This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs). A MOMDP is an extension of the MDP model for planning under uncertainty while trying to optimize several reward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicriteria problems when rewards refer to different features. In this setting, we study the determination of policies leading to Lorenz-non-dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was introduced in Social Choice for the measurement of inequalities. In this paper, we introduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs. The approximations are polynomial-sized subsets of those solutions.

We consider the problem of building relational probabilistic models with an underlying ontology that defines the classes and properties used in the model. Properties in the ontology form random variables when applied to individuals. When an individual is not in the domain of a property, the corresponding random variable is undefined. If we are uncertain about the types of individuals, we may be uncertain about whether random variables are defined. We discuss how to extend a recent result on reasoning with potentially undefined random variables to the relational case. Object properties may have classes of individuals as their ranges, giving rise to random variables whose ranges vary with populations. We identify and discuss some of the issues that arise when constructing relational probabilistic models using the vocabulary and constraints from an ontology, and we outline possible solutions to certain problems.

In this paper, we investigate the problem of predicting people's professions under social context. Previous work considering clothing information as well as fore/background context preliminarily proves the feasibility of predicting professions. In this paper, we discuss this problem in a more general case --- multiple people in one photo with arbitrary poses, and argue that with appropriately built partial body features, spatial relations, and background context, more appealing results are achieved by a probabilistic model. We conduct experiments on $14$ representative professions with over $7000$ images, and demonstrate the model's superiority with impressive results.

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities, because the evidence breaks many of the model's symmetries.Recent theoretical results paint a grim picture, showing that conditioning on binary relations is #P-hard, and in the worst case, no lifting can be expected. In this paper, we identify Boolean rank of the evidence as a key parameter in the complexity of conditioning. We contrast the hardness result by showing that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization that maintains the model's symmetries and admits efficient lifted inference.

Opponents are characterized by a Bayesian network intended to guide Monte-Carlo Tree Search through the game tree of No-Limit Texas Hold'em Poker. By using a probabilistic model of opponents, the network is able to integrate all available sources of information, including the infrequent revelations of hidden beliefs. These revelations are biased, and as such are difficult to incorporate into action prediction. The proposed network mitigates this bias via the expectation maximization algorithm and a probabilistic characterization of the hidden variables that generate observations. 

A central goal of AI is to reason efficiently in domains that are both complex and uncertain. Most attempts toward this end add probability to a tractable subset of first-order logic, but this results in intractable inference. To address this, Domingos and Webb (2012) introduced tractable Markov logic (TML), the first tractable first-order probabilistic representation. Despite its surprising expressiveness, TML has a number ofsignificant limitations. Chief among these is that it does not explicitly handle existence uncertainty, meaning that all possible worlds contain the same objects and relations. This leads to a number of conceptual problems, such as models that must contain meaningless combinations of attributes (e.g.,horses with wheels). Here we propose a new formalism, tractable probabilistic knowledge bases (TPKBs), that overcomes this problem. Like TML, TPKBs use probabilistic class and part hierarchies to ensure tractability, but TPKBs have a much cleaner and user-friendly object-oriented syntax and a well-founded semantics for existence uncertainty. TML is greatly complicated by the use of probabilistic theorem proving, an inference procedure that is much more powerful than necessary. In contrast, we introduce an inference procedure specifically designed for TPKBs, which makes them far more transparent and amenable to analysis and implementation. TPKBs subsume TML and therefore essentially all tractable models, including many high-treewidth ones.

Statistical relational learning (SRL) augments probabilistic models with relational representations and facilitates reasoning over sets of objects. When learning the probabilistic parameters for SRL models, however, one often resorts to reasoning over individual objects. To address this challenge, we compile a Markov logic network into a compact and efficient first-order data structure and use weighted first-order model counting to exactly optimize the likelihood of the parameters in a lifted manner. By exploiting the relational structure in the model, it is possible to learn more accurate parameters and dramatically improve the run time of the likelihood calculation. This allows us to calculate the exact likelihood for models where previously only approximate inference was feasible. Results on real-world data sets show that this approach learns more accurate models.

This paper aims at providing a preliminary discussion on how to deal with spatio-temporal information in the context of behaviour recognition. It draws comparison with how humans reason in other areas, such as law, and discusses some of the pros and cons of formalisms for handling uncertainty, starting with probability theory, continuing with the Dempster-Shafer theory, and concluding with fuzzy logic.

Recent years have witnessed the tremendous development of social media, which attracts a vast number of Internet users. The high-dimension content generated by these users provides an unique opportunity to understand their behavior deeply. As one of the most fundamental topics, location estimation attracts more and more research efforts. Different from the previous literature, we find that user's location is strongly related to user interest. Based on this, we first build a detection model to mine user interest from short text. We then establish the mapping between location function and user interest before presenting an efficient framework to predict the user's location with convincing fidelity. Thorough evaluations and comparisons on an authentic data set show that our proposed model significantly outperforms the state-of-the-arts approaches. Moreover, the high efficiency of our model also guarantees its applicability in real-world scenarios.

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.