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计算机视觉领域期刊和会议分析分为三个级别：tier-1:IJCAI (1+): International Joint Conference on Artificial Intelligence AAAI (1): National Conference on Artificial IntelligenceCOLT (1): Annual Conference on Computational Learning TheoryCVPR (1): IEEE International Conference on Computer Vision and Pattern RecognitionICCV (1): IEEE International Conference on Computer VisionICML (1): International Conference on Machine LearningNIPS (1): Annual Conference on Neural Information Processing SystemsACL (1-): Annual Meeting of the Association for Computational LinguisticsKR (1-): International Conference on Principles of Knowledge Representation and Reasoning SIGIR (1-): Annual International ACM SIGIR Conference on Research and Development in Information RetrievalSIGKDD (1-): ACM SIGKDD International Conference on Knowledge Discovery and Data Mining UAI (1-): International Conference on Uncertainty in Artificial Intelligence*Impact factor (According to Citeseer 03):IJCAI ：1.82 (top 4.09 %)AAAI ：1.49 (top 9.17%)COLT：1.49 (top 9.25%)ICCV ：1.78 (top 4.75%)ICML ：2.12 (top 1.88%)NIPS ：1.06 (top 20.96%)ACL ：1.44 (top 10.07%)KR ：1.76 (top 4.99%)SIGIR ：1.10 (top 19.08%)Average：1.56 (top 8.02%)IJCAI (1+): AI最好的综合性会议, 1969年开始, 每两年开一次, 奇数年开. 因为AI 实在太大,所以虽然每届基本上能录100多篇（现在已经到200多篇了），但分到每个领域就没几篇了，象machine learning、computer vision这么大的领域每次大概也就10篇左右, 所以难度很大. AAAI (1): 美国人工智能学会AAAI的年会. 是一个很好的会议, 但其档次不稳定, 可以给到1+,也可以给到1-或者2+, 总的来说我给它”1″. 这是因为它的开法完全受IJCAI制约: 每年开, 但如果这一年的IJCAI在北美举行, 那么就停开. 所以, 偶数年里因为没有IJCAI, 它就是最好的AI综合性会议, 但因为号召力毕竟比IJCAI要小一些, 特别是欧洲人捧AAAI场的比IJCAI少得多(其实亚洲人也是), 所以比IJCAI还是要稍弱一点, 基本上在1和1+之间; 在奇数年, 如果IJCAI不在北美, AAAI自然就变成了比IJCAI低一级的会议(1-或2+), 例如2005年既有IJCAI又有AAAI, 两个会议就进行了协调, 使得IJCAI的录用通知时间比AAAI的deadline 早那么几天, 这样IJCAI落选的文章可以投往AAAI.在审稿时IJCAI 的PC chair也在一直催, 说大家一定要快, 因为AAAI 那边一直在担心IJCAI的录用通知出晚了AAAI就麻烦了.COLT (1): 这是计算学习理论最好的会议, ACM主办, 每年举行. 计算学习理论基本上可以看成理论计算机科学和机器学习的交叉, 所以这个会被一些人看成是理论计算机科学的会而不是AI的会. 我一个朋友用一句话对它进行了精彩的刻画: “一小群数学家在开会”. 因为COLT的领域比较小, 所以每年会议基本上都是那些人. 这里顺便提一件有趣的事, 因为最近国内搞的会议太多太滥, 而且很多会议都是LNCS/LNAI出论文集, LNCS/LNAI基本上已经被搞臭了, 但很不幸的是, LNCS/LNAI中有一些很好的会议, 例如COLT.CVPR (1): 计算机视觉和模式识别方面最好的会议之一, IEEE主办, 每年举行. 虽然题目上有计算机视觉, 但个人认为它的模式识别味道更重一些. 事实上它应该是模式识别最好的会议, 而在计算机视觉方面, 还有ICCV 与之相当. IEEE一直有个倾向, 要把会办成”盛会”, 历史上已经有些会被它从quality很好的会办成”盛会”了. CVPR搞不好也要走这条路. 这几年录的文章已经不少了. 最近负责CVPR会议的TC的chair发信说, 对这个community来说, 让好人被误杀比被坏人漏网更糟糕, 所以我们是不是要减少好人被误杀的机会啊? 所以我估计明年或者后年的CVPR就要扩招了.ICCV (1): 介绍CVPR的时候说过了, 计算机视觉方面最好的会之一. IEEE主办, 每年举行. ICML (1): 机器学习方面最好的会议之一. 现在是IMLS主办, 每年举行. 参见关于NIPS的介绍.NIPS (1): 神经计算方面最好的会议之一, NIPS主办, 每年举行. 值得注意的是, 这个会每年的举办地都是一样的, 以前是美国丹佛, 现在是加拿大温哥华; 而且它是年底开会, 会开完后第2年才出论文集, 也就是说, NIPS’05的论文集是06年出. 会议的名字“Advances in Neural Information Processing Systems”, 所以, 与ICML\ECML这样的”标准的”机器学习会议不同, NIPS里有相当一部分神经科学的内容, 和机器学习有一定的距离. 但由于会议的主体内容是机器学习, 或者说与机器学习关系紧密, 所以不少人把NIPS看成是机器学习方面最好的会议之一. 这个会议基本上控制在Michael Jordan的徒子徒孙手中, 所以对Jordan系的人来说, 发NIPS并不是难事, 一些未必很强的工作也能发上去, 但对这个圈子之外的人来说, 想发一篇实在很难, 因为留给”外人”的口子很小. 所以对Jordan系以外的人来说, 发NIPS的难度比ICML更大. 换句话说, ICML比较开放, 小圈子的影响不象NIPS那么大, 所以北美和欧洲人都认, 而NIPS则有些人(特别是一些欧洲人, 包括一些大家)坚决不投稿. 这对会议本身当然并不是好事, 但因为Jordan系很强大, 所以它似乎也不太care. 最近IMLS(国际机器学习学会)改选理事, 有资格提名的人包括近三年在ICML\ECML\COLT发过文章的人, NIPS则被排除在外了. 无论如何, 这是一个非常好的会.ACL (1-): 计算语言学/自然语言处理方面最好的会议, ACL (Association of Computational Linguistics) 主办, 每年开.KR (1-): 知识表示和推理方面最好的会议之一, 实际上也是传统AI(即基于逻辑的AI) 最好的会议之一. KR Inc.主办, 现在是偶数年开.SIGIR (1-): 信息检索方面最好的会议, ACM主办, 每年开. 这个会现在小圈子气越来越重. 信息检索应该不算AI, 不过因为这里面用到机器学习越来越多, 最近几年甚至有点机器学习应用会议的味道了, 所以把它也列进来.SIGKDD (1-): 数据挖掘方面最好的会议, ACM主办, 每年开. 这个会议历史比较短, 毕竟, 与其他领域相比,数据挖掘还只是个小弟弟甚至小侄儿. 在几年前还很难把它列在tier-1里面, 一方面是名声远不及其他的top conference响亮, 另一方面是相对容易被录用. 但现在它被列在tier-1应该是毫无疑问的事情了.UAI (1-): 名字叫”人工智能中的不确定性”, 涉及表示\推理\学习等很多方面, AUAI (Association of UAI) 主办, 每年开.________________________________________tier-2:AAMAS (2+): International Joint Conference on Autonomous Agents and Multiagent Systems ECCV (2+): European Conference on Computer VisionECML (2+): European Conference on Machine LearningICDM (2+): IEEE International Conference on Data MiningSDM (2+): SIAM International Conference on Data MiningICAPS (2): International Conference on Automated Planning and SchedulingICCBR (2): International Conference on Case-Based ReasoningCOLLING (2): International Conference on Computational LinguisticsECAI (2): European Conference on Artificial IntelligenceALT (2-): International Conference on Algorithmic Learning TheoryEMNLP (2-): Conference on Empirical Methods in Natural Language ProcessingILP (2-): International Conference on Inductive Logic ProgrammingPKDD (2-): European Conference on Principles and Practice of Knowledge Discovery in Databases*Impact factor (According to Citeseer 03):ECCV ：1.58 (top 7.20 %)ECML ：0.83 (top 30.63 %)ICDM ：0.35 (top 59.86 %)ICCBR ：0.72 (top 36.69 %)ECAI ：0.69 (top 38.49 %)ALT ：0.63 (top 42.91 %)ILP ：1.06 (top 20.80 %)PKDD ：0.50 (top 51.26 %)Average：0.80 (top 32.02%)AAMAS (2+): agent方面最好的会议. 但是现在agent已经是一个一般性的概念, 几乎所有AI有关的会议上都有这方面的内容, 所以AAMAS下降的趋势非常明显.ECCV (2+): 计算机视觉方面仅次于ICCV的会议, 因为这个领域发展很快, 有可能升级到1-去. ECML (2+): 机器学习方面仅次于ICML的会议, 欧洲人极力捧场, 一些人认为它已经是1-了. 我保守一点, 仍然把它放在2+. 因为机器学习发展很快, 这个会议的reputation上升非常明显.ICDM (2+): 数据挖掘方面仅次于SIGKDD的会议, 目前和SDM相当. 这个会只有5年历史, 上升速度之快非常惊人. 几年前ICDM还比不上PAKDD, 现在已经拉开很大距离了.SDM (2+): 数据挖掘方面仅次于SIGKDD的会议, 目前和ICDM相当. SIAM的底子很厚, 但在CS里面的影响比ACM和IEEE还是要小, SDM眼看着要被ICDM超过了, 但至少目前还是相当的.ICAPS (2): 人工智能规划方面最好的会议, 是由以前的国际和欧洲规划会议合并来的. 因为这个领域逐渐变冷清, 影响比以前已经小了.ICCBR (2): Case-Based Reasoning方面最好的会议. 因为领域不太大, 而且一直半冷不热, 所以总是停留在2上.COLLING (2): 计算语言学/自然语言处理方面仅次于ACL的会, 但与ACL的差距比ICCV-ECCV 和ICML-ECML大得多.ECAI (2): 欧洲的人工智能综合型会议, 历史很久, 但因为有IJCAI/AAAI压着,很难往上升. ALT (2-): 有点象COLT的tier-2版, 但因为搞计算学习理论的人没多少, 做得好的数来数去就那么些group, 基本上到COLT去了, 所以ALT里面有不少并非计算学习理论的内容. EMNLP (2-): 计算语言学/自然语言处理方面一个不错的会. 有些人认为与COLLING相当, 但我觉得它还是要弱一点.ILP (2-): 归纳逻辑程序设计方面最好的会议. 但因为很多其他会议里都有ILP方面的内容, 所以它只能保住2-的位置了.PKDD (2-): 欧洲的数据挖掘会议, 目前在数据挖掘会议里面排第4. 欧洲人很想把它抬起来, 所以这些年一直和ECML一起捆绑着开, 希望能借ECML把它带起来.但因为ICDM和SDM。
关于人工智能的文献人工智能的历史并不久远，关于人工智能的文献有哪些呢？。
下面是为你整理的关于人工智能的文献，供大家阅览！人工智能的形成及其发展现状分析摘要：人工智能的历史并不久远，故将从人工智能的出现、形成、发展现状及前景几个方面对其进行分析，总结其发展过程中所出现的问题，以及发展现状中的不足之处，分析其今后的发展方向。
关键词：人工智能，发展过程，现状分析，前景。
一.弓I言人工智能最早是在1936年被英国的科学家图灵提出，并不为多数人所认知。
当时，他编写了一个下象棋的程序，这就是最早期的人工智能的应用。
也有著名的“图灵测试”，这也是最初判断是否是人工智能的方案，因此，图灵被尊称为“人工智能之父”。
人工智能从产生到发展经历了一个起伏跌宕的过程，直到目前为止，人工智能的应用技术也不是很成熟，而且存在相当的缺陷。
通过搜集的资料，将详细的介绍人工智能这个领域的具体情况，剖析其面临的挑战和未来的前景。
二.人工智能的发展历程1. 1956年前的孕育期(1) 从公元前伟大的哲学家亚里斯多德(Aristotle)到16世纪英国哲学家培根(F. Bacon)，他们提出的形式逻辑的三段论、归纳法以及“知识就是力量”的警句，都对人类思维过程的研究产生了重要影响。
