Recently, Brafman and Engel (2009) proposed new concepts of marginal and conditional utility that obey additive analogues of the chain rule and Bayes rule, which they employed to obtain a directed graphical model of utility functions that resembles Bayes nets. In this paper we carry this analogy a step farther by showing that the notion of utility independence, built on conditional utility, satisfies identical properties to those of probabilistic independence. This allows us to formalize the construction of graphical models for utility functions, directed and undirected, and place them on the firm foundations of Pearl and Paz's axioms of semi-graphoids. With this strong equivalence in place, we show how algorithms used for probabilistic reasoning such as Belief Propagation (Pearl 1988) can be replicated to reasoning about utilities with the same formal guarantees, and open the way to the adaptation of additional algorithms.

There have been many efforts to identify causal graphical features such as directed edges between random variables from observational data. Recently, Tian et al. proposed a new dynamic programming algorithm which computes marginalized posterior probabilities of directed edge features over all the possible structures in O( n 3 n ) time when the number of parents per node is bounded by a constant, where n is the number of variables of interest. However the main drawback of this approach is that deciding a single appropriate threshold for the existence of the directed edge feature is difficult due to the scale difference of the posterior probabilities between the directed edges forming v- structures and the directed edges not forming v -structures. We claim that computing posterior probabilities of both adjacencies and v -structures is necessary and more effective for discovering causal graphical features, since it allows us to find a single appropriate decision threshold for the existence of the feature that we are testing. For efficient computation, we provide a novel dynamic programming algorithm which computes the posterior probabilities of all of n ( n – 1)/2 adjacency and n ( n –1 choose 2) v -structure features in O( n 3 * 3 n ) time.

We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied by Conitzer, Rognlie, and Xia, and the distance rationalizability (DR) framework of Elkind, Faliszewski, and Slinko. The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.

We introduce a new discriminative piecewise linear model for classification. A two-step method is developed to construct the model. In the first step, we sample some boundary points that lie between positive and negative data, as well as corresponding directions from negative data to positive data. The sampling result gives a discriminative nonparametric decision surface, which preserves enough information to correctly classify all training data. To simplify this surface, in the second step we propose a nonparametric approach for linear surface segmentation using Dirichlet process mixtures. The final result is a piecewise linear model, in which the number of linear surface pieces is automatically determined by the Bayesian inference according to data. Experiments on both synthetic and real data verify the effectiveness of the proposed model.

We consider the task of assigning experts from a portfolio of specialists in order to solve a set of tasks. We apply a Bayesian model which combines collaborative filtering with a feature-based description of tasks and experts to yield a general framework for managing a portfolio of experts. The model learns an embedding of tasks and problems into a latent space in which affinity is measured by the inner product. The model can be trained incrementally and can track non-stationary data, tracking potentially changing expert and task characteristics. The approach allows us to use a principled decision theoretic framework for expert selection, allowing the user to choose a utility function that best suits their objectives. The model component for taking into account the performance feedback data is pluggable, allowing flexibility. We apply the model to manage a portfolio of algorithms to solve hard combinatorial problems. This is a well studied area and we demonstrate a large improvement on the state of the art in one domain (constraint solving) and in a second domain (combinatorial auctions) created a portfolio that performed significantly better than any single algorithm.

In Service-Oriented Computing (SOC) environments, the trustworthiness of each service is critical for a service client when selecting one from a large pool of services. The trust value of a service is usually in the range of [0,1] and is evaluated from the ratings given by service clients, which represent the subjective belief of these service clients on the satisfaction of delivered services. So a trust value can be taken as the subjective probability, with which one party believes that another party can perform an action in a certain situation. Hence, subjective probability theory should be adopted in trust evaluation. In addition, in SOC environments, a service usually invokes other services offered by different service providers forming a composite service. Thus, the global trust of a composite service should be evaluated based on complex invocation structures. In this paper, firstly, based on Bayesian inference, we propose a novel method to evaluate the subjective trustworthiness of a service component from a series of ratings given by service clients. Secondly, we interpret the trust dependency caused by service invocations as conditional probability, which is evaluated based on the subjective trust values of service components. Furthermore, we propose a joint subjective probability method to evaluate the subjective global trust of a composite service on the basis of trust dependency. Finally, we introduce the results of our conducted experiments to illustrate the properties of our proposed subjective global trust inference method.

Methods for discovering causal knowledge from observational data have been a persistent topic of AI research for several decades. Essentially all of this work focuses on knowledge representations for propositional domains. In this paper, we present several key algorithmic and theoretical innovations that extend causal discovery to relational domains. We provide strong evidence that effective learning of causal models is enhanced by relational representations. We present an algorithm, relational PC, that learns causal dependencies in a state-of-the-art relational representation, and we identify the key representational and algorithmic innovations that make the algorithm possible. Finally, we prove the algorithm's theoretical correctness and demonstrate its effectiveness on synthetic and real data sets.

Bayesian inference is an appealing approach for leveraging prior knowledge in reinforcement learning (RL). In this paper we describe an algorithm for discovering different classes of roles for agents via Bayesian inference. In particular, we develop a Bayesian policy search approach for Multi-Agent RL (MARL), which is model-free and allows for priors on policy parameters. We present a novel optimization algorithm based on hybrid MCMC, which leverages both the prior and gradient information estimated from trajectories. Our experiments in a complex real-time strategy game demonstrate the effective discovery of roles from supervised trajectories, the use of discovered roles for successful transfer to similar tasks, and the discovery of roles through reinforcement learning.

We present a method for unsupervised learning of event classes from videos in which multiple actions might occur simultaneously. It is assumed that all such activities are produced from an underlying set of event class generators. The learning task is then to recover this generative process from visual data. A set of event classes is derived from the most likely decomposition of the tracks into a set of labelled events involving subsets of interacting tracks. Interactions between subsets of tracks are modelled as a relational graph structure that captures qualitative spatio-temporal relationships between these tracks. The posterior probability of candidate solutions favours decompositions in which events of the same class have a similar relational structure, together with other measures of well-formedness. A Markov Chain Monte Carlo (MCMC) procedure is used to efficiently search for the MAP solution. This search moves between possible decompositions of the tracks into sets of unlabelled events and at each move adds a close to optimal labelling (for this decomposition) using spectral clustering. Experiments on real data show that the discovered event classes are often semantically meaningful and correspond well with groundtruth event classes assigned by hand.

Constructing models of mobile agents can be difficult without domain-specific knowledge. Parametric models flexible enough to capture all mobility patterns that an expert believes are possible are often large, requiring a great deal of training data. In contrast, nonparametric models are extremely flexible and can generalize well with relatively little training data. We propose modeling the mobility patterns of moving agents as a mixture of Gaussian processes (GP) with a Dirichlet process (DP) prior over mixture weights. The GP provides a flexible representation for each individual mobility pattern, while the DP assigns observed trajectories to particular mobility patterns. Both the GPs and the DP adjust the model's complexity based on available data, implicitly avoiding issues of over-fitting or under-fitting. We apply our model to a helicopter-based tracking task, where the mobility patterns of the tracked agents — cars — are learned from real data collected from taxis in the greater Boston area.