Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by parameters such as tree width and cycle-cut set size. In this paper we initiate a study to determine the potential of structure-based algorithms in real-life applications. We analyze empirically the structural properties of problems coming from the circuit diagnosis domain. Specifically, we locate those properties that capture the effectiveness of clustering and conditioning as well as of a family of conditioning+clustering algorithms designed to gradually trade space for time. We perform our analysis on 11 benchmark circuits widely used in the testing community. We also report on the effect of ordering heuristics on tree-clustering and show that, on our benchmarks, the well-known max-cardinality ordering is substantially inferior to an ordering called min-degree.
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in constraint reasoning, and a specialization of the belief updating algorithm for singly-connected networks. Our algorithm is exact for singly- connected constraint problems, but can work well as an approximation for arbitrary problems. We briefly discuss some empirical results, and related methods.
Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.
Technical University of Darmstadt（达姆施塔特工业大学）；University of Stuttgart（斯图加特大学）
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence, non-classical reasoning approaches are required. Here, we investigate probabilistic epistemic argumentation as a tool for automated reasoning about legal cases. We introduce a general scheme to model legal cases as probabilistic epistemic argumentation problems, explain how evidence can be modeled and sketch how explanations for legal decisions can be generated automat…
We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is commonly found in practice, especially in "evidential" and "Bayesian" reasoning. We formulate this in terms of the Maximization of Conditional Independence (MCI), and identify a variety of applications for this sort of default. We propose a formalization using Pointwise Circumscription. We compare MCI to Maximum Entropy, another kind of non-monotonic principle, an…
General problems in analyzing information in a probabilistic database are considered. The practical difficulties (and occasional advantages) of storing uncertain data, of using it conventional forward- or backward-chaining inference engines, and of working with a probabilistic version of resolution are discussed. The background for this paper is the incorporation of uncertain reasoning facilities in MRS, a general-purpose expert system building tool.
Carnegie Mellon University（卡内基梅隆大学）；Rockwell International Science Center（罗克韦尔国际科学中心）
Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different strategies for explaining probabilistic reasoning: The first, qualitative belief propagation, traces the qualitative effect of evidence through a belief network from one variable to the next. This propagation algorithm is an alternative to the graph reduction algorithms of Wellman (1988) for inference in qualitative probabilistic networks. It is based on a qualitativ…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a probabilistic logic with truth functional connectives. We propose an alternative mechanism, Incidence Calculus, which is based on a representation of uncertainty using sets of points, which might represent situations, models or possible worlds. Incidence Calculus does provide a probabilistic logic with truth functional connectives.
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) composed of labelled and unlabelled definite clauses to define the proof probabilities. We have a conservative extension of first-order reasoning, so that, for example, there is a one-one mapping between logical and random variables. We show how, in this framework, Inductive Logic Programming (ILP) can …
Università degli Studi di Brescia（布雷西亚大学）；Cardiff University（卡迪夫大学）；CCDC Army Research Laboratory（CCDC陆军研究实验室）；KU Leuven（鲁汶大学）；Blue Prism AI Labs（蓝棱镜人工智能实验室）；Ozyegin University（奥兹耶金大学）
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for probabilistic reasoning in order to determine the confidence (or epistemic uncertainty) in the probabilities in light of the training data. We propose an approach to overcome the independence assumption behind most of the approaches dealing with a large class of probabilistic reasoning that includes Bayesian networks as well as several instances of probabilistic logi…
This paper introduces Probabilistic Deduction (PD) as an approach to probabilistic structured argumentation. A PD framework is composed of probabilistic rules (p-rules). As rules in classical structured argumentation frameworks, p-rules form deduction systems. In addition, p-rules also represent conditional probabilities that define joint probability distributions. With PD frameworks, one performs probabilistic reasoning by solving Rule-Probabilistic Satisfiability. At the same time, one can obtain an argumentative reading to the probabilistic reasoning with arguments and attacks. In this work…
Institute of Information Systems, University of Lübeck（吕贝克大学信息系统研究所）
Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (TAMe), which incorporates (i) clustering for grouping submodels as well as (ii) statistical significance checks to test the fitness of the clustering outcome. In exchange for faster runtimes, TAMe introduces a bounded error that becomes negligible over time. Empirical results show that TAMe significantly improves the runtime performance of in…
AI Technology Office, Wright R&D Center（莱特研发中心人工智能技术办公室）
Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying the inference rules to produce stronger conclusions in the presence of functional relations. I describe how to accomplish these modifications in qualitative probabilistic networks by exhibiting the update procedures for graphical transformations involving probabilistic and deterministic variables and combinations. A simple example demonstrates that the augme…
Rockwell International Science Center（罗克韦尔国际科学中心）；Stanford University（斯坦福大学）
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and solution of probabilistic and decision-theoretic models for complex and uncertain domains. Given a query, a logical proof is produced if possible; if not, an influence diagram based on the query and the knowledge of the decision domain is produced and subsequently solved. A uniform declarative, first-order, knowledge representation is combined with a set of int…
The paper demonstrates that strict adherence to probability theory does not preclude the use of concurrent, self-activated constraint-propagation mechanisms for managing uncertainty. Maintaining local records of sources-of-belief allows both predictive and diagnostic inferences to be activated simultaneously and propagate harmoniously towards a stable equilibrium.
