Evolution of belief systems has always been in focus of cognitive research. In this paper we delineate a new model describing belief systems as a network of statements considered true. Testing the model a small number of parameters enabled us to reproduce a variety of well-known mechanisms ranging from opinion changes to development of psychological problems. The self-organizing opinion structure showed a scale-free degree distribution. The novelty of our work lies in applying a convenient set of definitions allowing us to depict opinion network dynamics in a highly favorable way, which resulted in a scale-free belief network. As an additional benefit, we listed several conjectural consequences in a number of areas related to thinking and reasoning.
We developed the language of Modifiable Temporal Belief Networks (MTBNs) as a structural and temporal extension of Bayesian Belief Networks (BNs) to facilitate normative temporal and causal modeling under uncertainty. In this paper we present definitions of the model, its components, and its fundamental properties. We also discuss how to represent various types of temporal knowledge, with an emphasis on hybrid temporal-explicit time modeling, dynamic structures, avoiding causal temporal inconsistencies, and dealing with models that involve simultaneously actions (decisions) and causal and non-…
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to…
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper, we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the prin…
Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes p if he knows that p is more plausible than its negation. We then consider some properties defining the int…
ENSTA Bretagne（布列塔尼国立高等先进技术学院）；Université de Rennes 1（雷恩第一大学）
The aim of this paper is to show the interest in fitting features with an $α$-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and $α$-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility func…
We present a novel inference algorithm for arbitrary, binary, undirected graphs. Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases, first we update the pairwise probabilities, given the marginal probabilities at each unit,using an analytic expression. Next, we update the marginal probabilities, given the pairwise probabilities by following the negative gradient of the Bethe free energy. Both steps are guaranteed to decrease the Bethe free energy, and since it is lower bounded, the algorithm …
Hierarchical Belief Modeling for Zero-Shot Opponent Adaptation in Partially Observable Multi-Agent Navigation
Tsinghua University（清华大学）；Stevens Institute of Technology（史蒂文斯理工学院）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Texas A&M University（德克萨斯A&M大学）
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference; because of the high-dimensional nature, however, one must often use approximate methods for this purpose. Belief propagation performs approximate inference, is efficient, and looks back on a long success-story. Yet, in most cases, belief propagation lacks any performance and convergence guarantees. Many realistic problems are presented by graphical models with loo…
Fudan University（复旦大学）；Australian National University（澳大利亚国立大学）；University of New South Wales（新南威尔士大学）
The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to avoid logical omniscience is to limit reasoning to a certain belief level, which intuitively measures the reasoning "depth." This paper investigates the computational complexity of reasoning with belief levels. First we show that while reasoning remains tractable if the level is constant, the complexity jumps to PSPACE-complete -- that is, beyond classical r…
The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different extensions to AGM to address three important criticisms applied to it. In this article, we propose a framework based on AGM that takes a position in each of these categories. Also, we discuss some features of our framework and study the satisfiability of AGM postulates in this new context.
