Graphs for Margins of Bayesian Networks

Directed acyclic graph (DAG) models—also called Bayesian networks—are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are present, then the set of possible marginal distributions over the remaining (observed) variables is generally not represented by any DAG. Larger classes of mixed graphical models have been introduced to overcome this; however, as we show, these classes are not sufficiently rich to capture all the marginal models that can arise. We introduce a new class of hyper‐graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG and provide graphical results towards characterizing equivalence of these models. Finally, we show that mDAGs correctly capture the marginal structure of causally interpreted DAGs under interventions on the observed variables.     

A New Inference Framework for Dependency Networks

Dependency networks (DNs) have been receiving more attention recently because their structures and parameters can be easily learned from data. The full conditional distributions (FCDs) are known conditions of DNs. Gibbs sampling is currently the most popular inference method on DNs. However, sampling methods converge slowly and it can be hard to diagnose their convergence. In this article, we introduce a set of linear equations to describe the relations between joint probability distributions (JPDs) and FCDs. These equations provide a novel perspective to understand reasoning on DNs. Based on these linear equations, we develop both exact and approximate algorithms for inference on DNs. Experiments show that the proposed approximate algorithms can produce effective results by maintaining low computational complexity.     

Bayesian Inference for Contact Networks Given Epidemic Data

Abstract. In this article, we estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with Gamma distributed exposed and infectious periods on a network where every edge exists with the same probability, independent of other edges. We employ a Bayesian framework and Markov chain Monte Carlo (MCMC) integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the parameter estimates under various prior assumptions and show that it is possible in many scientifically interesting cases to accurately recover the parameters. We demonstrate our approach by studying a measles outbreak in Hagelloch, Germany, in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network.     

Object-Oriented Bayesian Networks for Modeling the Respondent Measurement Error

In this article, Object-Oriented Bayesian Networks (OOBN) are proposed as a tool to model measurement errors in a categorical variable due to respondent. A mixed measurement error model is presented and an OOBN implementing such a model is introduced. The insertion of evidence represented by the observed value and its propagation throughout the network yields for each unit the probability distribution of the true value given the observed. Two methods are used to predict the individual true value and their performance is evaluated via simulation.     

Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks

We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples.     

基于EMD和神经网络的非线性时间序列预测方法

现实生活中的时间序列,通常伴随着大量的噪声和高度的波动性。对于这些非线性时间序列,运用传统的统计和计量经济模型进行分析预测,预测结果往往不够理想。文章基于经验模态分解(EMD)和人工神经网络提出改进方法。主体思想是"先分再合":先用EMD方法分解非线性时间序列,得到一系列易于分析的独立的子系列,然后利用神经网络(FNN)对每一个子系列进行分析和预测,最后再用自适应线性神经网络(ALNN)整合并得出最终结果。结合具体房价时间序列实例,证实了这种方法的优势。     

Estimation and Confidence Intervals for Clock Offset in Networks with Bivariate Exponential Delays

There is a large and increasing literature on statistical modeling-based estimation of the offset between two clocks. Recent work has focused on the construction of confidence intervals for offset. However, in most of this work it has been assumed that the network delays that occur during the synchronization process are independent. The network delays are often modeled as independent exponential random variables. Thus, we introduce the use of a bivariate exponential distribution to capture the anticipated correlation between the network delays and derive a maximum likelihood estimator and a confidence interval procedure for the offset parameter. We then illustrate how use of the independent model for network delays can lead to improper inference about the offset parameter.     

Spare Reliability for Capacitated Computer Networks Under Tolerable Error Rate and Latency Considerations

Error rate and transmission time are both critical factors in a computer system. In addition to guarantee the robustness of the computer system under both tolerable error rate and latency, enhancing the system reliability by a routing scheme, named spare reliability, is also a critical task. Virtually, each branch possesses multiple possible capacities. Such a network is termed a capacitated computer network (CCN). Hence, this article develops an efficient algorithm to derive the spare reliability of a CCN, where the spare reliability is the probability that data can be sent through multiple minimal paths considering routing scheme.     

Multistate Survival Models as Transient Electrical Networks

In multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan–Meier mass function. Thus, the Kaplan–Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause‐specific Kaplan–Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model.