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and data, and regarding the appropriateness of various alternative models. The application of such models is often an iterative process, in which the plausibility of the results confirms or disconfirms the validity of assumptions made in building the model. In current expert systems, by contrast, probabilistic information is encapsulated within modular rules (in…
PAGODA (Probabilistic Autonomous Goal-Directed Agent) is a model for autonomous learning in probabilistic domains [desJardins, 1992] that incorporates innovative techniques for using the agent's existing knowledge to guide and constrain the learning process and for representing, reasoning with, and learning probabilistic knowledge. This paper describes the probabilistic representation and inference mechanism used in PAGODA. PAGODA forms theories about the effects of its actions and the world state on the environment over time. These theories are represented as conditional probability distribut…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge. This knowledge is used to build a set of second-level arguments, which are structured for efficient recapture of the knowledge used to construct them. Finally, at the top level is a Bayesian network constructed from the arguments. The system is designed to facilitate not just propagation of beliefs and assimilation of evidence, but also the dynamic process of c…
Institute for Artificial Intelligence（人工智能研究所）；University of Bremen（不来梅大学）
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the reasons for this explosion is that so far the approaches do not sufficiently exploit the structure and similarity of possible worlds in order to encode the models more compactly. We propose fuzzy inference in Markov logic networks, which enables the use of taxonomic knowledge as a source of imposing structure onto possible worlds. We show that by exploiting this…
A computational scheme for reasoning about dynamic systems using (causal) probabilistic networks is presented. The scheme is based on the framework of Lauritzen and Spiegelhalter (1988), and may be viewed as a generalization of the inference methods of classical time-series analysis in the sense that it allows description of non-linear, multivariate dynamic systems with complex conditional independence structures. Further, the scheme provides a method for efficient backward smoothing and possibilities for efficient, approximate forecasting methods. The scheme has been implemented on top of the…
It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept formation. First it is shown that appropriate averaging-across-situations and renormalization of 4-valued p-bits operating in accordance with Constructible Duality (CD) logic yields PLN (Probabilistic Logic Networks) strength-and-confidence truth values. Then variations on the Curry-Howard correspondence are used to map these paraconsistent and probabilistic lo…
Banca d’Italia（意大利银行）；TU Wien（维也纳工业大学）；University of Oxford（牛津大学）
We provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), satisfying the requirements of ontological reasoning: full recursion, powerful existential quantification, expression of inductive definitions. Vadalog is a Knowledge Representation and Reasoning (KRR) language based on Warded Datalog+/-, a logical core language of existential rules, with a good balance between computational complexity and expressive power. Handling uncertainty is essential for reasoning with KGs. Yet Vadalog and Warded Datalog+/- are not covered by the existing probabilistic logic prog…
Arizona State University（亚利桑那州立大学）；SUNY Binghamton（纽约州立大学宾汉姆顿分校）
To be responsive to dynamically changing real-world environments, an intelligent agent needs to perform complex sequential decision-making tasks that are often guided by commonsense knowledge. The previous work on this line of research led to the framework called "interleaved commonsense reasoning and probabilistic planning" (icorpp), which used P-log for representing commmonsense knowledge and Markov Decision Processes (MDPs) or Partially Observable MDPs (POMDPs) for planning under uncertainty. A main limitation of icorpp is that its implementation requires non-trivial engineering efforts to …
Imperial Cancer Research Fund（帝国癌症研究基金会）；Queen Mary and Westfield College（玛丽女王与西菲尔德学院）
In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a probability will change or which hypothesis is most likely given certain evidence. This paper concentrates on such situations, and suggests a number of ways in which they may be resolved by refining the representation.
Current approaches to expert systems' reasoning under uncertainty fail to capture the iterative revision process characteristic of intelligent human reasoning. This paper reports on a system, called the Non-monotonic Probabilist, or NMP (Cohen, et al., 1985). When its inferences result in substantial conflict, NMP examines and revises the assumptions underlying the inferences until conflict is reduced to acceptable levels. NMP has been implemented in a demonstration computer-based system, described below, which supports threat correlation and in-flight route replanning by Air Force pilots.
