An intelligent agent will often be uncertain about various properties of its environment, and when acting in that environment it will frequently need to quantify its uncertainty. For example, if the agent wishes to employ the expected-utility paradigm of decision theory to guide its actions, it will need to assign degrees of belief (subjective probabilities) to various assertions. Of course, these degrees of belief should not be arbitrary, but rather should be based on the information available to the agent. This paper describes one approach for inducing degrees of belief from very rich knowledge bases, that can include information about particular individuals, statistical correlations, physical laws, and default rules. We call our approach the random-worlds method. The method is based on the principle of indifference: it treats all of the worlds the agent considers possible as being equally likely. It is able to integrate qualitative default reasoning with quantitative probabilistic reasoning by providing a language in which both types of information can be easily expressed. Our results show that a number of desiderata that arise in direct inference (reasoning from statistical information to conclusions about individuals) and default reasoning follow directly {from} the semantics of random worlds. For example, random worlds captures important patterns of reasoning such as specificity, inheritance, indifference to irrelevant information, and default assumptions of independence. Furthermore, the expressive power of the language used and the intuitive semantics of random worlds allow the method to deal with problems that are beyond the scope of many other non-deductive reasoning systems.
Statistical inference with belief functions: A survey
Institute for AI, Data Analysis and Systems (AIDAS)（人工智能、数据分析与系统研究所）；School of Engineering, Computing & Mathematics, Oxford Brookes University（工程、计算与数学学院，奥克斯伯里大学）
University of Waterloo（滑铁卢大学）；Toyota Research Institute（丰田研究院）
Prior beliefs are central to Bayesian accounts of cognition, but many of these accounts do not directly measure priors. More specifically, initial states of belief heavily influence how new information is assumed to be utilized when updating a particular model. Despite this, prior and posterior beliefs are either inferred from sequential participant actions or elicited through impoverished means. We had participants play a version of the game "Plinko", to first elicit individual participant priors in a theoretically agnostic manner. Subsequent learning and updating of participant beliefs was t…
University of Amsterdam（阿姆斯特丹大学）；University of Bayreuth（拜罗伊特大学）
We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations of 'radical uncertainty' is in terms of imprecise probabilities, i.e. representing the agent's knowledge as a set of probability measures. We add to this model a plausibility map, associating to each measure a plausibility number, as a way to go beyond what is known with certainty and represent the agent's beliefs about probability. There are a number of st…
A Linear Belief Function Approach to Portfolio Evaluation
University of Kansas（堪萨斯大学）；University of Akron（阿克伦大学）
通过详细阐述线性信念函数的概念（Dempster 1990; Liu 1996），我们提出了一种使用线性信念函数的专家系统的知识表示的基本方法。我们展示了如何使用基本矩阵来表示市场信息和金融知识，包括完全无知，统计观察，主观猜测，分布假设，线性关系和经验资产定价模型。然后，我们呼吁邓普斯特的规则的组合，以整合的知识，评估投资组合的表现的整体信念，并更新的信念，将额外的信息。我们用三只黄金股票的例子来说明这种方法。
Epistemological Relevance and Statistical Knowledge
University of Rochester（罗切斯特大学）
许多年来，至少从麦卡锡和海斯（McCarthy and Hayes，1969）开始，作家们一直在哀叹，并试图弥补所谓的事实，即我们往往没有足够的统计知识来管理信念的不确定性，做出不确定的推论，等等。如果我们拥有“充分的统计知识”，那么什么是“充分的统计知识”，以及如何利用充分的统计知识来控制和调节认识的不确定性，这些问题几乎从未被阐明。
Indian Statistical Institute（印度统计研究所）；Jadavpur University（贾达普大学）
A belief base revision is developed. The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them. The base revision operator is developed using Removed Set Revision strategy. The operator is characterized with respect to the postulates for base revisions operator satisfies.