(2) 17世纪德国数学家莱布尼兹(G..Leibniz)提出了万能符号和推理计算思想，为数理逻辑的产生和发展奠定了基础，播下了现代机器思维设计思想的种子。
而19世纪的英国逻辑学家布尔(G. Boole) 创立的布尔代数，实现了用符号语言描述人类思维活动的基本推理法则。
(3) 20世纪30年代迅速发展的数学逻辑和关于计算的新思想，使人们在计算机出现之前，就建立了计算与智能关系的概念。
被誉为人工智能之父的英国天才的数学家图灵(A. Tur-ing)在1936年提出了一种理想计算机的数学模型，即图灵机之后,1946年就由美国数学家莫克利(J. Mauchly)和埃柯特(J. Echert)研制出了世界上第一台数字计算机，它为人工智能的研究奠定了不可缺少的物质基础。
天津大学关于本科生学位论文统一格式的规定本科生毕业设计（论文）是实现人才培养目标的重要实践环节，对巩固、深化和升华学生所学理论知识，培养学生创新精神、独立工作能力、分析和解决问题能力、工程实践能力起着重要作用。
做好本科生毕业设计（论文）工作，同时也是培养学生科学精神、科学作风、良好的思想品德以及事业心和责任感等综合素质所不可缺少的环节。
为保证我校本科生学位论文的质量，实现学位论文的规范化，现制定《天津大学关于本科生学位论文统一格式的规定》，提出如下要求。
1.本科生学位论文结构学位论文应采用汉语撰写（英语专业除外），一般由以下部分组成，依次为：（1）封面，（2）任务书，（3）开题报告，（4）中英文摘要及关键词，（5）目录，（6）正文，（7）参考文献，（8）附录，（9）外文资料，（10）中文译文，（11）致谢。
2.关于学位论文各部分的具体说明2.1封面采用校教务处统一印制的封面，文中的封面从毕业设计（论文）模板下载。
2.2任务书包括设计(论文)题目、原始依据、参考文献、设计内容和要求。
设计（论文）题目、原始依据要填写明确，原始依据不得少于200字，包括设计(论文)的工作基础、研究条件、应用环境、工作目的；设计（研究）内容和要求不得少于200字，包括设计（研究）内容、主要指标与技术参数，并根据课题性质对学生提出具体要求。
论文题目是论文总体内容的体现，要醒目，力求简短，一般不宜超过25字，用三号字、黑体；任务书第1页除题目外，其余各项用三号字、宋体、加粗，第2、3页采用小四号宋体字。
任务书一式两份，指导教师和审题小组组长签字后，一份于第八学期前两周内交学院，另一份装订于毕业设计（论文）说明书中。
2.3开题报告开题报告格式由网上下载，要求不少于2000字。
内容包括：课题的来源及意义，国内外发展状况，本课题的研究目标、研究内容、研究方法、研究手段和进度安排，实验方案的可行性分析和已具备的实验条件以及主要参考文献等。
social rationality which can be used to guide an agent’s decisions making in realistic, multi-agent en-vironments, and this paper represents a preliminary step towards this goal. The robustness of the prin-ciple under varying constraints, will also be explored and this will lead to the development of socially bounded rational agents.5. References[1]S. Russell,Rationality and Intelligence, 14th International Joint Conference on ArtificialIntelligence, Montreal, Canada, August: pp 950-957, 1995.[2]J. Doyle,Rationality and its Roles in Reasoning,Computational Intelligence, Volume 8 No. 3,1992.[3]H. A. Simon,A Behavioural Model of Rational Choice,Quarterly journal of Economics, 69:pp99-118, 1955.[4]S. Russell and E. Wefald,Do the right thing,MIT Press, Cambridge Mass, 1991.[5] E.Horvitz,Reasoning Under Varying and Uncertain Resource Constraints,Proceedings of theSeventh National Conference on AI, Minneapolis,August:pp111-116,1988.[6] A.H. Bond and L. Gasser,Readings in DAI,Morgan Kauffman, San Mateo, California, 1988.[7]M. Huhns,Distributed Artificial Intelligence,Pittman, 1989.[8]R. Weihmayer and H. Velthuijsen,Applications of distributed AI and cooperative problemsolving to telecommunications,in J. Liebowitz and D. Prereau (eds), Ai Approahces to telecom-munications and network management, IOS Press, 1994.[9]H.V.D. Parunak,Applications of distribuited artificial intelligence in industry, in G.M.PO’Hare and N.R. Jennings (eds), Foundations of Distributed Artificial IntelligenceWiley:pp139-164, 1996.[10] C. Castelfranchi,Social Power: A Point Missed in Multi-Agent, DAI and HCI,DecentralizedA.I., Yves Demazeau & Jean-Pierre Muller eds., Elsevier Science Publishers,B.V (North Hol-land), 1990.[11]N.R. Jennings & J. Campos,Towards a Social Level Characterization of SociallyResponsible Agents,IEE Proceedings on Software Engineering: pp 11-25, 1997.[12] A. Newell,The Knowledge Level,Artificial intelligence, 18: pp87-127, 1982.[13] A. Shehory and S. Kraus,Task Allocation via Coalition formation amongautonomous agents,14th International Joint Conference on Artificial Intelligence, Montreal, Canada, August1995.[14]S. Ketchpel,Coalition Formation Amongst Autonomous Agents,in: Castelfranci Cristiano and Muller J-P (eds.), : From Reaction to Cognition, 5th European Workshop on Modelling Autonomous Agents in a Multi-Agent World, MAAMAW ‘93,Neuchatel, Switzerland, August 25-27, 1993., Selected papers, Lecture Notes in ArtificialIntelligence 957, Springer Verlag, Berling, Heidelberg, 1995, 73-88.together as a team is profitable or not [13], [14]. Along similar lines, an agent may wish to perform actions which are potentially helpful to the others who it is interacting with (be it for selfish or social motives). An example of this would be if an agent thought that by performing an action which was beneficial to others now, it may prompt others to favour (help) it in the future. It is therefore possible to further distinguish between the agent’s commitment to achieving benefit for the ‘society’ in general and the commitment to assisting those agents or groups with which it is currently interacting. Adding this consideration to the above equation we obtain:EU Ai (a) = w 1.EIU(a) + w 2.EPU(a) + w 3.ESU(a)where EPU is the E xpected P artners U tility (partners being those with whom the agent is currently interacting) and ESU is the benefit to the general society (this may be in terms of following social norms and conventions, or level of achievement of social goals):An agent may not necessarily interact with the same agents all of the time. Hence the notion of part-ners is a dynamic concept, with the agent likely to interact with different sets of agents to varying de-grees. From the previous equation, the utility to society is thus divided into utility of agents with whom the agent has some form of relationship (i.e. interacting and may be dependent in some way on each other) and the utility to the society in general (e.g. doing something for the common good). By making this distinction, agents can identify actions which are rational given the small community within the society that the agent is interacting with.In deliberating in this manner, an agent can exhibit more socially rational behaviour in terms of the small groups of agents which it finds itself interacting with on a regular basis. However, consideration of the wider social context can be seen as an extra bound on an agent in the same vein as the resource limitations mentioned in section one. It takes time and resources to calculate the utility an action af-fords to others. Resources which agents may not always have. In such cases, it would be advantageous to have a flexible control mechanism which, allows the agent to tailor the amount of social reasoning it performs to its current situation. Thus, in times of heavy resource constraints where it may be im-practical to take the effect of actions on others into consideration, the agent will make decisions based solely on individual benefits. In situations where it has more resources, it may be able to include the consideration of individual and partners utility for choosing action and in the most plentiful scenario,may use full social rationality. By having this flexibility the agent can manage its goal priorities (i.e individual and social goals) more