Northrop Research and Technology Center（诺斯罗普研究与技术中心）；University of Southern California（南加州大学）
This paper discuses multiple Bayesian networks representation paradigms for encoding asymmetric independence assertions. We offer three contributions: (1) an inference mechanism that makes explicit use of asymmetric independence to speed up computations, (2) a simplified definition of similarity networks and extensions of their theory, and (3) a generalized representation scheme that encodes more types of asymmetric independence assertions than do similarity networks.
In many domains, worst-case guarantees on the performance (e.g., prediction accuracy) of a decision function subject to distributional shifts and uncertainty about the environment are crucial. In this work we develop a method to quantify the robustness of decision functions with respect to credal Bayesian networks, formal parametric models of the environment where uncertainty is expressed through credal sets on the parameters. In particular, we address the maximum marginal probability (MARmax) problem, that is, determining the greatest probability of an event (such as misclassification) obtain…
We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults computed using both methods. We show that, at least for the example examined, the ordering of faults coincide as long as all the causal relations in the original probabilistic network are taken into account. We also provide a formal analysis of some network structures where the two methods will differ. Both kappa rankings and infinitesimal probabilities have be…
University of California Los Angeles（加州大学洛杉矶分校）；Washington University in St. Louis（圣路易斯华盛顿大学）
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework …
The University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Rockwell International Science Center（罗克韦尔国际科学中心）；American Airlines（美国航空公司）
We describe the integration of logical and uncertain reasoning methods to identify the likely source and location of software problems. To date, software engineers have had few tools for identifying the sources of error in complex software packages. We describe a method for diagnosing software problems through combining logical and uncertain reasoning analyses. Our preliminary results suggest that such methods can be of value in directing the attention of software engineers to paths of an algorithm that have the highest likelihood of harboring a programming error.
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present…
Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many decision-making problems, remains a hard query for PCs unless they satisfy highly restrictive structural constraints. In this paper, we develop a pruning algorithm that removes parts of the PC that are irrelevant to a marginal MAP query, shrinking the PC while maintaining the correct solution. This pruning technique is so effective that we are able to build…
Reasoning on large and complex real-world models is a computationally difficult task, yet one that is required for effective use of many AI applications. A plethora of inference algorithms have been developed that work well on specific models or only on parts of general models. Consequently, a system that can intelligently apply these inference algorithms to different parts of a model for fast reasoning is highly desirable. We introduce a new framework called structured factored inference (SFI) that provides the foundation for such a system. Using models encoded in a probabilistic programming …
Northeastern University（东北大学）；Brigham Young University（杨百翰大学）
As autonomous agents become more ubiquitous, they will eventually have to reason about the plans of other agents, which is known as theory of mind reasoning. We develop a planning-as-inference framework in which agents perform nested simulation to reason about the behavior of other agents in an online manner. As a concrete application of this framework, we use probabilistic programs to model a high-uncertainty variant of pursuit-evasion games in which an agent must make inferences about the other agents' plans to craft counter-plans. Our probabilistic programs incorporate a variety of complex …
The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming languages and in Descripion Logics. In this paper, we illustrate the work we have done in this research field by presenting a probabilistic semantics for description logics and reasoning and learning algorithms. In particular, we present in detail the system TRILL P, which computes the probability of queries w.r.t. probabilistic knowledge bases, which has been…
Explainable Knowledge Tracing via Probabilistic Embeddings and Pattern-based Reasoning
Shanghai Institute of AI Education, East China Normal University, Shanghai, 200241, China（上海人工智能教育研究院，华东师范大学，上海，200241，中国）；Shool of Computer Sicence and Technology, East China Normal University, Shanghai, 200241, China（计算机科学与技术学院，华东师范大学，上海，200241，中国）
Detecting Unfaithful Chain-of-Thought via Circuit-Guided Internal-External Discrepancy
Jilin University（吉林大学）；University of Central Florida（中央佛罗里达大学）；Arizona State University（亚利桑那州立大学）；University of Vienna（维也纳大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unifie…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning -- including conditional independence and Bayesian inference -- the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal m…
Credibility-Aware Multi-Modal Fusion Using Probabilistic Circuits
Erik Jonsson School of Engineering & Computer Science, The University of Texas at Dallas（德克萨斯大学达拉斯分校埃里克·琼森工程与计算机科学学院）；Air Force Research Laboratory（空军研究实验室）；TU Darmstadt（达姆施塔特工业大学）
