Hierarchical multi-channel hidden semi Markov graphical models for activity recognition

Recognizing human actions from a stream of unsegmented sensory observations is important for a number of applications such as surveillance and human-computer interaction. A wide range of graphical models have been proposed for these tasks, and are typically extensions of the generative hidden Markov models (HMMs) or their discriminative counterpart, conditional random fields (CRFs). These extensions typically address one of three key limitations in the basic HMM/CRF formalism – unrealistic models for the duration of a sub-event, not encoding interactions among multiple agents directly and not modeling the inherent hierarchical organization of activities. In our work, we present a family of graphical models that generalize such extensions and simultaneously model event duration, multi agent interactions and hierarchical structure. We also present general algorithms for efficient learning and inference in such models based on local variational approximations. We demonstrate the effectiveness of our framework by developing graphical models for applications in automatic sign language (ASL) recognition, and for gesture and action recognition in videos. Our methods show results comparable to state-of-the-art in the datasets we consider, while requiring far fewer training examples compared to low-level feature based methods.     

概率图模型推理方法的研究进展

近年来概率图模型已成为不确定性推理的研究热点,在人工智能、机器学习与计算机视觉等领域有广阔的应用前景.根据网络结构与查询问题类型的不同,系统地综述了概率图模型的推理算法.首先讨论了贝叶斯网络与马尔可夫网络中解决概率查询问题的精确推理算法与近似推理算法,其中主要介绍精确推理中的VE算法、递归约束算法和团树算法,以及近似推理中的变分近似推理和抽样近似推理算法,并给出了解决MAP查询问题的常用推理算法;然后分别针对混合网络的连续与混合情况阐述其推理算法,并分析了暂态网络的精确推理、近似推理以及混合情况下的推理;最后指出了概率图模型推理方法未来的研究方向.     

Factorial Hidden Markov Models

Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot.     

Variational Bayesian methods for spatial data analysis

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.     

概率生成模型变分推理方法综述

概率生成模型是知识表示的重要方法,在该模型上计算似然函数的概率推理问题一般是难解的.变分推理是重要的确定性近似推理方法,具有较快的收敛速度、坚实的理论基础.尤其随着大数据时代的到来,概率生成模型变分推理方法受到工业界和学术界的极大关注.综述了多种概率生成模型变分推理框架及最新进展,具体包括:首先综述了概率生成模型变分推理一般框架及基于变分推理的生成模型参数学习过程;然后对于条件共轭指数族分布,给出了具有解析优化式的变分推理框架及该框架下可扩展的随机化变分推理;进一步,对于一般概率分布,给出了基于随机梯度的黑盒变分推理框架,并简述了该框架下多种变分推理算法的具体实现;最后分析了结构化变分推理,通过不同方式丰富变分分布提高推理精度并改善近似推理一致性.此外,展望了概率生成模型变分推理的发展趋势.     

Improving probabilistic inference in graphical models with determinism and cycles

Many important real-world applications of machine learning, statistical physics, constraint programming and information theory can be formulated using graphical models that involve determinism and cycles. Accurate and efficient inference and training of such graphical models remains a key challenge. Markov logic networks (MLNs) have recently emerged as a popular framework for expressing a number of problems which exhibit these properties. While loopy belief propagation (LBP) can be an effective solution in some cases; unfortunately, when both determinism and cycles are present, LBP frequently fails to converge or converges to inaccurate results. As such, sampling based algorithms have been found to be more effective and are more popular for general inference tasks in MLNs. In this paper, we introduce Generalized arc-consistency Expectation Maximization Message-Passing (GEM-MP), a novel message-passing approach to inference in an extended factor graph that combines constraint programming techniques with variational methods. We focus our experiments on Markov logic and Ising models but the method is applicable to graphical models in general. In contrast to LBP, GEM-MP formulates the message-passing structure as steps of variational expectation maximization. Moreover, in the algorithm we leverage the local structures in the factor graph by using generalized arc consistency when performing a variational mean-field approximation. Thus each such update increases a lower bound on the model evidence. Our experiments on Ising grids, entity resolution and link prediction problems demonstrate the accuracy and convergence of GEM-MP over existing state-of-the-art inference algorithms such as MC-SAT, LBP, and Gibbs sampling, as well as convergent message passing algorithms such as the concave–convex procedure, residual BP, and the L2-convex method.     

