Optimising dynamic graphical models for video content analysis

A key problem in video content analysis using dynamic graphical models is to learn a suitable model structure given observed visual data. We propose a completed likelihood AIC (CL-AIC) scoring function for solving the problem. CL-AIC differs from existing scoring functions in that it aims to optimise explicitly both the explanation and prediction capabilities of a model simultaneously. CL-AIC is derived as a general scoring function suitable for both static and dynamic graphical models with hidden variables. In particular, we formulate CL-AIC for determining the number of hidden states for a hidden Markov model (HMM) and the topology of a dynamically multi-linked HMM (DML-HMM). The effectiveness of CL-AIC on learning the optimal structure of a dynamic graphical model especially given sparse and noisy visual date is shown through comparative experiments against existing scoring functions including Bayesian information criterion (BIC), Akaike’s information criterion (AIC), integrated completed likelihood (ICL), and variational Bayesian (VB). We demonstrate that CL-AIC is superior to the other scoring functions in building dynamic graphical models for solving two challenging problems in video content analysis: (1) content based surveillance video segmentation and (2) discovering causal/temporal relationships among visual events for group activity modelling.     

Locating multiple interacting quantitative trait loci using robust model selection

One of the most popular criteria for model selection is the Bayesian Information Criterion (BIC). It is based on an asymptotic approximation using Bayes rule when the sample size tends to infinity and the dimension of the model is fixed. Although it works well in classical applications, it performs less satisfactorily for high dimensional problems, i.e. when the number of regressors is very large compared to the sample size. For this reason, an alternative version of the BIC has been proposed for the problem of mapping quantitative trait loci (QTLs) considered in genetics. One approach is to locate QTLs by using model selection in the context of a regression model with an extremely large number of potential regressors. Since the assumption of normally distributed errors is often unrealistic in such settings, we extend the idea underlying the modified BIC to the context of robust regression.     

Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models

The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated.     

A backward elimination discrete optimization algorithm for model selection in spatio-temporal regression models

Regression models are used in geosciences to extrapolate data and identify significant predictors of a response variable. Criterion approaches based on the residual sum of squares (RSS), such as the Akaike Information Criterion, Bayesian Information Criterion (BIC), Deviance Information Criterion, or Mallows' Cp can be used to compare non-nested models to identify an optimal subset of covariates. Computational limitations arise when the number of observations or candidate covariates is large in comparing all possible combinations of the available covariates, and in characterizing the covariance of the residuals for each examined model when the residuals are autocorrelated, as is often the case in spatial and temporal regression analysis. This paper presents computationally efficient algorithms for identifying the optimal model as defined using any RSS-based model selection criterion. The proposed dual criterion optimal branch and bound (DCO B&B) algorithm is guaranteed to identify the optimal model, while a single criterion heuristic (SCH) B&B algorithm provides further computational savings and approximates the optimal solution. These algorithms are applicable both to multiple linear regression (MLR) and to response variables with correlated residuals. We also propose an approach for iterative model selection, where a single set of covariance parameters is used in each iteration rather than a different set of parameters being used for each examined model. Simulation experiments are performed to evaluate the performance of the algorithms for regression models, using MLR and geostatistical regression as prototypical regression tools and BIC as a prototypical model selection approach. Results show massive computational savings using the DCO B&B algorithm relative to performing an exhaustive search. The SCH B&B is shown to provide a good approximation of the optimal model in most cases, while the DCO B&B with iterative covariance parameter optimization yields the closest approximation to the DCO B&B algorithm while also providing additional computational savings.     

