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→Causal structures 因果结构
[[Feedforward neural network]]s are another example.
[[Feedforward neural network]]s are another example.
=== Causal structures ===
{{main|Bayesian network}}
Graphs in which vertices represent events occurring at a definite time, and where the edges are always point from the early time vertex to a late time vertex of the edge, are necessarily directed and acyclic. The lack of a cycle follows because the time associated with a vertex always increases as you follow any [[Path (graph theory)|path]] in the graph so you can never return to a vertex on a path. This reflects our natural intuition that causality means events can only affect the future, they never affect the past, and thus we have no [[causal loop]]s. An example of this type of directed acyclic graph are those encountered in the [[Causal sets|causal set approach to quantum gravity]] though in this case the graphs considered are [[#Transitive closure and transitive reduction|transitively complete]]. In the version history example, each version of the software is associated with a unique time, typically the time the version was saved, committed or released. For citation graphs, the documents are published at one time and can only refer to older documents.
用顶点表示事件，边表示因果关系的图通常是无环的。[38]事件由时间上的先后顺序来排列，所有箭头遵循从先发生事件指向后发生事件的原则，因此也不存在环。
这类有向无环图的一个例子是在量子引力的因果集方法中遇到的那些图，尽管在这种情况下所考虑的图是传递完全的。在版本历史示例中，软件的每个版本都与一个唯一的时间相关联，通常是保存、提交或发布版本的时间。对于引文图表，文档一次发布，只能引用较旧的文档。
Sometimes events are not associated with a specific physical time. Provided that pairs of events have a purely causal relationship, that is edges represent [[causality|causal relations]] between the events, we will have a directed acyclic graph.<ref>{{citation|title=Causal Learning|first1=Alison|last1=Gopnik|first2=Laura|last2=Schulz|publisher=Oxford University Press|year=2007|isbn=978-0-19-803928-0|page=4|url=https://books.google.com/books?id=35MKXlKoXIUC&pg=PA4}}.</ref> For instance, a [[Bayesian network]] represents a system of probabilistic events as vertices in a directed acyclic graph, in which the likelihood of an event may be calculated from the likelihoods of its predecessors in the DAG.<ref>{{citation|title=Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks|publisher=Society for Industrial and Applied Mathematics|first1=Ilya|last1=Shmulevich|first2=Edward R.|last2=Dougherty|year=2010|isbn=978-0-89871-692-4|page=58|url=https://books.google.com/books?id=RfshqEgO7KgC&pg=PA58}}.</ref> In this context, the [[moral graph]] of a DAG is the undirected graph created by adding an (undirected) edge between all parents of the same vertex (sometimes called ''marrying''), and then replacing all directed edges by undirected edges.<ref>{{citation |last1= Cowell |first1= Robert G. |author2-link=Philip Dawid|last2=Dawid|first2=A. Philip|author3-link=Steffen Lauritzen|last3=Lauritzen|first3=Steffen L.|author4-link=David Spiegelhalter|last4=Spiegelhalter|first4=David J.|title= Probabilistic Networks and Expert Systems |publisher= Springer |year= 1999 |isbn= 978-0-387-98767-5 |chapter= 3.2.1 Moralization|pages= 31–33 }}.</ref> Another type of graph with a similar causal structure is an [[influence diagram]], the vertices of which represent either decisions to be made or unknown information, and the edges of which represent causal influences from one vertex to another.<ref>{{citation|title=The Technology Management Handbook|first=Richard C.|last=Dorf|publisher=CRC Press|year=1998|isbn=978-0-8493-8577-3|page=9{{hyphen}}7<!-- Do not conver this hyphen into a dash! It is a section-page number, not a range of page numbers. -->|url=https://books.google.com/books?id=C2u8I0DFo4IC&pg=SA9-PA7}}.</ref> In [[epidemiology]], for instance, these diagrams are often used to estimate the expected value of different choices for intervention.<ref>{{citation|title=Encyclopedia of Epidemiology, Volume 1|first=Sarah|last=Boslaugh|publisher=SAGE|year=2008|isbn=978-1-4129-2816-8|page=255|url=https://books.google.com/books?id=wObgnN3x14kC&pg=PA255}}.</ref><ref name="pearl:95">{{citation | last = Pearl | first = Judea | doi = 10.1093/biomet/82.4.669 | issue = 4 | journal = Biometrika | pages = 669–709 | title = Causal diagrams for empirical research | volume = 82 | year = 1995| url = https://escholarship.org/uc/item/6gv9n38c }}.</ref>
Category:Directed graphs
类别: 有向图
Category:Directed acyclic graphs
范畴: 有向无圈图
The converse is also true. That is in any application represented by a directed acyclic graph there is a causal structure, either an explicit order or time in the example or an order which can be derived from graph structure. This follows because all directed acyclic graphs have a [[#Topological ordering|topological ordering]], i.e. there is at least one way to put the vertices in an order such that all edges point in the same direction along that order.