efficiently and hence make its decision making more socially ra-tional as its resource bounds increase. Additionally, if the agent has the ability to learn from previous decision making successes and failures, there is the potential that it could converge towards finding the right balance, depending on the situation, between individual and societal needs.4. Conclusions and future aimsRationality is a desirable property of agents since it provides a means of assessing and attaining intel-ligent behaviour. Previous work on rationality has concentrated on the benefits gained from making a decision based on an individualistic, selfish perspective. Given the increasing use of the multi-agent paradigm in tackling complex problems, some other principle of rationality needs to be considered which would guide the agent’s actions within a multi-agent environment. Social rationality provides a principle by which agents make decisions which strike a balance between the needs of the system/society and those of the individual agent. However, such a theory needs to also take into consideration the fact that the agent is bounded and that being ‘social’ is a limitation as well other considerations such as time and computational power. The ultimate aim of this research is to define a principle ofEPU(a) =ΣA p ∈S EU Ap (a)and ESU(a) =ΣA s ∈{S-A P }EU As (a)agent, of figure 1, is faced with many decisions before taking action and we believe an adequately formulated principle of social rationality would assist at all its choice points. A preliminary attempt by Jennings and Campos [11] to define social rationality using individual and global benefits is as fol-lows:Principle of Social Rationality: If a member of a responsible society1 canperform an action whose joint benefit is greater than its joint loss, then itmay select that action.As with Newell’s rationality hypothesis of the knowledge level [12], this principle conveys, at an ab-stract level, a normative theory of decision making which takes into account the benefits accrued from actions to the society that the agent inhabits. Joint benefit is defined as the benefit provided to the in-dividual plus the benefit afforded to society as a result of an action. Similarly, joint loss is the indi-vidual plus societal loss of performing an action. Although this definition focuses the agent into choosing more beneficial actions from the societal viewpoint, it lacks concrete guidance in the choice of alternatives and the concept of maintaining a balance between individual and system needs. Thus, in order to be applied in real systems the definition needs to be expanded to show how the agent chooses between actions and how the situation that the agent finds itself in effects its decision.As stated previously, the decision theoretic concept of maximizing the utility of an action is an intu-itive and appealing way of conceptualizing decision making. It provides a way of evaluating a set of alternatives by considering the expected utility of each alternative in that set. Jennings and Campos’principle of social rationality, can be mapped onto a utility based definition in the following way. Consider a society of agents S = {A1, A2,..., A n}, and let B Ai be the benefit afforded to agent A i by the action a and B S the benefit afforded to the society. Similarly, let L Ai be the loss (or cost) the action produces for A i and L S the loss afforded to society. Hence the expected utility, EU Ai(a), of an action a to agent A i isEU Ai(a) = (B Ai - L Ai) + (B S- L S)≡EU(a) =f (EIU(a), ESU(a))where EIU is the E xpected I ndividual U tility, and is the standard decision theoretic notion of the ex-pected utility of an action2. ESU is the E xpected S ocietal U tility and is the expected benefit that an action a produces to the society. Function f shows the relationship of the two utilities from the agents’perspective and ultimately defines the characteristics of the agent. A social agent would use a function which places a greater weighting on the social utility of actions, while a self-interested agent would place more emphasis on the individual utility of actions.As a first approximation, f might be defined to be the weighted addition of the individual and societal utilities:EU Ai(a) = w1.EIU(a)+ w2.ESU(a)where w1 and w2 are in the range [0,1] and are theimportance the agent places on the respectiveutility functions.Given a relatively large society, an agent is likely to find itself interacting with various other individ-ual agents, and in some cases groups of agents, at different times. For example, if an agent does not have the necessary resources to carry out a task it may enlist the help of another agent, or agents, in the society to help it. Work on coalition formation investigates how agents calculate whether working1. A responsible society is defined as a system of autonomous agents which balance individual needs with thoseof the overall system when making decisions. This is equivalent to our social agent.2.EIU(a) =∑P(s, a)U(s). P(s,a) is the probability of reaching a state s after performing action a, and U(s) is theutility of that state to the agentsolving capability, an agent may need to obtain the assistance from other agents to help it achieve a goal. To do this, an agent may use its knowledge about how other agents are dependent on certain resources in order to influence others to adopt one or more of its goals [10]. An example scenario would be the case where there are two transporter agents, each responsible for the delivery of some goods. One agent has a truck full of its goods, which it cannot empty alone. A second agent needs an empty truck to transport its goods to its customer. Given that the second agent needs an empty truck,the first agent can suggest that the second help it unload its truck, and then use the truck to deliver its goods. In another situation of interdependence, an agent may decide to work together as a team with others, as a necessary or more profitable means of achieving individual or system goals. Figure 1. dis-plays the main decision making components and reasoning complexity of a social agent. Given the situation the agent finds itself in, it faces a number of choices which control its actions. Not only must the agent decide the benefit of combining forces with other agents to work more efficiently, but also it must determine if it acts alone how it can produce most benefit from its