University of California San Diego（加州大学圣地亚哥分校）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）
Algorithmic solutions for multi-object tracking (MOT) are a key enabler for applications in autonomous navigation and applied ocean sciences. State-of-the-art MOT methods fully rely on a statistical model and typically use preprocessed sensor data as measurements. In particular, measurements are produced by a detector that extracts potential object locations from the raw sensor data collected for a discrete time step. This preparatory processing step reduces data flow and computational complexity but may result in a loss of information. State-of-the-art Bayesian MOT methods that are based on b…
Centre for Artificial Intelligence Research（人工智能研究中心）；CAIR（人工智能研究中心）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；CSIR Meraka（南非科学与工业研究理事会梅拉卡研究所）；University of Cape Town（开普敦大学）；University of Luxembourg（卢森堡大学）
Université de technologie de Compiègne（贡比涅技术大学）；CNRS UMR 7253 Heudiasyc（法国国家科学研究中心联合研究单位7253 赫迪亚西克实验室）；Shanghai University（上海大学）；UTSEUS（上海大学中欧工程技术学院）；Institut universitaire de France（法兰西大学研究院）
We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, an…
Institut Supérieur d’Informatique et de Multimédia, Université de Sfax（斯法克斯大学高等信息与多媒体学院）；Laboratoire OLID (LR19ES21), Institut Supérieur de Gestion Industrielle, Université de Sfax（斯法克斯大学高等工业管理学院OLID实验室（LR19ES21））；Institut des Hautes Etudes Commerciales, Université de Sfax（斯法克斯大学高等商业研究学院）
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability and rationality for real applications while performing revision, we propose the idea of credible belief base revision yielding to define two new formula-based revision operators using the suitable tools offered by evidence theory. These operators, uniformly presented in the same spirit of others in [9], stem from consistent subbases maximal with respect to c…
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent's belief state - whether representing the agent's `explicit beliefs' or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in a dynamic epi…
Institute of Mathematics and Statistics, Federal University of Bahia - UFBA（巴伊亚联邦大学数学与统计学院）
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transfo…
Centre for Complex Systems, The University of Sydney（悉尼大学复杂系统中心）；Securities Industry Research Centre of Asia-Pacific（亚太证券业研究中心）；CoreLogic, Inc.（CoreLogic公司）
Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their information-processing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the Kullblack-Leibler divergence between posterior decisions and prio…
US Army Research Laboratory（美国陆军研究实验室）；Massachusetts Institute of Technology（麻省理工学院）
Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown state of the world with their neighbors using a learning rule. Existing approaches assume agents have access to precise statistical models (in the form of likelihoods) for the state of the world. However in many situations, such models must be learned from finite data. We propose a social learning rule that takes into account uncertainty in the statistical mod…
Stanford University（斯坦福大学）；Università di Roma La Sapienza（罗马第一大学）；Ecole Normale（巴黎高等师范学院）
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is run after each step. Its outcome provides an heuristic to make choices at next step. This approach has been referred to as `decimation,' with reference to analogous procedures in statistical physics. The behavior of decimation procedures is poorly understood. Here we consider a simple randomized decimation algorithm based on belief propagation (BP), and analy…
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexit…
Ludwig-Maximilians-University of Munich (LMU)（慕尼黑大学（LMU））；Friedrich Alexander University Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；Birkbeck College London（伦敦伯克贝克学院）
We start with the distinction of outcome- and belief-based Bayesian models of the sequential update of agents' beliefs and subjective reliability of sources (trust). We then focus on discussing the influential Bayesian model of belief-based trust update by Eric Olsson, which models dichotomic events and explicitly represents anti-reliability. After sketching some disastrous recent results for this perhaps most promising model of belief update, we show new simulation results for the temporal dynamics of learning belief with and without trust update and with and without communication. The result…
Institute of Logic and Intelligence, Southwest University, China（逻辑与智能研究所，西南大学，中国）；University of Southampton, United Kingdom（南安普顿大学，英国）；Independent Scholar, United States（独立学者，美国）
Do language models have beliefs about the world? Dennett (1995) famously argues that even thermostats have beliefs, on the view that a belief is simply an informational state decoupled from any motivational state. In this paper, we discuss approaches to detecting when models have beliefs about the world, and we improve on methods for updating model beliefs to be more truthful, with a focus on methods based on learned optimizers or hypernetworks. Our main contributions include: (1) new metrics for evaluating belief-updating methods that focus on the logical consistency of beliefs, (2) a trainin…
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual be…