Stanford University（斯坦福大学）；IBM Almaden Research Center（IBM阿尔马登研究中心）
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. Roughly, revision treats a surprising observation as a sign that previous beliefs were wrong, while update treats a surprising observation as an indication that the world has changed. In general, we would expect that an agent making an observation may both want to revise some earlier beliefs and assume that some change has occurred in the world. We define a novel approach to belief change that allows us to d…
We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fix…
We propose a new approach to the theoretical analysis of Loopy Belief Propagation (LBP) and the Bethe free energy (BFE) by establishing a formula to connect LBP and BFE with a graph zeta function. The proposed approach is applicable to a wide class of models including multinomial and Gaussian types. The connection derives a number of new theoretical results on LBP and BFE. This paper focuses two of such topics. One is the analysis of the region where the Hessian of the Bethe free energy is positive definite, which derives the non-convexity of BFE for graphs with multiple cycles, and a conditio…
Universitá di Pisa（比萨大学）；Institute for Informatics and Telematics (IIT), National Research Council (CNR)（国家研究委员会信息学与远程通信研究所）
There is a clear desire to model and comprehend human behavior. Trends in research covering this topic show a clear assumption that many view human reasoning as the presupposed standard in artificial reasoning. As such, topics such as game theory, theory of mind, machine learning, etc. all integrate concepts which are assumed components of human reasoning. These serve as techniques to attempt to both replicate and understand the behaviors of humans. In addition, next generation autonomous and adaptive systems will largely include AI agents and humans working together as teams. To make this pos…
The debate on whether or not humans have free will has been raging for centuries. Although there are good arguments based on our current understanding of the laws of nature for the view that it is not possible for humans to have free will, most people believe they do. This discrepancy begs for an explanation. If we accept that we do not have free will, we are faced with two problems: (1) while freedom is a very commonly used concept that everyone intuitively understands, what are we actually referring to when we say that an action or choice is "free" or not? And, (2) why is the belief in free …
Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will give the MAP solution if the beliefs have no ties. In this paper we extend the setting under which BP can be used to provably extract the MAP. We define Convex BP as BP algorithms based on a convex free energy approximation and show that this class includes ordinary BP with single-cycle, …
The Wellcome Centre for Human Neuroimaging（韦康比人类神经影像中心）；UCL Queen Square Institute of Neurology（伦敦大学学院皇后广场神经学研究所）；Imperial College London（伦敦帝国理工学院）；University of Toronto（多伦多大学）；Google Research（谷歌研究院）；University of Amsterdam（阿姆斯特丹大学）
Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active infe…
From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How
Institute for Computational Biomedicine, RWTH Aachen University（计算生物医学研究所，亚琛工业大学）；Center for Computational Life Sciences, RWTH Aachen University（计算生命科学中心，亚琛工业大学）
A statistical system is classically defined on a set of microstates $E$ by a global energy function $H : E \to \mathbb{R}$, yielding Gibbs probability measures (softmins) $ρ^β(H)$ for every inverse temperature $β= T^{-1}$. Gibbs states are simultaneously characterized by free energy principles and the max-entropy principle, with dual constraints on inverse temperature $β$ and mean energy ${\cal U}(β) = \mathbb{E}_{ρ^β}[H]$ respectively. The Legendre transform relates these diverse variational principles which are unfortunately not tractable in high dimension. The global energy is generally giv…
MIT Computer Science and Artificial Intelligence Laboratory（麻省理工学院计算机科学与人工智能实验室）；Harvard School of Engineering and Applied Sciences（哈佛大学工程与应用科学学院）
This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents beliefs and decision-making processes. NIDs are graphical structures in which agents mental models are represented as nodes in a network; a mental model for an agent may itself use descriptions of the mental models of other agents. NIDs are demonstrated by examples, showing how they can be used to describe conflicting and cyclic belief structures, and certain forms of bounded rationality. In an opponent modeling domain, NIDs were able to outperform other comput…
Isopignistic Canonical Decomposition via Belief Evolution Network
University of Electronic Science and Technology of China（电子科技大学）；Institute of Fundamental and Frontier Science（基础与前沿研究院）；Vanderbilt University（范德堡大学）；School of Medicine（医学院）
In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. We generalize the Belief Propagation (BP) algorithms of sum-product and max-product and tree-rewaighted (TRW) sum and max product algorithms (TRBP) and introduce a new set of convergent algorithms based on "convex-free-energy" and Linear-Programming (LP) relaxation as a zero-temprature of a convex-free-energy. The main idea of this work arises from taking a general perspectiv…
It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum of the so-called Bethe free energy functional. For a general graphical model on a loopy graph the functional may show multiple minima, the iterative BP algorithm may converge to one of the minima or may not converge at all, and the global minimum of the Bethe free energy functional is not guaranteed to correspond to the optimal Maximum-Likelihood (ML) solutio…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Currently, in the study of multiagent systems, the intentions of agents are usually ignored. Nonetheless, as pointed out by Theory of Mind (ToM), people regularly reason about other's mental states, including beliefs, goals, and intentions, to obtain performance advantage in competition, cooperation or coalition. However, due to its intrinsic recursion and intractable modeling of distribution over belief, integrating ToM in multiagent planning and decision making is still a challenge. In this paper, we incorporate ToM in multiagent partially observable Markov decision process (POMDP) and propo…