Hidden Markov random field model selection criteria based on mean field-like approximations

Hidden Markov random fields appear naturally in problems such as image segmentation, where an unknown class assignment has to be estimated from the observations at each pixel. Choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis. A commonly used selection criterion is the Bayesian Information Criterion (BIC) of Schwarz (1978), but for hidden Markov random fields, its exact computation is not tractable due to the dependence structure induced by the Markov model. We propose approximations of BIC based on the mean field principle of statistical physics. The mean field theory provides approximations of Markov random fields by systems of independent variables leading to tractable computations. Using this principle, we first derive a class of criteria by approximating the Markov distribution in the usual BIC expression as a penalized likelihood. We then rewrite BIC in terms of normalizing constants, also called partition functions, instead of Markov distributions. It enables us to use finer mean field approximations and to derive other criteria using optimal lower bounds for the normalizing constants. To illustrate the performance of our partition function-based approximation of BIC as a model selection criterion, we focus on the preliminary issue of choosing the number of classes before the segmentation task. Experiments on simulated and real data point out our criterion as promising: It takes spatial information into account through the Markov model and improves the results obtained with BIC for independent mixture models.     

Mixture model selection via hierarchical BIC

The Bayesian information criterion (BIC) is one of the most popular criteria for model selection in finite mixture models. However, it implausibly penalizes the complexity of each component using the whole sample size and completely ignores the clustered structure inherent in the data, resulting in over-penalization. To overcome this problem, a novel criterion called hierarchical BIC (HBIC) is proposed which penalizes the component complexity only using its local sample size and matches the clustered data structure well. Theoretically, HBIC is an approximation of the variational Bayesian (VB) lower bound when sample size is large and the widely used BIC is a less accurate approximation. An empirical study is conducted to verify this theoretical result and a series of experiments is performed on simulated and real data sets to compare HBIC and BIC. The results show that HBIC outperforms BIC substantially and BIC suffers from underestimation.     

Information methods for model selection in linear mixed effects models with application to HCV data

In this paper, we derive a small sample Akaike information criterion, based on the maximized loglikelihood, and a small sample information criterion based on the maximized restricted loglikelihood in the linear mixed effects model when the covariance matrix of the random effects is known. Small sample corrected information criteria are proposed for a special case of linear mixed effects models, the balanced random-coefficient model, without assuming the random coefficients covariance matrix to be known. A simulation study comparing the derived criteria and several others for model selection in the linear mixed effects models is presented. We illustrate the behavior of the studied information criteria on real data from a study of subjects coinfected with HIV and Hepatitis C virus. Robustness of the criteria, in terms of the error distributed as a mixture of normal distributions, is also studied. Special attention is given to the behavior of the conditional AIC by Vaida and Blanchard (2005). Among the studied criteria, GIC performs best, while cAIC exhibits poor performance. Because of its inferior performance, as demonstrated in this work, we do not recommend its use for model selection in linear mixed effects models.     

Parameter estimation of Poisson mixture with automated model selection through BYY harmony learning

Finite mixture is widely used in the fields of information processing and data analysis. However, its model selection, i.e., the selection of components in the mixture for a given sample data set, has been still a rather difficult task. Recently, the Bayesian Ying-Yang (BYY) harmony learning has provided a new approach to the Gaussian mixture modeling with a favorite feature that model selection can be made automatically during parameter learning. In this paper, based on the same BYY harmony learning framework for finite mixture, we propose an adaptive gradient BYY learning algorithm for Poisson mixture with automated model selection. It is demonstrated well by the simulation experiments that this adaptive gradient BYY learning algorithm can automatically determine the number of actual Poisson components for a sample data set, with a good estimation of the parameters in the original or true mixture where the components are separated in a certain degree. Moreover, the adaptive gradient BYY learning algorithm is successfully applied to texture classification.     

Video Behaviour Mining Using a Dynamic Topic Model

This paper addresses the problem of fully automated mining of public space video data, a highly desirable capability under contemporary commercial and security considerations. This task is especially challenging due to the complexity of the object behaviors to be profiled, the difficulty of analysis under the visual occlusions and ambiguities common in public space video, and the computational challenge of doing so in real-time. We address these issues by introducing a new dynamic topic model, termed a Markov Clustering Topic Model (MCTM). The MCTM builds on existing dynamic Bayesian network models and Bayesian topic models, and overcomes their drawbacks on sensitivity, robustness and efficiency. Specifically, our model profiles complex dynamic scenes by robustly clustering visual events into activities and these activities into global behaviours with temporal dynamics. A Gibbs sampler is derived for offline learning with unlabeled training data and a new approximation to online Bayesian inference is formulated to enable dynamic scene understanding and behaviour mining in new video data online in real-time. The strength of this model is demonstrated by unsupervised learning of dynamic scene models for four complex and crowded public scenes, and successful mining of behaviors and detection of salient events in each.     

