MPE) criteria are used to train writer-independent handwriting models. For model adaptation during decoding, an unsupervised confidence-based discriminative training on a word and frame level within a two-pass decoding process is proposed. The proposed methods are evaluated for closed-vocabulary isolated handwritten word recognition on the IFN/ENIT Arabic handwriting database, where the word error rate is decreased by 33% relative compared to a ML trained baseline system. On the large-vocabulary line recognition task of the IAM English handwriting database, the word error rate is decreased by 25% relative.     

基于高斯混合模型的分量对称正定矩阵模型

高斯混合模型(GMM)可以利用多个高斯分量捕捉图像集的变化信息,是一种良好的图像集描述方法.结合分量对称正定矩阵表示方法(CSPD),文中提出基于GMM的CSPD模型(G-CSPD).模型将图像集分成大小相同的子图像集,使用GMM描述每个子图像集,最终得到一个G-CSPD矩阵,该矩阵中元素描述子图像集之间相似性.在3个图像集上的实验表明,G-CSPD是具有鉴别性的图像集描述方法.     

结合组稀疏效应和多核学习的图像标注

图像中存在的纹理、颜色和形状等异构视觉特征,在表示特定高层语义时所起作用的重要程度不同,为了在图像标注过程中更加有效地利用这些异构特征,提出了一种基于组稀疏(group sparsity)的多核学习方法(multiple kernel learning with group sparsity,简称MKLGS),为不同图像语义选择不同的组群特征.MKLGS先将包含多种异构特征的非线性图像数据映射到一个希尔伯特空间,然后利用希尔伯特空间中的核函数以及组LASSO(groupLASSO)对每个图像类别选择最具区别性特征的集合,最终训练得到分类模型对图像进行标注.通过与目前其他图像标注算法进行对比,实验结果表明,基于组稀疏的多核学习方法在图像标注中能取得很好的效果.     

混合空间新型贝叶斯网络模型的图像分割应用研究

现有研究工作没有确定概率向量模型的混合部分比例,所以无法解决MCMC方法的迭代收敛性问题。在具有空间平滑约束的高斯混合模型GMM基础上提出新型贝叶斯网络模型并应用于图像分割领域。模型应用隐Dirichlet分布LDA的概率密度模型和Gauss-Markov随机域MRF的隐Dirichlet参数混合过程来实现参数平滑过程,具有如下优点:针对空间平滑约束规范概率向量模型比例;使用最大后验概率MAP和期望最大化算法EM完成闭合参数的更新操作过程。实验表明,本模型比其他应用GMM方法的图像分割效果好。该模型已成功应用到自然图像和有噪声干扰的自然艺术图像分割过程中。     

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。     

Sequence classification via large margin hidden Markov models

We address the sequence classification problem using a probabilistic model based on hidden Markov models (HMMs). In contrast to commonly-used likelihood-based learning methods such as the joint/conditional maximum likelihood estimator, we introduce a discriminative learning algorithm that focuses on class margin maximization. Our approach has two main advantages: (i) As an extension of support vector machines (SVMs) to sequential, non-Euclidean data, the approach inherits benefits of margin-based classifiers, such as the provable generalization error bounds. (ii) Unlike many algorithms based on non-parametric estimation of similarity measures that enforce weak constraints on the data domain, our approach utilizes the HMM’s latent Markov structure to regularize the model in the high-dimensional sequence space. We demonstrate significant improvements in classification performance of the proposed method in an extensive set of evaluations on time-series sequence data that frequently appear in data mining and computer vision domains.     

基于非线性重构模型的植物叶片图像集分类方法

提出一种基于非线性重构模型的植物叶片图像集的分类识别方法。该方法首先使用高斯受限玻尔兹曼机(GRBMs)通过非监督预训练来初始化模型的权值;然后针对每一个植物叶片图像集用初始化的模型训练得到一个特定的模型;最后根据测试样本的最小重构误差和测试样本集的最多投票策略来判定测试样本集的类别。该方法通过图像预处理来处理图像,避免了图像在缩放时发生形变,并采用基于k-means的特征提取方法来提取植物叶片图像特征。实验结果表明,该方法能够准确地对植物叶片图像集进行分类识别。     

Searching for Complex Human Activities with No Visual Examples

We describe a method of representing human activities that allows a collection of motions to be queried without examples, using a simple and effective query language. Our approach is based on units of activity at segments of the body, that can be composed across space and across the body to produce complex queries. The presence of search units is inferred automatically by tracking the body, lifting the tracks to 3D and comparing to models trained using motion capture data. Our models of short time scale limb behaviour are built using labelled motion capture set. We show results for a large range of queries applied to a collection of complex motion and activity. We compare with discriminative methods applied to tracker data; our method offers significantly improved performance. We show experimental evidence that our method is robust to view direction and is unaffected by some important changes of clothing.     

