Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known, though, or may only described by assumptions such as "small universes are more likely". Without a universe, inference is no longer possible for lifted algorithms, losing their advantage of tractable inference. The aim of this paper is to define a semantics for models with unknown universes decoupled from a specific constraint language to enable lifted and thereby, tractable inference.
School of Computing and Information, University of Pittsburgh（匹兹堡大学计算机与信息学院）
PRAM puts agent-based models on a sound probabilistic footing as a basis for integrating agent-based and probabilistic models. It extends the themes of probabilistic relational models and lifted inference to incorporate dynamical models and simulation. It can also be much more efficient than agent-based simulation.
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse linear equations, and constraint propagation. In this framework, the probability model is represented as a generalized relational database. Subsequent probabilistic requests can be processed as standard relational queries. Conventional database management systems can be easily adopted for implementing such an approximate reasoning system.
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…
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…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is…
Noisy probabilistic relational rules are a promising world model representation for several reasons. They are compact and generalize over world instantiations. They are usually interpretable and they can be learned effectively from the action experiences in complex worlds. We investigate reasoning with such rules in grounded relational domains. Our algorithms exploit the compactness of rules for efficient and flexible decision-theoretic planning. As a first approach, we combine these rules with the Upper Confidence Bounds applied to Trees (UCT) algorithm based on look-ahead trees. Our second a…
KU Leuven University（荷语鲁汶大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）
We propose a framework for learning a fragment of probabilistic computation tree logic (pCTL) formulae from a set of states that are labeled as safe or unsafe. We work in a relational setting and combine ideas from relational Markov Decision Processes with pCTL model-checking. More specifically, we assume that there is an unknown relational pCTL target formula that is satisfied by only safe states, and has a horizon of maximum $k$ steps and a threshold probability $α$. The task then consists of learning this unknown formula from states that are labeled as safe or unsafe by a domain expert. We …
The ways in which an agent's actions affect the world can often be modeled compactly using a set of relational probabilistic planning rules. This paper addresses the problem of learning such rule sets for multiple related tasks. We take a hierarchical Bayesian approach, in which the system learns a prior distribution over rule sets. We present a class of prior distributions parameterized by a rule set prototype that is stochastically modified to produce a task-specific rule set. We also describe a coordinate ascent algorithm that iteratively optimizes the task-specific rule sets and the prior …
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…
Imperial College of Science, Technology and Medicine（帝国理工学院）
Bayesian networks have been used extensively in diagnostic tasks such as medicine, where they represent the dependency relations between a set of symptoms and a set of diseases. A criticism of this type of knowledge representation is that it is restricted to this kind of task, and that it cannot cope with the knowledge required in other artificial intelligence applications. For example, in computer vision, we require the ability to model complex knowledge, including temporal and relational factors. In this paper we extend Bayesian networks to model relational and temporal knowledge for high-le…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the structural regularities of a domain, and principled support for probabilistic inference. In addition to these two aspects, however, many applications also involve a third aspect-the need to reason about similarities-which has not been directly supported in existing frameworks. This paper introduces probabilistic similarity logic (PSL), a general-purpose framework …
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose unifying techniques from probabilistic databases and relational embedding models with the goal of performing complex queries on incomplete and uncertain data. We formalize a probabilistic database model with respect to which all queries are done. This allows us to leverage the rich literature of theory and algorithms from probabilistic databases for solving problems. While this formalization can be used with any relational embedding model, the lack of a well-defined joint probability distribution causes simple query problems to become provably hard. With this in mind, we introduce \…
LARODEC Laboratory（拉罗德克实验室）；ISG（突尼斯高等管理学院）；Université de Tunis（突尼斯大学）；DUKe research group（DUKe研究组）；LINA Laboratory UMR 6241（LINA实验室（法国国家科研中心联合研究单位6241））；University of Nantes（南特大学）；DataForPeople
The validation of any database mining methodology goes through an evaluation process where benchmarks availability is essential. In this paper, we aim to randomly generate relational database benchmarks that allow to check probabilistic dependencies among the attributes. We are particularly interested in Probabilistic Relational Models (PRMs), which extend Bayesian Networks (BNs) to a relational data mining context and enable effective and robust reasoning over relational data. Even though a panoply of works have focused, separately , on the generation of random Bayesian networks and relationa…
Oregon State University（俄勒冈州立大学）；Tufts University（塔夫茨大学）
Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of decision diagrams (FODD) and developed a value iteration algorithm for this representation. This paper develops several improvements to the FODD algorithm that make the approach practical. These include, …
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is directly represented by a Bayesian network. By using a powerful way of specifying conditional probability distributions in these networks, the resulting formalism is more expressive than the previous ones. Particularly, it provides for constraints on equalities of events, and it allows to define complex, nested combination functions.
