Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Dynamic Bayesian networks (DBN) are a class of graphical models that has become a standard tool for modeling various stochastic time-varying phenomena. In many applications, the primary goal is to infer the network structure from measurement data. Several efficient learning methods have been introduced for the inference of DBNs from time series measurements. Sometimes, however, it is either impossible or impractical to collect time series data, in which case, a common practice is to model the non-time series observations using static Bayesian networks (BN). Such an approach is obviously sub-optimal if the goal is to gain insight into the underlying dynamical model. Here, we introduce Bayesian methods for the inference of DBNs from steady state measurements. We also consider learning the structure of DBNs from a combination of time series and steady state measurements. We introduce two different methods: one that is based on an approximation and another one that provides exact computation. Simulation results demonstrate that dynamic network structures can be learned to an extent from steady state measurements alone and that inference from a combination of steady state and time series data has the potential to improve learning performance relative to the inference from time series data alone.     

基于高阶时空模型的视觉传感网络数据关联方法

数据关联是视觉传感网络联合监控系统的基本问题之一. 本文针对存在漏检条件下视觉传感网络的数据关联问题, 提出高阶时空观测模型并在此基础上建立了数据关联问题的动态贝叶斯网络描述. 给出了数据关联精确推理算法并分析了其计算复杂性, 接着根据不同的独立性假设提出两种近似推理算法以降低算法运算量, 并将提出的推理算法嵌入到EM算法框架中,使该算法能够应用于目标外观模型未知的情况. 仿真和实验结果表明了所提方法的有效性.     

Performance of hidden Markov model and dynamic Bayesian network classifiers on handwritten Arabic word recognition

This paper presents a comparative study of two machine learning techniques for recognizing handwritten Arabic words, where hidden Markov models (HMMs) and dynamic Bayesian networks (DBNs) were evaluated. The work proposed is divided into three stages, namely preprocessing, feature extraction and classification. Preprocessing includes baseline estimation and normalization as well as segmentation. In the second stage, features are extracted from each of the normalized words, where a set of new features for handwritten Arabic words is proposed, based on a sliding window approach moving across the mirrored word image. The third stage is for classification and recognition, where machine learning is applied using HMMs and DBNs. In order to validate the techniques, extensive experiments were conducted using the IFN/ENIT database which contains 32,492 Arabic words. Experimental results and quantitative evaluations showed that HMM outperforms DBN in terms of higher recognition rate and lower complexity.     

Approximate Continuous Top-<Emphasis Type="Italic">k</Emphasis> Query over Sliding Window

Continuous top-k query over sliding window is a fundamental problem in database, which retrieves k objects with the highest scores when the window slides. Existing studies mainly adopt exact algorithms to tackle this type of queries, whose key idea is to maintain a subset of objects in the window, and try to retrieve answers from it. However, all the existing algorithms are sensitive to query parameters and data distribution. In addition, they suffer from expensive overhead for incremental maintenance, and thus cannot satisfy real-time requirement. In this paper, we define a novel query named (ε, δ)-approximate continuous top-k query, which returns approximate answers for top-k query. In order to efficiently support this query, we propose an efficient framework, named PABF (Probabilistic Approximate Based Framework), to support approximate top-k query over sliding window. We firstly maintain a self-adaptive pruning value, which could filter out newly arrived objects who have a probability less than 1 ? δ of being a query result. For those objects that are not filtered, we combine them together, if the score difference among them is less than a threshold. To efficiently maintain these combined results, the framework PABF also proposes a multi-phase merging algorithm. Theoretical analysis indicates that even in the worst case, we require only logarithmic complexity for maintaining each candidate.     

Malware detection based on deep learning algorithm

In this study we represent malware as opcode sequences and detect it using a deep belief network (DBN). Compared with traditional shallow neural networks, DBNs can use unlabeled data to pretrain a multi-layer generative model, which can better represent the characteristics of data samples. We compare the performance of DBNs with that of three baseline malware detection models, which use support vector machines, decision trees, and the k-nearest neighbor algorithm as classifiers. The experiments demonstrate that the DBN model provides more accurate detection than the baseline models. When additional unlabeled data are used for DBN pretraining, the DBNs perform better than the other detection models. We also use the DBNs as an autoencoder to extract the feature vectors of executables. The experiments indicate that the autoencoder can effectively model the underlying structure of input data and significantly reduce the dimensions of feature vectors.