de:Graph (Graphentheorie)#Teilgraphen.2C Wege und Zyklen
de:Graph (Graphentheorie)#Teilgraphen.2C Wege und Zyklen
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<small>This page was moved from [[wikipedia:en:Directed acyclic graph]]. Its edit history can be viewed at [[有向无环图/edithistory]]</small></noinclude>
[[Category:待整理页面]]
=== Causal structures 因果结构 ===
=== Causal structures 因果结构 ===
For instance, when one cell of a [[spreadsheet]] changes, it is necessary to recalculate the values of other cells that depend directly or indirectly on the changed cell. For this problem, the tasks to be scheduled are the recalculations of the values of individual cells of the spreadsheet. Dependencies arise when an expression in one cell uses a value from another cell. In such a case, the value that is used must be recalculated earlier than the expression that uses it. Topologically ordering the dependency graph, and using this topological order to schedule the cell updates, allows the whole spreadsheet to be updated with only a single evaluation per cell.<ref name="hgt1181">{{citation |title=Handbook of Graph Theory |first1=Jonathan L. |last1=Gross |first2=Jay |last2=Yellen |first3=Ping |last3=Zhang | author3-link = Ping Zhang (graph theorist)|edition=2nd |publisher=CRC Press |year=2013 |isbn=978-1-4398-8018-0 |page=1181 |url=https://books.google.com/books?id=cntcAgAAQBAJ&pg=PA1181}}.</ref> Similar problems of task ordering arise in [[makefile]]s for program compilation<ref name="hgt1181" /> and [[instruction scheduling]] for low-level computer program optimization.<ref>{{citation |title=The Compiler Design Handbook: Optimizations and Machine Code Generation |first1=Y. N. |last1=Srikant |first2=Priti |last2=Shankar |edition=2nd |publisher=CRC Press|year=2007 |isbn=978-1-4200-4383-9 |pages=19–39 |url=https://books.google.com/books?id=1kqAv-uDEPEC&pg=SA19-PA39}}.</ref>
For instance, when one cell of a [[spreadsheet]] changes, it is necessary to recalculate the values of other cells that depend directly or indirectly on the changed cell. For this problem, the tasks to be scheduled are the recalculations of the values of individual cells of the spreadsheet. Dependencies arise when an expression in one cell uses a value from another cell. In such a case, the value that is used must be recalculated earlier than the expression that uses it. Topologically ordering the dependency graph, and using this topological order to schedule the cell updates, allows the whole spreadsheet to be updated with only a single evaluation per cell.<ref name="hgt1181">{{citation |title=Handbook of Graph Theory |first1=Jonathan L. |last1=Gross |first2=Jay |last2=Yellen |first3=Ping |last3=Zhang | author3-link = Ping Zhang (graph theorist)|edition=2nd |publisher=CRC Press |year=2013 |isbn=978-1-4398-8018-0 |page=1181 |url=https://books.google.com/books?id=cntcAgAAQBAJ&pg=PA1181}}.</ref> Similar problems of task ordering arise in [[makefile]]s for program compilation<ref name="hgt1181" /> and [[instruction scheduling]] for low-level computer program optimization.<ref>{{citation |title=The Compiler Design Handbook: Optimizations and Machine Code Generation |first1=Y. N. |last1=Srikant |first2=Priti |last2=Shankar |edition=2nd |publisher=CRC Press|year=2007 |isbn=978-1-4200-4383-9 |pages=19–39 |url=https://books.google.com/books?id=1kqAv-uDEPEC&pg=SA19-PA39}}.</ref>
有时事件与特定的物理时间无关。假设事件对具有纯因果关系，即边表示事件之间的因果关系，我们将得到一个有向无环图。举例来说，贝叶斯网络表示多个概率事件的关联网络。顶点表示事件，后续事件的发生可能性则可以通过其在有向无环图的前驱节点的发生概率计算出来。[39]在此基础上，一个有向无环图的端正图（英语：moral graph）通过以下方法而得到：将单个顶点的所有父节点之间添加一条无向边，再将所有的有向边换成无向边。[40]
另外一种具有相似因果结构的图是影响图（英语：influence diagram）。其顶点表示决策或不确定的事件，边表示两个顶点之间的因果关系。[41]在流行病学中，这些表示因果关系的图表常常用来评估不同干预手段的效果。[42][43]
The converse is also true. That is in any application represented by a directed acyclic graph there is a causal structure, either an explicit order or time in the example or an order which can be derived from graph structure. This follows because all directed acyclic graphs have a topological ordering, i.e. there is at least one way to put the vertices in an order such that all edges point in the same direction along that order.
反之亦然。也就是说，在由有向无环图表示的任何应用程序中，都有一个因果结构，或者是示例中的显式顺序或时间，或者是可以从图结构派生的顺序。这是因为所有有向无环图都具有拓扑排序，即至少有一种方法可以将顶点按顺序排列，使所有边沿着该顺序指向同一方向。