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits ran…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover a variety of plate models and of probabilistic relational models. We study the complexity of inferences when network, query and domain are the input (the inferential and the combined complexity), when the network is fixed and query and domain are the input (the query/data complexity), and when the network and query are fixed and the domain is the input (the …
University of Massachusetts（马萨诸塞大学）；Microsoft Research（微软研究院）
Instead of requiring a domain expert to specify the probabilistic dependencies of the data, in this work we present an approach that uses the relational DB schema to automatically construct a Bayesian graphical model for a database. This resulting model contains customized distributions for columns, latent variables that cluster the data, and factors that reflect and represent the foreign key links. Experiments demonstrate the accuracy of the model and the scalability of inference on synthetic and real-world data.
In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov netwo…
KU Leuven（鲁汶大学）；Université libre de Bruxelles（布鲁塞尔自由大学）；Örebro University（厄勒布鲁大学）
Probabilistic model checking has been developed for verifying systems that have stochastic and nondeterministic behavior. Given a probabilistic system, a probabilistic model checker takes a property and checks whether or not the property holds in that system. For this reason, probabilistic model checking provide rigorous guarantees. So far, however, probabilistic model checking has focused on propositional models where a state is represented by a symbol. On the other hand, it is commonly required to make relational abstractions in planning and reinforcement learning. Various frameworks handle …
KU Leuven（鲁汶大学）；University of Washington, Seattle（西雅图华盛顿大学）
Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetr…
Dealing with structured data needs the use of expressive representation formalisms that, however, puts the problem to deal with the computational complexity of the machine learning process. Furthermore, real world domains require tools able to manage their typical uncertainty. Many statistical relational learning approaches try to deal with these problems by combining the construction of relevant relational features with a probabilistic tool. When the combination is static (static propositionalization), the constructed features are considered as boolean features and used offline as input to a …
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）
Probabilistic inference over large data sets is a challenging data management problem since exact inference is generally #P-hard and is most often solved approximately with sampling-based methods today. This paper proposes an alternative approach for approximate evaluation of conjunctive queries with standard relational databases: In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema i…
Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and accurate inference on such problems using Markov chain Monte Carlo (MCMC) techniques with customized proposal distributions. Currently, implementing such a system requires coding MCMC state representations and acceptance probability calculations that are specific to a particular application. An alternative approach, which we pursue in this paper, is to use a gene…
This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random variables, which is necessary for applications with numeric data. The first contribution is the introduction of context-specific likelihood weighting (CS-LW), a new sampling algorithm that exploits context-specific independencies for computational gains. Next, a new hybrid PLP, DC#, is introduced, which integrates the syntax of Distributional Clauses with Bayesi…
Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of stati…
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.
Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this …
University of Florence（佛罗伦萨大学）；University of Siena（锡耶纳大学）
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these rea…
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；singularIT GmbH（singularIT有限公司）；University of Münster（明斯特大学）；University of Lübeck（吕贝克大学）
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient inference and seek to scale with the degree of symmetry of a probability model. A limitation of existing exact lifted inference techniques is that they do not apply to non-relational representations like factor graphs. In this work we provide the first example of an exact lifted inference algorithm for arbitrary discrete factor graphs. In addition we describe …
A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these models are not projective in the sense that the marginal of the distribution for size-$n$ structures on induced sub-structures of size $k<n$ is equal to the given distribution for size-$k$ structures. Projectivity is very beneficial in that it directly enables lifted inference and statistically consistent learning from sub-sampled relational structures. In earlie…
International Research Center for Neurointelligence (IRCN)（国际神经智能研究中心）；The University of Tokyo（东京大学）；Graduate School of Engineering, Nagoya Institute of Technology（名古屋技术大学工学院）；Hitachi, Ltd.（日立株式会社）
KU Leuven（荷语鲁汶大学）；Czech Technical University in Prague（布拉格捷克理工大学）
Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational mod…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics, respectively based on stable and on well-founded models. We show that the semantics based on stable models (referred to as the "credal semantics") produces sets of probability models that dominate infinitely monotone Choquet capacities, we describe several useful consequences of this result. We then examine the complexity of inference with probabilistic logic p…
The University of British Columbia（不列颠哥伦比亚大学）；KU Leuven（鲁汶大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeable, undistinguished objects as a whole. In this paper, we study the domain recursion inference rule, which, despite its central role in early theoretical results on domain-lifted inference, has later been believed redundant. We show that this rule is more powerful than expected, a…
SRI International（SRI国际研究所）；U. of Texas at Dallas（德克萨斯大学达拉斯分校）；U. of California, Irvine（加州大学欧文分校）
We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently, propositional, equalities on discrete sorts, and inequalities, more specifically difference arithmetic, on bounded integers). While many solutions to probabilistic inference over logic representations have been proposed, SGDPLL(T) is simultaneously (1) lifted, (2) exact and (3) modulo theories, that is, parameterized by a background logic theory. This offers a foun…
