Relational probabilistic models have the challenge of aggregation, where one variable depends on a population of other variables. Consider the problem of predicting gender from movie ratings; this is challenging because the number of movies per user and users per movie can vary greatly. Surprisingly, aggregation is not well understood. In this paper, we show that existing relational models (implicitly or explicitly) either use simple numerical aggregators that lose great amounts of information, or correspond to naive Bayes, logistic regression, or noisy-OR that suffer from overconfidence. We propose new simple aggregators and simple modifications of existing models that empirically outperform the existing ones. The intuition we provide on different (existing or new) models and their shortcomings plus our empirical findings promise to form the foundation for future representations.

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, and in fact significantly extends the range of models for which lifted inference runs in time polynomial in the number of individuals in the domain. This includes an open problem called S4, the symmetric transitivity model, and a first-order logic encoding of the birthday paradox. We further identify new classes S2FO2 and S2RU of domain-liftable theories, which respectively subsume FO2 and recursively unary theories, the largest classes of domain-liftable theories known so far, and show that using domain recursion can achieve exponential speedup even in theories that cannot fully be lifted with the existing set of inference rules.

Relational logistic regression (RLR) is a representation of conditional probability in terms of weighted formulae for modelling multi-relational data. In this paper, we develop a learning algorithm for RLR models. Learning an RLR model from data consists of two steps: 1- learning the set of formulae to be used in the model (a.k.a. structure learning) and learning the weight of each formula (a.k.a. parameter learning). For structure learning, we deploy Schmidt and Murphy's hierarchical assumption: first we learn a model with simple formulae, then more complex formulae are added iteratively only if all their sub-formulae have proven effective in previous learned models. For parameter learning, we convert the problem into a non-relational learning problem and use an off-the-shelf logistic regression learning algorithm from Weka, an open-source machine learning tool, to learn the weights. We also indicate how hidden features about the individuals can be incorporated into RLR to boost the learning performance. We compare our learning algorithm to other structure and parameter learning algorithms in the literature, and compare the performance of RLR models to standard logistic regression and RDN-Boost on a modified version of the MovieLens data-set.

Compiling a Bayesian network into a secondary structure, such as a junction tree or arithmetic circuit allows for offline computations before observations arrive, and quick inference for the marginal of all variables. However, query-based algorithms, such as variable elimination and recursive conditioning, that compute the posterior marginal of few variables given some observations, allow pruning of irrelevant variables, which can reduce the size of the problem. Madsen and Jensen show how lazy evaluation of junction trees can allow both compilation and pruning. In this paper, we adapt the lazy evaluation to arithmetic circuits, allowing the best of both worlds: pruning due to observations and query variables as well as compilation while exploiting local structure and determinism.

This book examines the foundations of combining logic and probability into what are called relational probabilistic models. It introduces representations, inference, and learning techniques for probability, logic, and their combinations. ISBN 9781627058414, 189 pages.

The AAAI-14 Workshop program was held Sunday and Monday, July 27–28, 2012, at the Québec City Convention Centre in Québec, Canada. The AAAI-14 workshop program included fifteen workshops covering a wide range of topics in artificial intelligence. The titles of the workshops were AI and Robotics; Artificial Intelligence Applied to Assistive Technologies and Smart Environments; Cognitive Computing for Augmented Human Intelligence; Computer Poker and Imperfect Information; Discovery Informatics; Incentives and Trust in Electronic Communities; Intelligent Cinematography and Editing; Machine Learning for Interactive Systems: Bridging the Gap between Perception, Action and Communication; Modern Artificial Intelligence for Health Analytics; Multiagent Interaction without Prior Coordination; Multidisciplinary Workshop on Advances in Preference Handling; Semantic Cities -- Beyond Open Data to Models, Standards and Reasoning; Sequential Decision Making with Big Data; Statistical Relational AI; and The World Wide Web and Public Health Intelligence. This article presents short summaries of those events.

The AAAI-14 Workshop program was held Sunday and Monday, July 27–28, 2012, at the Québec City Convention Centre in Québec, Canada. Canada. The AAAI-14 workshop program included fifteen workshops covering a wide range of topics in artificial intelligence. The titles of the workshops were AI and Robotics; Artificial Intelligence Applied to Assistive Technologies and Smart Environments; Cognitive Computing for Augmented Human Intelligence; Computer Poker and Imperfect Information; Discovery Informatics; Incentives and Trust in Electronic Communities; Intelligent Cinematography and Editing; Machine Learning for Interactive Systems: Bridging the Gap between Perception, Action and Communication; Modern Artificial Intelligence for Health Analytics; Multiagent Interaction without Prior Coordination; Multidisciplinary Workshop on Advances in Preference Handling; Semantic Cities — Beyond Open Data to Models, Standards and Reasoning; Sequential Decision Making with Big Data; Statistical Relational AI; and The World Wide Web and Public Health Intelligence. This article presents short summaries of those events.

We consider the problem of, given a probabilistic model on a set of random variables, how to add a new variable that depends on the other variables, without changing the original distribution. In particular, we consider relational models (such as Markov logic networks (MLNs)), where we cannot directly define conditional probabilities. In relational models, there may be an unbounded number of parents in the grounding, and conditional distributions need to be defined in terms of aggregators. The question we ask is whether and when it is possible to represent conditional probabilities at all in various relational models. Some aggregators have been shown to be representable by MLNs, by adding auxiliary variables; however it was unknown whether they could be defined without auxiliary variables. For other aggregators, it was not known whether they can be represented by MLNs at all. We obtained surprisingly strong negative results on the capability of flexible undirected relational models such as MLNs to represent aggregators without affecting the original model's distribution. We provide a map of what aspects of the models, including the use of auxiliary variables and quantifiers, result in the ability to represent various aggregators. In addition, we provide proof techniques which can be used to facilitate future theoretic results on relational models, and demonstrate them on relational logistic regression (RLR).

Relational logistic regression (RLR) was presented at the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR-2014). RLR is the directed analogue of Markov logic networks. Whereas Markov logic networks define distributions in terms of weighted formulae, RLR defines conditional probabilities in terms of weighted formulae. They agree for the supervised learning case when all variables except a query leaf variable are observed. However, they are quite different in representing distributions. The KR-2014 paper defined the RLR formalism, defined canonical forms for RLR in terms of positive conjunctive formulae, indicated the class of conditional probability distributions that can and cannot be represented by RLR, and defined many other aggregators in terms of RLR. In this paper, we summarize these results and compare RLR to Markov logic networks.

Various representations and inference methods have been proposed for lifted probabilistic inference in relational models. Many of these methods choose an order to eliminate (or branch on) the parameterized random variables. Similar to such methods for non-relational probabilistic inference, the order of elimination has a significant role in the performance of the algorithms. Since finding the best order is NP-complete even for non-relational models, heuristics have been proposed to find good orderings in the non-relational models. In this paper, we show that these heuristics are inefficient for relational models, because they fail to consider the population sizes associated with logical variables. We extend existing heuristics for non-relational models and propose new heuristics for relational models. We evaluate the existing and new heuristics on a range of generated relational graphs.