视觉信息处理中的马尔可夫随机场

由于视觉信息处理中存在大量的不确定性,概率图模型在计算机视觉领域有着广泛的应用,备受广大学者的关注。许多视觉问题都可以通过建立概率图模型进行求解,随着高效求解算法的提出和发展,马尔可夫随机场在解决计算机视觉领域的大规模数据问题中具有很大的优势。首先简要地介绍了概率图模型的概念,然后对马尔可夫随机场模型的定义、特性和推导求解进行了分析和讨论,在此基础上,以马尔可夫随机场在视觉信息的应用为线索,对目前基于马尔可夫随机场的计算机视觉信息处理的主要技术进行了概述和比较研究。     

概率图模型学习技术研究进展

概率图模型能有效处理不确定性推理,从样本数据中准确高效地学习概率图模型是其在实际应用中的关键问题.概率图模型的表示由参数和结构两部分组成,其学习算法也相应分为参数学习与结构学习.本文详细介绍了基于概率图模型网络的参数学习与结构学习算法,并根据数据集是否完备而分别讨论各种情况下的参数学习算法,还针对结构学习算法特点的不同把结构学习算法归纳为基于约束的学习、基于评分搜索的学习、混合学习、动态规划结构学习、模型平均结构学习和不完备数据集的结构学习.并总结了马尔科夫网络的参数学习与结构学习算法.最后指出了概率图模型学习的开放性问题以及进一步的研究方向.     

A PENALTY-LOGIC SIMPLE-TRANSITION MODEL FOR STRUCTURED SEQUENCES

We study the problem of learning to infer hidden-state sequences of processes whose states and observations are propositionally or relationally factored. Unfortunately, standard exact inference techniques such as Viterbi and graphical model inference exhibit exponential complexity for these processes. The main motivation behind our work is to identify a restricted space of models, which facilitate efficient inference, yet are expressive enough to remain useful in many applications. In particular, we present the penalty-logic simple-transition model, which utilizes a very simple-transition structure where the transition cost between any two states is constant. While not appropriate for all complex processes, we argue that it is often rich enough in many applications of interest, and when it is applicable there can be inference and learning advantages compared to more general models. In particular, we show that sequential inference for this model, that is, finding a minimum-cost state sequence, efficiently reduces to a single-state minimization (SSM) problem. We then show how to define atemporal-cost models in terms of penalty logic, or weighted logical constraints, and how to use this representation for practically efficient SSM computation. We present a method for learning the weights of our model from labeled training data based on Perceptron updates. Finally, we give experiments in both propositional and relational video-interpretation domains showing advantages compared to more general models.     

Robust adaptive algorithm for nonlinear systems with unknown measurement noise and uncertain parameters by variational Bayesian inference

This paper studies an adaptive algorithm for the estimation problem of nonlinear systems with unknown or missing measurement noise and uncertain parameters using variational Bayesian (VB) inference. We combine VB inference with the Monte Carlo sampling technique to settle this problem. There are many cases of missing information, and because of the difficulty in obtaining the analytical results, the existing control methods for uncertain systems lack generality. We present a set of nonlinear recursive adaptive filtering algorithms that address the unknown parameters and probability density function. The proposed algorithms yield a separable variational approximation of the joint posterior distribution of noise parameters with uncertain parameters and states on each step separately. Estimation convergence and robustness against disturbances are guaranteed. A convergence result for VB inference is presented. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms.     

Latent classification models for binary data

One of the simplest, and yet most consistently well-performing set of classifiers is the naïve Bayes models (a special class of Bayesian network models). However, these models rely on the (naïve) assumption that all the attributes used to describe an instance are conditionally independent given the class of that instance. To relax this independence assumption, we have in previous work proposed a family of models, called latent classification models (LCMs). LCMs are defined for continuous domains and generalize the naïve Bayes model by using latent variables to model class-conditional dependencies between the attributes. In addition to providing good classification accuracy, the LCM has several appealing properties, including a relatively small parameter space making it less susceptible to over-fitting. In this paper we take a first step towards generalizing LCMs to hybrid domains, by proposing an LCM for domains with binary attributes. We present algorithms for learning the proposed model, and we describe a variational approximation-based inference procedure. Finally, we empirically compare the accuracy of the proposed model to the accuracy of other classifiers for a number of different domains, including the problem of recognizing symbols in black and white images.     