     

A sparse-response deep belief network based on rate distortion theory

Deep belief networks (DBNs) are currently the dominant technique for modeling the architectural depth of brain, and can be trained efficiently in a greedy layer-wise unsupervised learning manner. However, DBNs without a narrow hidden bottleneck typically produce redundant, continuous-valued codes and unstructured weight patterns. Taking inspiration from rate distortion (RD) theory, which encodes original data using as few bits as possible, we introduce in this paper a variant of DBN, referred to as sparse-response DBN (SR-DBN). In this approach, Kullback–Leibler divergence between the distribution of data and the equilibrium distribution defined by the building block of DBN is considered as a distortion function, and the sparse response regularization induced by L₁-norm of codes is used to achieve a small code rate. Several experiments by extracting features from different scale image datasets show that our approach SR-DBN learns codes with small rate, extracts features at multiple levels of abstraction mimicking computations in the cortical hierarchy, and obtains more discriminative representation than PCA and several basic algorithms of DBNs.     

基于滑动窗口均值先验的非同构动态贝叶斯网络转换点检测算法*

为了放宽动态贝叶斯网络中的同构假设,提出非同构贝叶斯网络.基于此种情况,文中提出结合先验知识的可逆跳转的马尔可夫链蒙特卡洛算法(APK-RJ-MCMC).算法基本假设为如果一个时间点左右窗口中数据均值间的欧氏距离越大,则这个时间点作为转换点的可能性越高.基于上述假设,可得到关于每个时间点作为转换点可能性的粗略估计,将其作为先验知识调控可逆跳转的马尔可夫蒙特卡洛采样技术(RJ-MCMC)采样转换点时的生成、消除、转换动作的提议概率之比,进而调节状态跳转时的接受概率.在人工数据集和基因数据集上的实验表明,相比其它算法,APK-RJ-MCMC在转换点检测上具有更高的检测后验概率.     

Medical image analysis using wavelet transform and deep belief networks

This paper introduces a three-step framework for classifying multiclass radiography images. The first step utilizes a de-noising technique based on wavelet transform (WT) and the statistical Kolmogorov Smirnov (KS) test to remove noise and insignificant features of the images. An unsupervised deep belief network (DBN) is designed for learning the unlabelled features in the second step. Although small-scale DBNs have demonstrated significant potential, the computational cost of training the restricted Boltzmann machine is a major issue when scaling to large networks. Moreover, noise in radiography images can cause a significant corruption of information that hinders the performance of DBNs. The combination of WT and KS test in the first step helps improve performance of DBNs. Discriminative feature subsets obtained in the first two steps serve as inputs into classifiers in the third step for evaluations. Five frequently used classifiers including naive Bayes, radial basis function network, random forest, sequential minimal optimization, and support vector machine and four different case studies are implemented for experiments using the Image Retrieval in Medical Application data set. The experimental results show that the three-step framework has significantly reduced computational cost and yielded a great performance for multiclass radiography image classification. Along with effective applications in image processing in other fields published in the literature, deep learning network in this paper has again demonstrated its robustness in handling a complex set of medical images. This implies that the proposed approach can be implemented in real practice for analysing noisy radiography images, which have many useful medical applications such as diagnosis of diseases related to lung, breast, musculoskeletal or pediatric studies.     

Adaptive learning of dynamic Bayesian networks with changing structures by detecting geometric structures of time series

A dynamic Bayesian network (DBN) is one of popular approaches for relational knowledge discovery such as modeling relations or dependencies, which change over time, between variables of a dynamic system. In this paper, we propose an adaptive learning method (autoDBN) to learn DBNs with changing structures from multivariate time series. In autoDBN, segmentation of time series is achieved first through detecting geometric structures transformed from time series, and then model regions are found from the segmentation by designed finding strategies; in each found model region, a DBN model is established by existing structure learning methods; finally, model revisiting is developed to refine model regions and improve DBN models. These techniques provide a special mechanism to find accurate model regions and discover a sequence of DBNs with changing structures, which are adaptive to changing relations between multivariate time series. Experimental results on simulated and real time series show that autoDBN is very effective in finding accurate/reasonable model regions and gives lower error rates, outperforming the switching linear dynamic system method and moving window method.