actions balancing individual and societal needs. Agents which merely follow the individual perspective of rationality only perform actions which bring themselves the most benefit. In multi-agent system research however, the design objective is to produce successful behaviour at both the individual and the system level.We believe rationality needs to be considered not only from the indi-viduals point of view, but also from the societal perspective. An agentadopting a selfish strategy may in-hibit the achievement of system/so-cial goals. For example if one agenthas sole control over a resourcewhich is required by others, then byselfishly using all of this resourceitself it can inhibit other agents achieving their goals and hence thesystem producing the desired be-haviour. It may even be the casethat decisions taken from a more social perspective actually producegreater benefit for the individualthan taking the individualistic pointof view. Decision making at a soci-etal level can thus be seen to becomposed of a multitude of factorsincluding current situation and in-dividual and global utility consid-erations. To produce a socially rational choice the agent needs to be able to determine the effect of its actions on others by estimating the benefit that a course of action would provide. In order to do this,the agent needs to know the goals and the preferences of the other agents in the society. Using this information, the agent can determine how desirable the outcome of its actions are to others and hence make decisions which are more socially acceptable.3. Towards social rationalityFor agents situated in a social context, it is clear that they require a fundamental decision making prin-ciple to help guide their behaviour in the same way that individual utility maximisation works for aso-cial agents. This principle should take into consideration both resource bounds (to be practical) and task and social interdependencies (to interact effectively). Such a principle of social rationality pro-vides the agent with a normative theory of decision making within a multi-agent context. The social situation assessment choice of strategy work individually work as a team all actions yourself “use” other agents coalition formation choice of team choice of structure/from current state of world from previous experience Figure 1: Flow of decision making in a socially rational agent how to attain goals choice of how to form team Problem strategySocially Rational Agents - Some Preliminary ThoughtsLisa M. Hogg and Nick R. JenningsDepartment of Electronic EngineeringQueen Mary & Westfield College, University of London.{L.M.Hogg, N.R.Jennings}@AbstractRationality relates to making the right decisions and producing successful behaviour. The notion ofbuilding rational agents is one of the main aims of research into artificial intelligence. The current pre-dominant approach is to develop agents which follow a decision theoretic notion of rationality in whichthe agent maximizes the expected utility of its actions. Although this is intuitively and formally appeal-ing, it lacks applicability in real systems where the agent is faced with resource limitations. Furthermore,this view fails to adequately cope with the case in which an agent is embedded within a system of inter-acting agents. In such an environment, the agent has the further consideration of the effects of its actionson other agents and the effect of their actions on itself. Therefore to operate effectively in such environ-ments the agents need a principle of social rationality. In this paper we outline our preliminary thoughtson devising such a principle and indicate how it helps the agent strike a balance between its individualneeds and the needs of the overall system.1. Theories of rationalityRationality is all about doing the ‘right’ thing, where right equates to performing successful actions [1]. Agent rationality is concerned with intelligent decision making as defined by the mapping of per-cepts into actions. Thus determining whether an agent is behaving rationally can only be ascertained by examining the information that it possesses and by evaluating the success of the actions that it per-forms based upon this information. The predominant theory of rational decision making in agents is that of the economic principle of maximizing the expected gain of actions [2]. Decision theoretic ra-tionality dictates that the agent should choose an action which will maximize the expected utility of performing that action given the probability of reaching a desired state in the world and the desirabil-ity of that state. However, this theory makes the assumption that the agent has both complete infor-mation and sufficient time to carry out the necessary reasoning. In reality, however, agents have limitations on their deliberation with regard to the resources they have available. Hence theories of decision making need to take such boundedness into consideration if the agents are to be applied in real systems. Recognising this shortcoming, work on bounded rationality [3], [4], [5] takes into con-sideration the fact that the agent is faced with resource limitations which affect its reasoning. Despite numerous attempts at overcoming the problems of resource bounds on reasoning, there is yet to emerge a definitive concept of bounded rationality which can be applied in real systems. In addition, most work on ideal and bounded rationality fails to recognize the importance of the fact that many systems are composed of several interacting agents and that the decisions that each agent makes have consequences on the others within the system. To this end, this work proposes an alternative view of rationality, which takes these factors into consideration. It also explores how resource limitations fur-ther affect the agents reasoning in this context.2. Shortcomings of individual rationality in multi-agent systemsThe successful combination of several autonomous, intelligent agents working together is the aim of research into multi-agent systems [6], [7]. Increasingly, the multi-agent paradigm is being used to build real, complex systems [8], [9]. Reasons for this include the inherent natural distribution of prob-lem components and the maturing of distributed computing technology. In such systems, the agents are interdependent, due to resource limitations and problem interdependencies, andl need to interact with one another in order to achieve their goals. For example, due to lack of knowledge or problem。