BYY Harmony Learning on Finite Mixture: Adaptive Gradient Implementation and A Floating RPCL Mechanism

In tackling the learning problem on a set of finite samples, Bayesian Ying-Yang (BYY) harmony learning has developed a new learning mechanism that makes model selection implemented either automatically during parameter learning or in help of evaluating a new class of model selection criteria. In this paper, parameter learning with automated model selection has been studied for finite mixture model via an adaptive gradient learning algorithm for BYY harmony learning on a specific bidirectional architecture (BI-architecture). Via theoretical analysis, it has shown that the adaptive gradient learning implements a mechanism of floating rival penalized competitive learning (RPCL) among the components in the mixture. Also, the simulation results are demonstrated well for the adaptive gradient algorithm on the sample data sets from Gaussian mixtures with certain degree of overlap. Moreover, the adaptive gradient algorithm is applied to classification of the Iris data and unsupervised color image segmentation.     

Beyond Tracking: Modelling Activity and Understanding Behaviour

In this work, we present a unified bottom-up and top-down automatic model selection based approach for modelling complex activities of multiple objects in cluttered scenes. An activity of multiple objects is represented based on discrete scene events and their behaviours are modelled by reasoning about the temporal and causal correlations among different events. This is significantly different from the majority of the existing techniques that are centred on object tracking followed by trajectory matching. In our approach, object-independent events are detected and classified by unsupervised clustering using Expectation-Maximisation (EM) and classified using automatic model selection based on Schwarz's Bayesian Information Criterion (BIC). Dynamic Probabilistic Networks (DPNs) are formulated for modelling the temporal and causal correlations among discrete events for robust and holistic scene-level behaviour interpretation. In particular, we developed a Dynamically Multi-Linked Hidden Markov Model (DML-HMM) based on the discovery of salient dynamic interlinks among multiple temporal processes corresponding to multiple event classes. A DML-HMM is built using BIC based factorisation resulting in its topology being intrinsically determined by the underlying causality and temporal order among events. Extensive experiments are conducted on modelling activities captured in different indoor and outdoor scenes. Our experimental results demonstrate that the performance of a DML-HMM on modelling group activities in a noisy and cluttered scene is superior compared to those of other comparable dynamic probabilistic networks including a Multi-Observation Hidden Markov Model (MOHMM), a Parallel Hidden Markov Model (PaHMM) and a Coupled Hidden Markov Model (CHMM). First online version published in February, 2006     

Cooperative behavior acquisition for mobile robots in dynamically changing real worlds via vision-based reinforcement learning and development

In this paper, we first discuss the meaning of physical embodiment and the complexity of the environment in the context of multi-agent learning. We then propose a vision-based reinforcement learning method that acquires cooperative behaviors in a dynamic environment. We use the robot soccer game initiated by RoboCup (Kitano et al., 1997) to illustrate the effectiveness of our method. Each agent works with other team members to achieve a common goal against opponents. Our method estimates the relationships between a learner's behaviors and those of other agents in the environment through interactions (observations and actions) using a technique from system identification. In order to identify the model of each agent, Akaike's Information Criterion is applied to the results of Canonical Variate Analysis to clarify the relationship between the observed data in terms of actions and future observations. Next, reinforcement learning based on the estimated state vectors is performed to obtain the optimal behavior policy. The proposed method is applied to a soccer playing situation. The method successfully models a rolling ball and other moving agents and acquires the learner's behaviors. Computer simulations and real experiments are shown and a discussion is given.     