Mean-field variational approximate Bayesian inference for latent variable models

The ill-posed nature of missing variable models offers a challenging testing ground for new computational techniques. This is the case for the mean-field variational Bayesian inference. The behavior of this approach in the setting of the Bayesian probit model is illustrated. It is shown that the mean-field variational method always underestimates the posterior variance and, that, for small sample sizes, the mean-field variational approximation to the posterior location could be poor.     

Combining Statistical Language Models via the Latent Maximum Entropy Principle

We present a unified probabilistic framework for statistical language modeling which can simultaneously incorporate various aspects of natural language, such as local word interaction, syntactic structure and semantic document information. Our approach is based on a recent statistical inference principle we have proposed—the latent maximum entropy principle—which allows relationships over hidden features to be effectively captured in a unified model. Our work extends previous research on maximum entropy methods for language modeling, which only allow observed features to be modeled. The ability to conveniently incorporate hidden variables allows us to extend the expressiveness of language models while alleviating the necessity of pre-processing the data to obtain explicitly observed features. We describe efficient algorithms for marginalization, inference and normalization in our extended models. We then use these techniques to combine two standard forms of language models: local lexical models (Markov N-gram models) and global document-level semantic models (probabilistic latent semantic analysis). Our experimental results on the Wall Street Journal corpus show that we obtain a 18.5% reduction in perplexity compared to the baseline tri-gram model with Good-Turing smoothing.Editors: Dan Roth and Pascale Fung     

On Learning Gene Regulatory Networks Under the Boolean Network Model

Boolean networks are a popular model class for capturing the interactions of genes and global dynamical behavior of genetic regulatory networks. Recently, a significant amount of attention has been focused on the inference or identification of the model structure from gene expression data. We consider the Consistency as well as Best-Fit Extension problems in the context of inferring the networks from data. The latter approach is especially useful in situations when gene expression measurements are noisy and may lead to inconsistent observations. We propose simple efficient algorithms that can be used to answer the Consistency Problem and find one or all consistent Boolean networks relative to the given examples. The same method is extended to learning gene regulatory networks under the Best-Fit Extension paradigm. We also introduce a simple and fast way of finding all Boolean networks having limited error size in the Best-Fit Extension Problem setting. We apply the inference methods to a real gene expression data set and present the results for a selected set of genes.     

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.     

Variational EM method for blur estimation using the spike-and-slab image prior

Most state-of-the-art blind image deconvolution methods rely on the Bayesian paradigm to model the deblurring problem and estimate both the blur kernel and latent image. It is customary to model the image in the filter space, where it is supposed to be sparse, and utilize convenient priors to account for this sparsity. In this paper, we propose the use of the spike-and-slab prior together with an efficient variational Expectation Maximization (EM) inference scheme to estimate the blur in the image. The spike-and-slab prior, which constitutes the gold standard in sparse machine learning, selectively shrinks irrelevant variables while mildly regularizing the relevant ones. The proposed variational Expectation Maximization algorithm is more efficient than usual Markov Chain Monte Carlo (MCMC) inference and, also, proves to be more accurate than the standard mean-field variational approximation. Additionally, all the prior model parameters are estimated by the proposed scheme. After blur estimation, a non-blind restoration method is used to obtain the actual estimation of the sharp image. We investigate the behavior of the prior in the experimental section together with a series of experiments with synthetically generated and real blurred images that validate the method's performance in comparison with state-of-the-art blind deconvolution techniques.     

Improving the Mean-Field Approximation in Belief Networks Using Bahadur's Reparameterisation of the Multivariate Binary Distribution

We develop a new extension to the Mean-Field approximation for inference in graphical models which has advantages over other approximation schemes which have been proposed. The method is economical in its use of variational parameters and the approximating conditional distribution can be specified with direct reference to the dependence structure of the variables in the graphical model. We apply the method to sigmoid belief networks.     

Bayesian inference for wind field retrieval

In many problems in spatial statistics it is necessary to infer a global problem solution by combining local models. A principled approach to this problem is to develop a global probabilistic model for the relationships between local variables and to use this as the prior in a Bayesian inference procedure. We use a Gaussian process with hyper-parameters estimated from numerical weather prediction models, which yields meteorologically convincing wind fields. We use neural networks to make local estimates of wind vector probabilities. The resulting inference problem cannot be solved analytically, but Markov Chain Monte Carlo methods allow us to retrieve accurate wind fields.