基于贝叶斯网络的基因调控研究

为研究基因间的网络调控关系,通过贝叶斯网络方法将概率论知识与图论结合,有效构造了基因间的贝叶斯网络模型并进行了推理.针对一组白血病基因表达数据,首先进行数据标准化、离散化等预处理;其次使用决策树ID3算法求出基因间节点的顺序,并使用K2算法进行贝叶斯网络的结构学习,找出各基因间的网络拓扑结构;再次通过极大似然估计进行参数学习,求出网络中父节点与子节点间的概率依赖关系;最后对构建的贝叶斯网络模型进行了有效性验证,检验数据分析表明,贝叶斯网络对基因间调控关系的预测分析有较高精度.     

高维数据下的贝叶斯网络结构学习

贝叶斯网络模型作为一种传统有效的大数据图模型,因其具有因果和概率性语义等特点受到学者们的广泛研究。为了解决基于高维数据构建贝叶斯网络的难题,本文提出了一种适用于高维数据的贝叶斯网络结构学习算法—LTB算法,该算法由Lasso、Tabu Search算法和BIC结合。首先,运用Lasso降低协变量的维数,筛选出与目标变量关系密切的协变量将作为贝叶斯网络的顶点。然后,选择Tabu Search作为元启发式算法,选择BIC作为计算得分的方法,两者结合构建全局最优的贝叶斯网络结构。实证分析表明,LTB算法应用于上证综指影响因素的研究,既可以获得上证综指与其影响因素间的因果关系,也可以利用条件概率得到上证综指影响因素间的组合方式。     

两部分潜变量模型的变分贝叶斯推断

两部分潜变量模型是一种被广泛用于探索半连续数据中不可观测异质性的统计方法.文章对两部分潜变量建立变分贝叶斯推断程序.相比于马尔可夫链蒙特卡洛(MCMC)抽样方法,变分贝叶斯方法具有计算速度快、可提供确定性解等优点.利用Logistic模型一个随机表示,构造了一个适当的变分分布族来近似后验.变分分布通过坐标上升变分算法获得;给出了变分参数的更新计划,建立了变量选择和模型评价贝叶斯程序.经验结果展示了该方法的有效性和实用价值.     

函数型空间自回归模型的贝叶斯估计

函数型数据广泛地存在于社会的各个领域, 函数型数据分析也成为越来越热的统计研究方向. 经典的函数型回归模型一般假设响应变量是一个独立变量, 而在经济学, 环境科学等领域会经常遇到响应变量具有空间相依关系. 因此针对带有空间响应变量的部分函数型空间自回归模型, 基于函数型主成分分析和MCMC算法研究了模型的贝叶斯估计. 运用■表示定理来逼近函数型系数的思想, 以及应用Gibbs抽样和Metropolis-Hastings算法相结合的混合MCMC算法来获得模型中未知参数和函数型系数的贝叶斯估计结果. 最后通过模拟研究和对加拿大气温数据的实证分析来表明所提出的贝叶斯估计方法是可行有效的.     

隐马尔可夫因子分析模型的半参数贝叶斯分析

因子模型在刻画潜在因素(因子)与观测变量间的影响关系并进而解释多元观测指标(变量)间的相关性方面具有重要作用.在实际应用中,观测数据往往呈现出时序变异多峰,偏态等特性.将经典的因子分析延伸到带有时齐隐马尔可夫模型的动力因子模型,并建立了半参数贝叶斯分析程序.分块GIBBS抽样器用以后验抽样.经验结果展示所建立的统计程序是有效的.     