基于期望最大理论的无监督图像分割

本文提出了一种新的基于期望最大化以及贝叶斯信息准则的图像分割方法。首先，运用K均值方法初始化图像分布，运用期望最大算法估计输入图像参数数据，且图像中类的数目由贝叶斯消息准则自动确定。运用最大似然标准将像素归类于最相近的类中。本法的优点在于不过分依赖于原始估计，可以用来进行无监督的图像的分割。运用两幅真实图像进行了实验，结果表明此方法有效。     

Simultaneous feature selection and clustering using mixture models

Clustering is a common unsupervised learning technique used to discover group structure in a set of data. While there exist many algorithms for clustering, the important issue of feature selection, that is, what attributes of the data should be used by the clustering algorithms, is rarely touched upon. Feature selection for clustering is difficult because, unlike in supervised learning, there are no class labels for the data and, thus, no obvious criteria to guide the search. Another important problem in clustering is the determination of the number of clusters, which clearly impacts and is influenced by the feature selection issue. In this paper, we propose the concept of feature saliency and introduce an expectation-maximization (EM) algorithm to estimate it, in the context of mixture-based clustering. Due to the introduction of a minimum message length model selection criterion, the saliency of irrelevant features is driven toward zero, which corresponds to performing feature selection. The criterion and algorithm are then extended to simultaneously estimate the feature saliencies and the number of clusters.     

图像场景分类中视觉词包模型方法综述

目的关于图像场景分类中视觉词包模型方法的综述性文章在国内外杂志上还少有报导,为了使国内外同行对图像场景分类中的视觉词包模型方法有一个较为全面的了解,对这些研究工作进行了系统总结。方法在参考国内外大量文献的基础上,对现有图像场景分类(主要指针对单一图像场景的分类)中出现的各种视觉词包模型方法从低层特征的选择与局部图像块特征的生成、视觉词典的构建、视觉词包特征的直方图表示、视觉单词优化等多方面加以总结和比较。结果回顾了视觉词包模型的发展历程,对目前存在的多种视觉词包模型进行了归纳,比较常见方法各自的优缺点,总结了视觉词包模型性能评价方法,并对目前常用的标准场景库进行汇总,同时给出了各自所达到的最高精度。结论图像场景分类中视觉词包模型方法的研究作为计算机视觉领域方兴未艾的热点研究领域,在国内外研究中取得了不少进展,在计算机视觉领域的研究也不再局限于直接应用模型描述图像内容,而是更多地考虑图像与文本的差异。虽然视觉词包模型在图像场景分类的应用中还存在很多亟需解决的问题,但是这丝毫不能掩盖其研究的重要意义。     

Identification of neural dynamic models for fault detection and isolation: the case of a real sugar evaporation process

The paper deals with problems of fault detection of industrial processes using dynamic neural networks. The considered neural network has a feed-forward multi-layer structure and dynamic characteristics are obtained by using dynamic neuron models. Two optimisation problems are associated with neural networks. The first one is selection of a proper network structure which is solved by using information criteria such as the Akaike Information Criterion or the Final Prediction Error. In turn, the training of the network is performed by a stochastic approximation algorithm. The effectiveness of the proposed fault detection and isolation system is checked using real data recorded in Lublin Sugar Factory, Poland. Additionally, a comparison with alternative approaches is presented.     

On Weight Design of Maximum Weighted Likelihood and an Extended EM Algorithm

The recent Maximum Weighted Likelihood (MWL) [18], [19] has provided a general learning paradigm for density-mixture model selection and learning, in which weight design, however, is a key issue. This paper will therefore explore such a design, and through which a heuristic extended Expectation-Maximization (X-EM) algorithm is presented accordingly. Unlike the EM algorithm [1], the X-EM algorithm is able to perform model selection by fading the redundant components out from a density mixture, meanwhile estimating the model parameters appropriately. The numerical simulations demonstrate the efficacy of our algorithm.