International Journal on Artificial Intelligence Tools© World Scientific Publishing CompanyA BAYESIAN METANETWORKVAGAN TERZIYANDepartment of Mathematical Information Technology, University of Jyvaskyla,P.O. Box 35 (Agora), FIN-40014 Jyvaskyla, Finlandvagan@it.jyu.fiReceived (9 July 2003)Accepted (15 March 2004)Bayesian network (BN) is known to be one of the most solid probabilistic modeling tools. Thetheory of BN provides already several useful modifications of a classical network. Amongthose there are context-enabled networks such as multilevel networks or recursive multinets,which can provide separate BN modelling for different combinations of contextual features’values. The main challenge of this paper is the multilevel probabilistic meta-model (BayesianMetanetwork), which is an extension of traditional BN and modification of recursive multinets.It assumes that interoperability between component networks can be modeled by another BN.Bayesian Metanetwork is a set of BN, which are put on each other in such a way thatconditional or unconditional probability distributions associated with nodes of every previousprobabilistic network depend on probability distributions associated with nodes of the nextnetwork. We assume parameters (probability distributions) of a BN as random variables andallow conditional dependencies between these probabilities. Several cases of two-levelBayesian Metanetworks were presented, which consist on interrelated predictive and contextualBN models.Keywords: Bayesian networks, context, multinets1 IntroductionA Bayesian network (BN) has proven to be a valuable tool for encoding, learning and reasoning about probabilistic (causal) relationships [1]. A BN for a set of variables X ={X1, …, Xn} is a directed acyclic graph with a network structure S that encodes a set of conditional independence assertions about variables in X , and a set P of local probability distributions associated with each variable [2]. Simple BN example is shown in Fig. 1.Inference in BN generally targets the calculation of some probability of interest. Inference algorithms exploit the conditional (in)dependence between variables (1), see e.g. joint probability (2) for Fig. 1; marginalization rule (3); and Bayesian rule (4).∏==n i i i n X Parents X P X X X P 121))(|(),...,,((1))|()(),(i j i i j x X y Y P x X P x X y Y P ==⋅====(2)Fig. 1. Example of a simple Bayesian network∑==⋅===ii j i j x X y Y P x X P y Y P )|()()( (3))()|()()|(j i j i j i y Y P x X y Y P x X P y Y x X P ===⋅==== (4)Learning BN generally means the refinement of the structure and local probability distributions of a BN given data. The simplest version of this problem is using data to update the probabilities of a given BN network structure. An important task in learning BN from data is model selection [3]. Each attribute in ordinary BN has the same status, so they are just combined into possible models-candidates to encode conditional dependencies. Some modifications of BN however require distinguishing between attributes, e.g. as follows:• Target attribute , which probability is being estimated based on set of evidence.• Predictive attribute , which values being observed effect probability distribution of a target attribute(s) via some structure of other predictive attributes according to causal dependencies among them.• Contextual attribute , which has no direct visible effect to target attributes but influences some of probability distributions within the predictive model. A contextual attribute can be conditionally dependent on some other contextual attribute.Causal independence in a BN refers to the situation where multiple causes provided by predictive attributes contribute independently to a common effect on a target attribute. With causal independence, the probability function can be described using a binary operator that can be applied to values from each of the parent predictive attributes (see (1)). Context specific independence refers to the fact that some random variables are probabilistically independent of each other in a certain context.In [4], Butz exploited contextual independencies based on assumption that while a conditional independence must hold over all contexts, a contextual independence need only hold for one particular context. He shows how contextual independencies can be modeled using multiple BN. Boutilier et al [5] presents two algorithms to exploit context specific independence in a BN. The first is network transformation and clustering. With this method, the context specific independencies are qualitatively encoded within thenetwork structure of the transformed network and appropriate conditional probability tables are represented as decision trees. The other algorithm works by selecting a set of variables that, once instantiated, makes the network singly connected. With context specific independence this essentially reduces total inference time for queries. Zhang [6] used generalized rules for contextual variable elimination algorithm, which capture context specific independence in variables. Geiger and Heckerman [7] used similarity networks to make context specific independencies explicit in BN. In a similarity network, the edges between the variables can be thought of as a network whose edges can appear or disappear depending on the values of certain variables in the network. This allows for different BNs to perform inference for different contexts.Domain ontologies seem to be an excellent source of contextual data, which can be used for modelling context-sensitive BNs. Additional knowledge about (semantic) relations between BN nodes other than causal ones can be considered as a sample of a very useful context, which can affect the interpretation of the original structure of the BN. Helsper and Gaag [8] describe an interesting combination of medical ontologies as explicit documentation of the cancer domain knowledge and the BN, which encodes cause-symptom relationships in this domain. For example, the knowledge that pertains to haematogenous metastases may be considered from different points of view and resulting in the two alternative depictions (see Fig. 2).Fig bining BN with ontology [9]Alternative (a) in Fig. 2 describes that the process of metastasis via blood vessels may result in metastases in the lungs and metastases in the liver, which are known from the ontological