考虑基因与基因间的交互作用的基因组选择方法研究

综合考虑主基因效应以及基因间的交互效应对植物选育种的作用是基因组选择研究关注的热点问题之一.目前已有的研究大多忽略了基因的交互效应,这主要是由于考虑交互效应会大大增加备选基因的数目,从而导致已有的统计建模方法不稳定.本文将基因效应与基因间的交互效应同时引入模型,提出三步模型构建方法以达到简化计算和提高模型预测精度的目标.第一步,不考虑具体模型,通过距离相关筛除方法删掉与响应变量显著无关的基因;第二步,在剩下的基因中,利用贝叶斯方法筛选可能的基因;第三步,基于选出的基因,同时考虑单基因效应和交互效应,利用惩罚方法选择模型并估计参数.通过模拟计算说明我们提出的方法与已有的一步模型选择方法相比具有计算简单、稳健、运行时间少并且预测精度高等优点.最后,将本文的方法应用于油菜花数据,实证分析表明,我们提出的方法显著地提高花期性状的预测精度.     

中位数回归的贝叶斯变量选择方法

当数据呈现厚尾特征或含有异常值时,基于惩罚最小二乘或似然函数的传统变量选择方法往往表现不佳.本文基于中位数回归和贝叶斯推断方法,研究线性模型的贝叶斯变量选择问题.通过选取回归系数的Spike and Slab先验,利用贝叶斯模型选择理论提出了中位数回归的贝叶斯估计方法,并提出了有效的后验Gibbs抽样程序.大量数值模拟和波士顿房价数据分析充分说明了所提方法的有效性.     

利用动态贝叶斯网构建基因调控网络的研究进展

构建基因调控网络是21世纪人类科学所面临的重要挑战之一。基因调控网络是一个基因组内基因相互作用而形成的关系网络,它从全基因组水平上以系统和全局的角度来研究复杂的生命现象及其本质。本文阐述了近几年来此领域的研究进展,着重介绍利用动态贝叶斯网络重构基因调控网络的若干模型,包括加权核l1模型,正则化模型、高斯混合贝叶斯网模型和自回归时间变化模型。     

两部分因子分析模型的贝叶斯推断

半连续数据在经济和社会科学调查中普遍存在.在分析该类数据时,经典两部分回归模型经常被用来刻画协变量对响应变量可变性的影响.然而,包含协变量并不能完全解释响应变量的可变性.忽略未被观测的数据异质性将导致方差的剧烈波动.在本文中,我们将两部分回归模型推广到两部分因子分析模型.多变量半连续数据未观测的异质性由潜在因子部分来解释.此外,通过引入潜在性因子,多重变量间的相依性也以线性组合方式通过共享因子变量得到刻画.在贝叶斯框架内,我们运用马尔可夫链蒙特卡洛(MCMC)方法来进行后验分析.GIBBS采样器被用于从后验分布中抽取样本.基于模拟的随机样本,未知参数估计和模型评价等统计推断问题获得解决.随机模拟和可卡因使用数据分析等实证结果显示了该方法的有效性和实用性.     

基于一类重尾分布的函数型线性回归模型的稳健性估计

假定随机误差分布来自具有重尾特征的scale mixtures of normal分布族,运用贝叶斯方法研究了函数型线性回归模型的稳健性估计,其中模型的响应变量为标量,解释变量为函数型变量.数值模拟结果表明:当响应变量的观测数据存在离群值时,建立的方法得到的模型参数的估计,要优于正态分布假定下的模型参数的估计.     

Inference of an oscillating model for the yeast cell cycle

High-throughput techniques allow measurement of hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex regulatory processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods for estimating model parameters fail in this setting, since they overfit the data. This is even the case, if the focus is on modeling subnetworks of, at most, a few tens of components. In a Bayesian learning approach, this problem is avoided by a restriction of the search space with prior probability distributions over model parameters.This paper combines both differential equation models and a Bayesian approach. We model the periodic behavior of proteins involved in the cell cycle of the budding yeast Saccharomyces cerevisiae, with differential equations, which are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state, and lots of efforts have been made to explain the observed periodic behavior. We introduce an approach to infer an oscillating network from experimental data. First, an oscillating core network is learned. This is extended by further components by using a Bayesian approach in a second step. A specifically designed hierarchical prior distribution over interaction strengths prevents overfitting, and drives the solutions to sparse networks with only a few significant interactions.We apply our method to a simulated and a real world dataset and reveal main regulatory interactions. Moreover, we are able to reconstruct the dynamic behavior of the network.     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

A Gaussian Mixed Model for Learning Discrete Bayesian Networks

In this paper, we address the problem of learning discrete Bayesian networks from noisy data. A graphical model based on a mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network is considered. The network learning is formulated as a maximum likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable—from simple regression analysis to learning gene/protein regulatory networks from microarray data.     

