Gaining insight with recursive partitioning of generalized linear models

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearly give rise to different model parameter values. We present an approach that combines generalized linear models (GLM) with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's influence on a parametric model. This method conducts recursive partitioning of a GLM by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a GLM. We will show the method's versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization, and compare it to alternative approaches.     

Bayesian Classifiers Applied to the Tennessee Eastman Process

Fault diagnosis includes the main task of classification. Bayesian networks (BNs) present several advantages in the classification task, and previous works have suggested their use as classifiers. Because a classifier is often only one part of a larger decision process, this article proposes, for industrial process diagnosis, the use of a Bayesian method called dynamic Markov blanket classifier that has as its main goal the induction of accurate Bayesian classifiers having dependable probability estimates and revealing actual relationships among the most relevant variables. In addition, a new method, named variable ordering multiple offspring sampling capable of inducing a BN to be used as a classifier, is presented. The performance of these methods is assessed on the data of a benchmark problem known as the Tennessee Eastman process. The obtained results are compared with naive Bayes and tree augmented network classifiers, and confirm that both proposed algorithms can provide good classification accuracies as well as knowledge about relevant variables.     

A reflected feature space for CART

We present an algorithm for learning oblique decision trees, called HHCART(G). Our decision tree combines learning concepts from two classification trees, HHCART and Geometric Decision Tree (GDT). HHCART(G) is a simplified HHCART algorithm that uses linear structure in the training examples, captured by a modified GDT angle bisector, to define splitting directions. At each node, we reflect the training examples with respect to the modified angle bisector to align this linear structure with the coordinate axes. Searching axis parallel splits in this reflected feature space provides an efficient and effective way of finding oblique splits in the original feature space. Our method is much simpler than HHCART because it only considers one reflected feature space for node splitting. HHCART considers multiple reflected feature spaces for node splitting making it more computationally intensive to build. Experimental results show that HHCART(G) is an effective classifier, producing compact trees with similar or better results than several other decision trees, including GDT and HHCART trees.     

环境民事侵权中无过错责任的走向

在环境侵权中,无过错责任原则的运用加强了对环境民事损害的受害者的民事救济,但是也带来了一系列问题,诸如有可能掩盖行为人的过错,掩盖政府责任,以及可能使一些在无过错情况下致害的企业陷入困境甚至破产,而即使企业破产其有限的资产也不足以满足众多受害者的正当赔偿要求。因此,在民法框架下,环境侵权中民事责任的承担,最多应当止于过错推定原则。再往前走一步,就会走到无过错责任原则,走到这一步,就应当超出民法的范围,走向社会法领域,而不应再停留在民法之中。     

论学校在学生伤害事故中的责任

近年来,学生伤害事故及其引发的法律纠纷越来越多,日益成为困扰学校工作的严重问题。文章在对学校与学生之间法律关系进行论述的基础上,结合相关法律规定,提出学校责任是一种过错责任及学校过错的判断标准,并分析了不同情况下学校承担责任的方式。     

Wide Diameters of Cartesian Product Graphs and Digraphs

In graph theory and study of fault tolerance and transmission delay of networks, connectivity and diameter of a graph are two very important parameters and have been deeply studied by many authors. Wide diameter combining connectivity with diameter is a more important parameter to measure fault tolerance and efficiency of parallel processing computer networks and has received much attention in the recent years. Diameter with width k of a graph G is defined as the minimum integer d for which between any two distinct vertices in G there exist at least k internally disjoint paths of length at most d. In the present paper, the tight upper bounds of wide diameter of the Cartesian product graphs are obtained. Some known results can be deduced or improved from ours.     

Understanding Community Resilience from a PRA Perspective Using Binary Decision Diagrams

Probabilistic risk assessment (PRA) is a useful tool to assess complex interconnected systems. This article leverages the capabilities of PRA tools developed for industrial and nuclear risk analysis in community resilience evaluations by modeling the food security of a community in terms of its built environment as an integrated system. To this end, we model the performance of Gilroy, CA, a moderate‐size town, with regard to disruptions in its food supply caused by a severe earthquake. The food retailers of Gilroy, along with the electrical power network, water network elements, and bridges are considered as components of a system. Fault and event trees are constructed to model the requirements for continuous food supply to community residents and are analyzed efficiently using binary decision diagrams (BDDs). The study also identifies shortcomings in approximate classical system analysis methods in assessing community resilience. Importance factors are utilized to rank the importance of various factors to the overall risk of food insecurity. Finally, the study considers the impact of various sources of uncertainties in the hazard modeling and performance of infrastructure on food security measures. The methodology can be applicable for any existing critical infrastructure system and has potential extensions to other hazards.     

Lognormal Approximations of Fault Tree Uncertainty Distributions

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed‐form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling‐based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed‐form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks’s method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models.     

Toward an Application Guide for Safety Integrity Level Allocation in Railway Systems

The work in the article presents the development of an application guide based on feedback and comments stemming from various railway actors on their practices of SIL allocation to railway safety‐related functions. The initial generic methodology for SIL allocation has been updated to be applied to railway rolling stock safety‐related functions in order to solve the SIL concept application issues. Various actors dealing with railway SIL allocation problems are the intended target of the methodology; its principles will be summarized in this article with a focus on modifications and precisions made in order to establish a practical guide for railway safety authorities. The methodology is based on the flowchart formalism used in CSM (common safety method) European regulation. It starts with the use of quantitative safety requirements, particularly tolerable hazard rates (THR). THR apportioning rules are applied. On the one hand, the rules are related to classical logical combinations of safety‐related functions preventing hazard occurrence. On the other hand, to take into account technical conditions (last safety weak link, functional dependencies, technological complexity, etc.), specific rules implicitly used in existing practices are defined for readjusting some THR values. SIL allocation process based on apportioned and validated THR values is finally illustrated through the example of “emergency brake” subsystems. Some specific SIL allocation rules are also defined and illustrated.     

A Tabu Search Heuristic for the Location of Multi-Type Protection Devices on Electrical Supply Tree Networks

The problem of determining the number of multi-type protection devices and their locations on electrical supply tree networks with subtree dependency is investigated. The aim is to reduce the amount of inconvenience caused to customers that are affected by any given fault on the networks. An appropriate implementation of tabu search is proposed. We exploit a variable neighborhood and a soft aspiration level, and we embed a data structure and reduction tests into the search to speed up the process. Computational tests are performed on randomly generated electrical tree networks varying in size and branch complexity with encouraging results.