context to be subclasses of the class haematogenous metastasis. Alternative (b) captures a relation at a higher level: the process of metastasis via blood vessels may result in haematogenous metastases, which according to the context may be in the lungs or in the liver. Imagine a scenario when some BN learning algorithm has produced structure (a). Imagine also that our context as part of OWL ontology is knowledge about: class haematogenous metastasis is a disjoint_union_of class metastases in the lungs and class metastases in the liver. According to this context it is possible to automatically transfer BN structure from alternative (a) to more compact alternative (b) and then make appropriate recalculation of the BN parameters.If a Bayesian network is to be modified to better represent probability of a target attribute, one can either change its graphical structure, or its parameters or both [9]. There are two ways for changing the structure of a Bayesian network: one can change the nodes in the graph (add, delete or combine nodes) or change the arrows in the graph (add, delete or re-orient arrows) or both. In Bang et al. [9] a combination of these two strategies for network modification is considered. To generate a causal network that satisfies the causal Markov condition the flexibility is needed to add either a new arrow or a new common cause (a hidden node). The complexity of generated network can be measured in terms of the number of parameters required in the network. Results show that in most situations adding an arrow will increase complexity least, but in cases where two or more nodes share a large number of parents, adding a hidden node can even decrease complexity.In [10] a multi-level BN was presented that accurately models the system and allows for sensor integration in an evidential framework. It was shown that a multi-level BN performs better than a simple single-level BN. Multilayer networks are usually sensitive to conditional probabilities, which should be defined with greater accuracy because small differences in their values may result in radically different target concept estimation. Choosing between a simple BN and a multilevel network one needs to carefully evaluate an expected benefit against the increased costs of the knowledge management [11].Bayesian multinets were first introduced in [12] and then studied in [13] as a type of classifiers. A Bayesian multinet is composed of the prior probability distribution of the class node and a set of local networks, each corresponding to a value that the class node can take. Bayesian multinets can be viewed as a generalization of BNs. A BN forces the relations among the features to be the same for all the values that the class node takes; by contrast a Bayesian multinet allows the relations among the features to be different, i.e. for different values the class node takes, the features can form different local networks with different structures. While multinet is more general than BN, it is often less complex since some of the local networks can be simpler than others, while BN needs to have a complex structure in order to express all the relationships among the features [13]. In [14] dynamic Bayesian multinets are introduced where a Markov chain state at time determines conditional independence patterns between random variables lying within a local time window surrounding it. It is demonstrated that multinets can in many cases outperform other dynamic models with a similar number of parameters. A recursive Bayesian multinet was introduced by Pena et al [15] as a decision tree with component Bayesian networks at the leaves. The key idea was to decompose the learning Bayesian network problem into learning component networks from incomplete data.As our main goal in this paper, we are presenting another view to the Bayesian “multinets” towards making them to be really “metanetworks”, i.e. by assuming that interoperability between component Bayesian networks can be also modeled by another Bayesian network.The rest of paper organized as follows. In Section 2 we present two models of a contextual effect to probability distributions in BN. In Section 3 we introduce a Bayesian Metanetwork, basic inference in it and few cases of interaction between its predictive and contextual levels. We conclude in Section 4.2 Modelling Contextual Effect on Bayesian Network ParametersIn this chapter, we first consider the model of direct effect of a contextual parameter on conditional (2.1) and unconditional (2.2) probabilities in a BN (or actually indirect effect to a target attribute’s probability), which is one of the basic components of the Bayesian Metanetwork concept.2.1. Contextual Effect on Conditional ProbabilitySimplest possible case is shown in Fig. 3 where one contextual attribute affects the conditional probability between one predictive and one target attribute.P(P(Y|X))Fig. 3. Simple model of contextual effect on conditional probabilityThe case shown in Fig. 3 can be described as follows:• X ={x 1, x 2, …, x n } – predictive attribute with n values;• Z ={z 1, z 2, …, z q } – contextual attribute with q values;• P(Y|X) = {p 1(Y |X), p 2(Y |X), …, p r (Y |X)} – conditional dependence attribute(random variable) between X and Y with r possible values;• P(P(Y|X)|Z) – conditional dependence between attribute Z and attribute P(Y|X); Assume that our goal is to compute P(Y). For that first we calculate the probability for the “conditional dependence” attribute:∑===⋅===qm m k m k z Z X Y p X Y P P z Z P X Y p X Y P P 1]}|)|()|([)({))|()|(( (5)Then we estimate the following joint probability:)()]|()|([)]|()|(,|[))|()|(,,(i k k i j k i j x X P X Y p X Y P P X Y p X Y P x X y Y P X Y p X Y P x X y Y P =⋅=⋅======== (6)Taking into account that: )|()]|()|(,|[i j k k i j x X y Y p X Y p X Y P x X y Y P ======we can rewrite (6) as follows:)()]|()|([)|())|()|(,,(i k i j k k i j x X P X Y p X Y P P x X y Y p X Y p X Y P x X y Y P =⋅=⋅======= (7)Substituting (5) to (7) we get:∑===⋅=⋅=⋅=======q m m k m i i j k k i j z Z X Y p X Y P P z Z P x X P x X y Y p X Y p X Y P x X y Y P 1]}|)|()|([)({)()|())|()|(,,((8)Applying marginalization in (8) we obtain:})]|)|()|(()([)()|({)(111∑∑∑=====⋅=××=⋅====q m m k m r k ni i i j k j z Z X Y p X Y P P z Z P x X P x X y Y p y Y P (9)or in more compact form (with attributes only and without values) the general calculation scheme will be as follows:})]|)|(()([)|()({)()|(44443444421metalevel