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.     

A PC algorithm variation for ordinal variables

Bayesian networks are graphical models that represent the joint distribution of a set of variables using directed acyclic graphs. The graph can be manually built by domain experts according to their knowledge. However, when the dependence structure is unknown (or partially known) the network has to be estimated from data by using suitable learning algorithms. In this paper, we deal with a constraint-based method to perform Bayesian networks structural learning in the presence of ordinal variables. We propose an alternative version of the PC algorithm, which is one of the most known procedures, with the aim to infer the network by accounting for additional information inherent to ordinal data. The proposal is based on a nonparametric test, appropriate for ordinal variables. A comparative study shows that, in some situations, the proposal discussed here is a slightly more efficient solution than the PC algorithm.     

Qualitative chain graphs and their application

For many problem domains, such as medicine, chain graphs are more attractive than Bayesian networks as they support representing interactions between variables that have no natural direction. In particular, interactions between variables that result from certain feedback mechanisms can be represented by chain graphs. Using qualitative abstractions of probabilistic interactions is also of interest, as these allow focusing on patterns in the interactions rather than on the numerical detail. Such patterns are often known by experts and sufficient for making decisions. So far, qualitative abstractions of probabilistic interactions have only been developed for Bayesian networks in the form of qualitative probabilistic networks. In this paper, such qualitative abstractions are developed for chain graphs with the practical aim of using qualitative knowledge as constraints on the hyperspace of probability distributions. The usefulness of qualitative chain graphs is explored for modelling and reasoning about the interactions between diseases.     

复杂疾病的分子网络模型研究

复杂疾病是危害人类健康的主要杀手.不同于单基因缺陷性遗传病,复杂疾病的发生发展与多个基因之间、基因与环境之间的相互作用有关,致病机理复杂,其早期诊断及治疗困难是21世纪生物医学研究的重大挑战之一.随着生物知识的不断积累和多层次"组学"数据的井喷式涌现,复杂疾病研究迎来了新的"组学革命",研究模式从以往的只关注某个分子扩展到对分子之间相互形成的生物分子网络的系统分析.作为系统生物学核心概念,生物分子网络系统整合大量生物知识和高通量生物数据,是研究复杂疾病的强有力工具.本文以分子网络为主线,以数学建模为工具来研究复杂疾病,针对复杂疾病关系和复杂疾病的发生发展机制等复杂疾病研究的关键热点问题,分析和集成高通量多层次组学数据,构建并求解生物分子网络的数学模型,在若干复杂疾病相关系统生物学问题中取得有生物学意义的结果.本文提出若干生物网络建模、分析及应用的方法并提供若干应用软件,为从系统层面理解复杂疾病提供重要参考;同时,网络模型在若干实例中的应用得到若干有生物学意义的结论,为揭示复杂疾病机理、推动疾病治疗与预防起到了一定的作用.     

A Bayesian record linkage model incorporating relational data

In this article, we introduce a novel Bayesian approach for linking multiple social networks in order to discover the same real world person having different accounts across networks. In particular, we develop a latent model that allows us to jointly characterize the network and linkage structures relying on both relational and profile data. In contrast to other existing approaches in the machine learning literature, our Bayesian implementation naturally provides uncertainty quantification via posterior probabilities for the linkage structure itself or any function of it. Our findings clearly suggest that our methodology can produce accurate point estimates of the linkage structure even in the absence of profile information, and also, in an identity resolution setting, our results confirm that including relational data into the matching process improves the linkage accuracy. We illustrate our methodology using real data from popular social networks such as Twitter , Facebook , and YouTube .