Mixed-membership naive Bayes models

In recent years, mixture models have found widespread usage in discovering latent cluster structure from data. A popular special case of finite mixture models is the family of naive Bayes (NB) models, where the probability of a feature vector factorizes over the features for any given component of the mixture. Despite their popularity, naive Bayes models do not allow data points to belong to different component clusters with varying degrees, i.e., mixed memberships, which puts a restriction on their modeling ability. In this paper, we propose mixed-membership naive Bayes (MMNB) models. On one hand, MMNB can be viewed as a generalization of NB by putting a Dirichlet prior on top to allow mixed memberships. On the other hand, MMNB can also be viewed as a generalization of latent Dirichlet allocation (LDA) with the ability to handle heterogeneous feature vectors with different types of features, e.g., real, categorical, etc.. We propose two variational inference algorithms to learn MMNB models. The first one is based on ideas originally used in LDA, and the second one uses substantially fewer variational parameters, leading to a significantly faster algorithm. Further, we extend MMNB/LDA to discriminative mixed-membership models for classification by suitably combining MMNB/LDA with multi-class logistic regression. The efficacy of the proposed mixed-membership models is demonstrated by extensive experiments on several datasets, including UCI benchmarks, recommendation systems, and text datasets.     

Semisupervised learning for a hybrid generative/discriminative classifier based on the maximum entropy principle

This paper presents a method for designing semi-supervised classifiers trained on labeled and unlabeled samples. We focus on probabilistic semi-supervised classifier design for multi-class and single-labeled classification problems, and propose a hybrid approach that takes advantage of generative and discriminative approaches. In our approach, we first consider a generative model trained by using labeled samples and introduce a bias correction model, where these models belong to the same model family, but have different parameters. Then, we construct a hybrid classifier by combining these models based on the maximum entropy principle. To enable us to apply our hybrid approach to text classification problems, we employed naive Bayes models as the generative and bias correction models. Our experimental results for four text data sets confirmed that the generalization ability of our hybrid classifier was much improved by using a large number of unlabeled samples for training when there were too few labeled samples to obtain good performance. We also confirmed that our hybrid approach significantly outperformed generative and discriminative approaches when the performance of the generative and discriminative approaches was comparable. Moreover, we examined the performance of our hybrid classifier when the labeled and unlabeled data distributions were different.     

Conditional ordinal random fields for structured ordinal-valued label prediction

Predicting labels of structured data such as sequences or images is a very important problem in statistical machine learning and data mining. The conditional random field (CRF) is perhaps one of the most successful approaches for structured label prediction via conditional probabilistic modeling. In such models, it is traditionally assumed that each label is a random variable from a nominal category set (e.g., class categories) where all categories are symmetric and unrelated from one another. In this paper we consider a different situation of ordinal-valued labels where each label category bears a particular meaning of preference or order. This setup fits many interesting problems/datasets for which one is interested in predicting labels that represent certain degrees of intensity or relevance. We propose a fairly intuitive and principled CRF-like model that can effectively deal with the ordinal-scale labels within an underlying correlation structure. Unlike standard log-linear CRFs, learning the proposed model incurs non-convex optimization. However, the new model can be learned accurately using efficient gradient search. We demonstrate the improved prediction performance achieved by the proposed model on several intriguing sequence/image label prediction tasks.     

Expectation-maximization algorithms for inference in Dirichlet processes mixture

Mixture models are ubiquitous in applied science. In many real-world applications, the number of mixture components needs to be estimated from the data. A popular approach consists of using information criteria to perform model selection. Another approach which has become very popular over the past few years consists of using Dirichlet processes mixture (DPM) models. Both approaches are computationally intensive. The use of information criteria requires computing the maximum likelihood parameter estimates for each candidate model whereas DPM are usually trained using Markov chain Monte Carlo (MCMC) or variational Bayes (VB) methods. We propose here original batch and recursive expectation-maximization algorithms to estimate the parameters of DPM. The performance of our algorithms is demonstrated on several applications including image segmentation and image classification tasks. Our algorithms are computationally much more efficient than MCMC and VB and outperform VB on an example.     

图像中多语种文本提取的高斯混合建模方法

建立了相邻字符区域的高斯混合模型,用于区分字符与非字符.在此基础上,提出了一种从图像中提取多语种文本的方法.首先对输入图像进行二值化,并执行形态学闭运算,使二值图像中每个字符成为一个单独的连通成分.然后根据各连通成分重心的Voronoi区域,形成连通成分之间的邻接关系;最后在贝叶斯框架下,基于相邻字符区域的高斯混合模型计算相应的伪概率,以此为判据将每个连通成分标注为字符或非字符.利用所提出的文本提取方法,进行了复杂中英文文本的提取实验,获得大于97%的准确率和大于80%的召回率,证实了方法的有效性.