Large-scale probabilistic knowledge bases are becoming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics underlying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to intervals. While still assuming a finite domain, this semantics can provide meaningful answers when some probabilities are not precisely known. For this open world setting, we propose an efficient evaluation algorithm for unions of conjunctive queries. Our open-world algorithm incurs no overhead compared to closed-world reasoning and runs in time linear in the size of the database for tractable queries. All other queries are #P-hard, implying a data complexity dichotomy between linear time and #P. For queries involving negation, however, open-world reasoning can become NP-, or even NP^PP-hard. Finally, we discuss additional knowledge representation layers that can further strengthen open-world reasoning about big uncertain data.

This paper is set to study the applicability of AGM-like operations to probabilistic bases. We focus on the problem of consistency restoration, also called consolidation or contraction by falsity. We aim to identify the reasons why the set of AGM postulates based on discrete operations of deletions and accretions is too coarse to treat finely adjustable probabilistic formulas. We propose new principles that allow one to deal with the consolidation of inconsistent probabilistic bases, presenting a finer method called liftable contraction. Furthermore, we show that existing methods for probabilistic consolidation via distance minimization are particular cases of the methods proposed.

Knowledge compilation has been successfully used to solve beyond NP problems, including some PP-complete and NP PP -complete problems for Bayesian networks. In this work we show how knowledge compilation can be used to solve problems in the more intractable complexity class PP^PP.  This class contains NP PP and includes interesting AI problems, such as non-myopic value of information. We show how to solve the prototypical PP PP -complete problem MajMajsat in linear-time once the problem instance is compiled into a special class of Sentential Decision Diagrams. To show the practical value of our approach, we adapt it to answer the Same-Decision Probability (SDP) query, which was recently introduced for Bayesian networks. The SDP problem is also PP PP P-complete. It is a value-of-information query that quantifies the robustness of threshold-based decisions and comes with a corresponding algorithm that was also recently proposed. We present favorable experimental results, comparing our new algorithm based on knowledge compilation with the state-of-the-art algorithm for computing the SDP.

We provide new insights into the area of combining abstract argumentation frameworks with probabilistic reasoning. In particular, we consider the scenario when assessments on the probabilities of a subset of the arguments is given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalize this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistent-tolerant reasoning.

The ability to infer intentions, emotions, and other unobservable psychological states from people's behavior is a hallmark of human social cognition, and an essential capability for future Artificial Intelligence systems. The commonsense theories of psychology and sociology necessary for such inferences have been a focus of logic-based knowledge representation research, but have been difficult to employ in robust automated reasoning architectures. In this paper we model behavior interpretation as a process of logical abduction, where the reasoning task is to identify the most probable set of assumptions that logically entail the observable behavior of others, given commonsense theories of psychology and sociology. We evaluate our approach using Triangle-COPA, a benchmark suite of 100 challenge problems based on an early social psychology experiment by Fritz Heider and Marianne Simmel. Commonsense knowledge of actions, social relationships, intentions, and emotions are encoded as defeasible axioms in first-order logic. We identify sets of assumptions that logically entail observed behaviors by backchaining with these axioms to a given depth, and order these sets by their joint probability assuming conditional independence. Our approach solves almost all (91) of the 100 questions in Triangle-COPA, and demonstrates a promising approach to robust behavior interpretation that integrates both logical and probabilistic reasoning.

In this paper, we focus on a novel knowledge reuse scenario where the knowledge in the source schema needs to be translated to a semantically heterogeneous target schema. We refer to this task as “knowledge translation” (KT). Unlike data translation and transfer learning, KT does not require any data from the source or target schema. We adopt a probabilistic approach to KT by representing the knowledge in the source schema, the mapping between the source and target schemas, and the resulting knowledge in the target schema all as probability distributions, specially using Markov random fields and Markov logic networks. Given the source knowledge and mappings, we use standard learning and inference algorithms for probabilistic graphical models to find an explicit probability distribution in the target schema that minimizes the Kullback-Leibler divergence from the implicit distribution. This gives us a compact probabilistic model that represents knowledge from the source schema as well as possible, respecting the uncertainty in both the source knowledge and the mapping. In experiments on both propositional and relational domains, we find that the knowledge obtained by KT is comparable to other approaches that require data, demonstrating that knowledge can be reused without data.

We consider a new formulation of abduction in which degrees of "plausibility" of explanations, along with the rules of the domain, are learned from concrete examples (settings of attributes). Our version of abduction thus falls in the " learning to reason " framework of Khardon and Roth. Such approaches enable us to capture a natural notion of "plausibility" in a domain while avoiding the extremely difficult problem of specifying an explicit representation of what is "plausible." We specifically consider the question of which syntactic classes of formulas have efficient algorithms for abduction. We find that the class of k -DNF explanations can be found in polynomial time for any fixed k ; but, we also find evidence that even weak versions of our abduction task are intractable for the usual class of conjunctions . This evidence is provided by a connection to the usual, inductive PAC-learning model proposed by Valiant. We also consider an exception-tolerant variant of abduction. We observe that it is possible for polynomial-time algorithms to tolerate a few adversarially chosen exceptions, again for the class of k -DNF explanations. All of the algorithms we study are particularly simple, and indeed are variants of a rule proposed by Mill.

In Supreme Court parlance and the political science literature, an ideal point positions a justice in a continuous space and can be interpreted as a quantification of the justice's policy preferences. We present an automated approach to infer such ideal points for justices of the US Supreme Court. This approach combines topic modeling over case opinions with the voting (and endorsing) behavior of justices. Furthermore, given a topic of interest, say the Fourth Amendment, the topic model can be optionally seeded with supervised information to steer the inference of ideal points. Application of this methodology over five years of cases provides interesting perspectives into the leaning of justices on crucial issues, coalitions underlying specific topics, and the role of swing justices in deciding the outcomes of cases.

Instead of using a uniform metric, instance specific distance learning methods assign multiple metrics for different localities, which take data heterogeneity into consideration. Therefore, they may improve the performance of distance based classifiers, e.g., kNN. Existing methods obtain multiple metrics of test data by either transductively assigning metrics for unlabeled instances or designing distance functions manually, which are with limited generalization ability. In this paper, we propose isMets (Instance Specific METric Subspace) framework which can automatically span the whole metric space in a generative manner and is able to inductively learn a specific metric subspace for each instance via inferring the expectation over the metric bases in a Bayesian manner. The whole framework can be solved with Variational Bayes (VB). Experiment on synthetic data shows that the learned results are with good interpretability. Moreover, comprehensive results on real world datasets validate the effectiveness and robustness of isMets.

We propose Bayesian AutoEncoder (BAE) in order to construct a recognition system which uses feedback information. BAE constructs a generative model of input data as a Bayes Net. The network trained by BAE obtains its hidden variables as the features of given data. It can execute inference for each variable through belief propagation, using both feedforward and feedback information. We confirmed that BAE can construct small networks with one hidden layer and extract features as hidden variables from 3x3 and 5x5 pixel input data.