Z X Y P X Z X Y P P Z P X Y P X P Y P ∑∑∑∀∀∀⋅⋅⋅=. (10)Consider artificial example scenario for Fig. 3: •Target attribute (someone’s wellness): Y = {Rich, Poor}; •Predictive attribute (someone’s intension to work): X = {Hardworking, Lazy}; •Known probability distribution: P(Hardworking) = 0.3; P(Lazy) = 0.7. •Contextual attribute (someone’s country of residence): Z = {USA, Ukraine, TheRestWorld}; •Probability distribution: P(USA) =0.2; P(Ukraine) = 0.1; P(TheRestWorld) = 0.7. •Assume that we know two possible conditional probability distributions for P(Y|X) as it is shown in Table 1.Table 1. Probability distribution for P(X|Y) in the example________________________________________________p 1(Y|X) Hardworking Lazy________________________________________________Rich 0.8 0.1Poor 0.2 0.9 ________________________________________________p 2(Y|X) Hardworking Lazy________________________________________________Rich 0.6 0.5Poor 0.4 0.5 ________________________________________________• Assume conditional dependence between contextual attribute Z and P(Y|X) to be as shown in Table 2.Table 2. Conditional dependence between context (attribute Z) and conditionalprobability P(Y|X) in the example______________________________________________________________________P(P(Y|X)|Z)USA Ukraine TheRestWorld ______________________________________________________________________ p 1(Y|X)0.9 0.2 0.7 p 2(Y|X)0.1 0.8 0.3 ______________________________________________________________________• So we have: n = 2; q = 3; r = 2.Assume that task is to calculate P (Y), i.e. P(Y=Rich) and P(Y=Poor).First calculate the following according to (5):;69.07.07.02.01.09.02.0)]|)|()|(()([311=×+×+×===⋅=∑=m m m z Z X Y p X Y P P zZ PSimilarly: .31.0)]|)|()|(()([312===⋅=∑=m m m z Z X Y p X Y P P zZ P Now we apply (9):;3782.031.07.05.031.03.06.069.07.01.069.03.08.0)(=××+××+××+××==Rich Y PSimilarly:.6218.0)(==Poor Y P2.2. Contextual Effect on Unconditional ProbabilitySimplest possible case is shown in Fig. 4 where one contextual attribute affects unconditional probability distribution of a predictive attribute.P(P(X)|Z )Z P(Z)P(P(X))Fig. 4. Simple model of contextual effect on unconditional probabilityIn the case shown in the Fig. 4 we have the following input data: •X ={x 1, x 2, …, x n } – predictive attribute with n values; •Z ={z 1, z 2, …, z q } – contextual attribute with q values and P(Z) – probability distribution for values of Z; •P(X) = {p 1(X), p 2(X), …, p r (X)} – probability distribution attribute for X (random variable) with r possible values (different possible probability distributions for X) and P(P(X)) is probability distribution for values of attribute P(X); •P(Y|X) is a conditional probability distribution of Y given X; • P(P(X)|Z) is a conditional probability distribution for attribute P(X) given Z;Assuming that goal is to compute P(Y), first we calculate the following probability:∑===⋅===qm m k m k z Z X p X P P z Z P X p X P P 1]}|)()([)({))()((. (11)Then we estimate the following joint probability:))()(())()(|())()(,|())()(,())()(,|())()(,,(X p X P P X p X P x X P X p X P x X y Y P X p X P x X P X p X P x X y Y P X p X P x X y Y P k k i k i j k i k i j k i j =⋅==⋅=======⋅========(12)Taking into account the independence of parameters Y and P(X) given X and also that: )())()(,(i k k i x X p X p X P x X P ====we can rewrite (12) as follows:)())()(()|())()(,,(i k k i j k i j x X p X p X P P x X y Y P X p X P x X y Y P =⋅=⋅======= (13)Substituting (11) to (13) we get: ∑===⋅=⋅=⋅=======q m m k m i k i j k i j z Z X p X P P z Z P x X p x X y Y P X p X P x X y Y P 1))|)()(()(()()|())()(,,((14)Applying summarization in (14) we obtain:})]|)()(()([)()|({)(111∑∑∑=====⋅=××=⋅====q m m k m r k ni i k i j j z Z X p X P P z Z P x X p x X y Y P y Y P (15)or in more compact form the general calculation scheme will be as follows:})]|)(()([)|()({)()(44443444421metalevel Z X P X Z X P P Z P X Y P X P Y P ∑∑∑∀∀∀⋅⋅⋅=. (16)Consider artificial example scenario for Fig. 4:• Target attribute (someone’s wellness): Y = {Rich, Poor};• Predictive attribute (someone’s intension to work): X = {Hardworking, Lazy}; • Assume that we have two possible probability distributions for X as it is shown in Table 3.Table 3. Two probability distributions for X in the example________________________________________________P(X) Hardworking Lazy________________________________________________p 1(X) 0.2 0.8p 2(X) 0.5 0.5________________________________________________ • Contextual attribute (someone’s country of residence): Z = {USA, Ukraine, TheRestWorld};• Probability distribution: P(USA) =0.2; P(Ukraine) = 0.1; P(TheRestWorld) = 0.7. • Assume that we know conditional probability distribution matrix for P(Y|X) as it is presented in Table 4.Table 4. Conditional probability P(Y|X) in the example________________________________________________P(Y|X) Hardworking Lazy________________________________________________Rich 0.7 0.4Poor 0.3 0.6 ________________________________________________• Let conditional dependence between contextual attribute Z and attribute P(X) to be as it is shown in Table 5.Table 5. Conditional dependence between context (attribute Z) andprobability distribution P(X) in the example______________________________________________________________________P(P(X)|Z)USA Ukraine TheRestWorld ______________________________________________________________________ p 1(X)0.4 0.2 0.3 p 2(X) 0.60.8 0.7 ______________________________________________________________________• So we have: n = 2; q = 3; r = 2.Assume that task is to calculate P (Y), i.e. P(Y=Rich) and P(Y=Poor).First we calculate the following according to (11):;31.03.07.02.01.04.02.0)]|)()(()([311=×+×+×===⋅=∑=m m m z Z X p X P P zZ P;69.07.07.08.01.06.02.0)]|)()(()([312=×+×+×===⋅=∑=m m mz Z X p X P P zZ PNow we apply (15):+××××)(=+×==RichY××7.0+×P5.04.0692.069;5221.0.0.031.05.08.04.0317.0.0=PoorYP(=.4779.0)3 Bayesian Metanetwork for Managing Probability DistributionsWe define a Bayesian Metanetwork in a way implementing the basic intuition we had defining a Semantic Metanetwork few years ago. Semantic Metanetwork [16] was defined as a set of semantic networks, which are put on each other in such a way that links of every previous semantic network are in the same time nodes of the next network. In a Semantic Metanetwork every higher level controls semantic structure of the lower level. Simple controlling rules might be, for example, in what