Representational power of restricted boltzmann machines and deep belief networks

Deep belief networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton, Osindero, and Teh (2006) along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a restricted Boltzmann machine (RBM), used to represent one layer of the model. Restricted Boltzmann machines are interesting because inference is easy in them and because they have been successfully used as building blocks for training deeper models. We first prove that adding hidden units yields strictly improved modeling power, while a second theorem shows that RBMs are universal approximators of discrete distributions. We then study the question of whether DBNs with more layers are strictly more powerful in terms of representational power. This suggests a new and less greedy criterion for training RBMs within DBNs.     

Active inference for dynamic Bayesian networks with an application to tissue engineering

In temporal domains, agents need to actively gather information to make more informed decisions about both the present and the future. When such a domain is modeled as a temporal graphical model, what the agent observes can be incorporated into the model by setting the respective random variables as evidence. Motivated by a tissue engineering application where the experimenter needs to decide how early a laboratory experiment can be stopped so that its possible future outcomes can be predicted within an acceptable uncertainty, we first present a dynamic Bayesian network (DBN) model of vascularization in engineered tissues and compare it with both real-world experimental data and agent-based simulations. We then formulate the question of “how early an experiment can be stopped to guarantee an acceptable uncertainty about the final expected outcome” as an active inference problem for DBNs and empirically and analytically evaluate several search algorithms that aim to find the ideal time to stop a tissue engineering laboratory experiment.     

对弧进行删除的Bayes网络近似方法

弧的删除是一种对Bayes网络模型进行近似的方法。文中以Kullback-Leibler偏差作为近似网络和原网络概率分布误差的测度,给出了近似网络在此测度意义下的最优参数。同时,也给出了通过对原网络删除多条弧进行近似的启发式算法,当给定一个误差上界时,可以使用此算法寻找满足误差要求的近似网络。     

A non-homogeneous dynamic Bayesian network with a hidden Markov model dependency structure among the temporal data points

In the topical field of systems biology there is considerable interest in learning regulatory networks, and various probabilistic machine learning methods have been proposed to this end. Popular approaches include non-homogeneous dynamic Bayesian networks (DBNs), which can be employed to model time-varying regulatory processes. Almost all non-homogeneous DBNs that have been proposed in the literature follow the same paradigm and relax the homogeneity assumption by complementing the standard homogeneous DBN with a multiple changepoint process. Each time series segment defined by two demarcating changepoints is associated with separate interactions, and in this way the regulatory relationships are allowed to vary over time. However, the configuration space of the data segmentations (allocations) that can be obtained by changepoints is restricted. A complementary paradigm is to combine DBNs with mixture models, which allow for free allocations of the data points to mixture components. But this extension of the configuration space comes with the disadvantage that the temporal order of the data points can no longer be taken into account. In this paper I present a novel non-homogeneous DBN model, which can be seen as a consensus between the free allocation mixture DBN model and the changepoint-segmented DBN model. The key idea is to assume that the underlying allocation of the temporal data points follows a Hidden Markov model (HMM). The novel HMM–DBN model takes the temporal structure of the time series into account without putting a restriction onto the configuration space of the data point allocations. I define the novel HMM–DBN model and the competing models such that the regulatory network structure is kept fixed among components, while the network interaction parameters are allowed to vary, and I show how the novel HMM–DBN model can be inferred with Markov Chain Monte Carlo (MCMC) simulations. For the new HMM–DBN model I also present two new pairs of MCMC moves, which can be incorporated into the recently proposed allocation sampler for mixture models to improve convergence of the MCMC simulations. In an extensive comparative evaluation study I systematically compare the performance of the proposed HMM–DBN model with the performances of the competing DBN models in a reverse engineering context, where the objective is to learn the structure of a network from temporal network data.     

引入分割团的BK推理算法及其在Robocup中的应用

BK算法是动态贝叶斯网络(DBNs)的一种主要近似推理方法,但对网络的人工分割会引入较大误差.首先通过将决策结点转换成随机结点,给出基于DBNs的Roboeup协作问题的一种建模方法;然后,给出一种引入分割团的新BK算法,以减小网络分割产生的误差,并对Robocup中的两个球员配合射门问题进行推理.引入分割团的BK算法和1.5片联合树推理算法的比较实验结果表明,引入分割团使BK算法在精度损失较小的情况下,时间性能有显著提高.     

挖掘滑动窗口中的数据流频繁项算法

滑动窗口是一种对最近一段时间内的数据进行挖掘的有效的技术,本文提出一种基于滑动窗口的流数据频繁项挖掘算法.算法采用了链表队列策略大大简化了算法,提高了挖掘的效率.对于给定的阈值S、误差ε和窗口长度n,算法可以检测在窗口内频度超过Sn的数据流频繁项,且使误差在εn以内.算法的空间复杂度为O(ε-1),对每个数据项的处理和查询时间均为O(1).在此基础上,我们还将该算法进行了扩展,可以通过参数的变化得到不同的流数据频繁项挖掘算法,使得算法的时间和空间复杂度之间得到调节.通过大量的实验证明,本文算法比其它类似算法具有更好的精度以及时间和空间效率.     

Distance-based outlier queries in data streams: the novel task and algorithms

This work proposes a method for detecting distance-based outliers in data streams under the sliding window model. The novel notion of one-time outlier query is introduced in order to detect anomalies in the current window at arbitrary points-in-time. Three algorithms are presented. The first algorithm exactly answers to outlier queries, but has larger space requirements than the other two. The second algorithm is derived from the exact one, reduces memory requirements and returns an approximate answer based on estimations with a statistical guarantee. The third algorithm is a specialization of the approximate algorithm working with strictly fixed memory requirements. Accuracy properties and memory consumption of the algorithms have been theoretically assessed. Moreover experimental results have confirmed the effectiveness of the proposed approach and the good quality of the solutions.     

单元化单隐变量变结构DDBN推理算法

变结构动态贝叶斯网络（DBN）描述的是一个非稳态随机过程,是一种更灵活、更有效的动态网络。为了克服现有变结构DBN的推理算法不能实现在线推理的缺陷,提出了一种近似在线推理算法--单元化单隐变量变结构离散DBN（DDBN）推理算法。在定义了单隐变量变结构离散动态贝叶斯模型和单元的基础上,提出了算法的基本思想,并从理论上对算法进行了推导。仿真实验验证了该算法的正确性和有效性。     

基于动态贝叶斯网络的连续语音识别框架及其Token传递模型

近年来,由于动态贝叶斯网络(DBN)相对于传统的隐马尔可夫模型(HMM)更具可解释性、可分解性以及可扩展性,基于DBN的语音识别引起学者们越来越多的关注.但是,目前关于基于DBN的语音识别的研究主要集中在孤立语音识别上,连续语音识别的框架和识别算法还远没有HMM成熟和灵活.为了解决基于DBN的连续语音识别的灵活性和可扩展性,将在基于HMM的连续语音识别中很好地解决了上述问题的Token传递模型加以修改,使之适用于DBN.在该模型基础上,为基于DBN的连续语音识别提出了一个基本框架,并在此框架下提出了一个新的独立于上层语言模型的识别算法.还介绍了作者开发的一套基于该框架的可用于连续语音识别及其他时序系统的工具包DTK.     

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.     

An evolutionary hyper-heuristic to optimise deep belief networks for image reconstruction

Deep Belief Networks (DBN) have become a powerful tools to deal with a wide range of applications. On complex tasks like image reconstruction, DBN’s performance is highly sensitive to parameter settings. Manually trying out different parameters is tedious and time consuming however often required in practice as there are not many better options. This work proposes an evolutionary hyper-heuristic framework for automatic parameter optimisation of DBN. The hyper-heuristic framework introduced here is the first of its kind in this domain. It involves a high level strategy and a pool of evolutionary operators such as crossover and mutation to generates DBN parameter settings by perturbing or modifying the current setting of a DBN. Providing a large set of operators could be beneficial to form a more effective high level strategy, but in the same time would increase the search space hence make it more difficulty to form a good strategy. To address this issue, a non-parametric statistical test is introduced to identify a subset of effective operators for different phases of the hyper-heuristic search. Three well-known image reconstruction datasets were used to evaluate the performance of the proposed framework. The results reveal that the proposed hyper-heuristic framework is very competitive when compared to the state of art methods.