contexts certain link of a semantic structure can exist and in what context it should be deleted from the semantic structure.Definition. Bayesian Metanetwork is a set of Bayesian networks, which are put on each other in such a way that conditional or unconditional probability distributions associated with nodes of every previous probabilistic network depend on probability distributions associated with nodes of the next network.First consider 2-level Bayesian Metanetwork (the idea is shown in Fig. 5). Context variables in it are considered to be on a second (contextual) level to control the conditional probabilities associated with predictive level of the network. Standard Bayesian inference is applied in Bayesian network of each level.Fig. 5. Two-level Bayesian Metanetwork for managing conditional probabilitiesA sample of a Bayesian Metanetwork (for simplicity projected to 2-D space), which is part of the metanetwork in Fig. 5, is presented in Fig. 6. Bayesian (meta)network in Fig. 6 has the following parameters:Attributes of the predictive level:A with values {a1,a2,…,a na};B with values {b1,b2,…,b nb} and probability P(A);X with values {x1,x2,…,x nx}; Y with values {y1,y2,…,y ny} and probability P(X);Conditional probabilities of the predictive level: P(B|A) which is random variable with set of values {p1(B|A), p2(B|A),…, p mp(B|A)}. Important to notice that this parameter serves as an ordinary conditional probability in the predictive level of Bayesian metanetwork and it also serves as an attribute node on the contextual level.P(Y|X) which is random variable with possible values {p 1(Y|X), p 2(Y|X),…, p np (Y|X)} and also considered as an attribute node on a contextual level of Bayesian Metanetwork.Conditional probability from the contextual level: P(P(Y|X),P(B|A)), which defines conditional probability between two contextual attributes P(B|A) and P(Y|X).P(P(B|A))P(Y|X)P(P(Y|X))Fig. 6. An example of Bayesian Metanetwork. The nodes of the 2nd -level network correspond to the conditional probabilities of the 1st -level network P(B|A) and P(Y|X). The arc in the 2nd -level network corresponds to the conditional probability P(P(Y|X)|P(B|A))The probability of the target attribute P(Y) can be computed by applying basic Bayesian inference on both levels of the metanetwork. First we are exploring the basic level of the BMN. Finding joint probability:));|()|(()()|())|()|(,())|()|(,|())|()|(,,()|(X Y p X Y P P x X P x X y Y p X Y p X Y P x X P X Y p X Y P x X y Y P X Y p X Y P x X y Y P k i i j k tindependen k i x X y Y p k i j k i j i j k =⋅=⋅======⋅==========444443444442144444443444444421 Then making marginalization:;))]|()|(()()|([)(∑∑=⋅=⋅====k ik i i j k j X Y p X Y P P x X P x X y Y p y Y P (17)Now exploring the metalevel (joint probability first):));|()|(())|()|(|)|()|(())|()|(),|()|((A B p A B P P A B p A B P X Y p X Y P P A B p A B P X Y p X Y P P r r k r k =⋅======Then marginalization on the metalevel: ];))|()|(())|()|(|)|()|(([))|()|((∑=⋅=====r r r k k A B p A B P P A B p A B P X Y p X Y P P X Y p X Y P P (18)Finally from (17) and (18) we are getting the target probability:))]}.|()|(())|()|((|)|()|(([)()|({)(A B p A B P P A B p A B P P X Y p X Y P P x X P x X y Y p y Y P r r r k i ki i j k j =×==××=⋅====∑∑∑Similar inference as for above case can be also applied to other cases of a Metanetwork where unconditional, conditional or both probability distributions associated with nodes of predictive level of the metanetwork depend on probability distributions associated with nodes of the contextual level of the metanetwork (Fig. 7). P(P(X)|P(A))P(P(A))P(A)X P(P(X)) P(X)P(P(Y|X)|P(A))P(P(A))P(A)P(Y|X)P(P(Y|X)) YP(P(Y|X)|P(A))P(P(A))P(A)P(Y|X)P(P(Y|X))P(P(B))P(B)P(P(A)|P(B))Fig. 7. Some other (than in Fig. 5) cases of Bayesian Metanetwork: In metanetwork (a) unconditional probability distributions associated with nodes of the predictive level network depend on probability distributions associated with nodes of the contextual level network, 2-D fragment is shown in (b); in (c) the contextual level metanetwork models conditional dependence particularly between unconditional and conditional probabilities of the predictive level (see also (d)); in (e) and (f) the combination of two previous cases is shown.4 ConclusionsThe main challenge of this paper is the multilevel probabilistic meta-model (Bayesian Metanetwork), which is an extension of traditional BN and modification of recursive multinets. The model assumes that interoperability between component networks can be also modeled by another BN. Bayesian Metanetwork is a set of BN, which are put on each other in such a way that conditional or unconditional probability distributions associated with nodes of every previous probabilistic network depend on probability distributions associated with nodes of the next network. We assume parameters (probability distributions) of a BN as random variables and allow conditional dependencies between these probabilities. Several cases of two-level Bayesian Metanetworks were presented, which consist on interrelated predictive and contextual BN models. By recursive application of the same “meta”-principle we can assume that a Bayesian metanetwork might have as many levels as necessary depending on the dynamics and complexity of the context. In this paper we have considered only some basic concepts, definitions and inference in a Bayesian Metanetwork. Some preliminary usage cases were discussed in [17], where context-sensitive mobile user preferences were modeled by Bayesian metanetworks. The basic algorithm for learning Bayesian metanetworks from data can be found in [18]. However further research is needed for providing advanced learning algorithms for such networks as well as for proving its efficiency on real-world examples.AcknowledgementsI am grateful for Dr. Oleksandra Vitko for fruitful discussions and valuable comments within the scope of this paper. Also I appreciate anonymous reviewers for their useful feedback and concrete suggestions to improve the paper. The partial support for this research, provided by TEKES (SmartResource project) and cooperating companies: TeliaSonera, Metso Automation, TietoEnator, Science Park, Agora Center and University of Jyvaskyla, was also highly appreciated.References1.J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of PlausibleInference, (Morgan Kaufmann, 1988).2.M. 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