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.

Lifting can greatly reduce the cost of inference on first-order probabilistic graphical models, but constructing the lifted network can itself be quite costly. In online applications (e.g., video segmentation) repeatedly constructing the lifted network for each new inference can be extremely wasteful, because the evidence typically changes little from one inference to the next. The same is true in many other problems that require repeated inference, like utility maximization, MAP inference, interactive inference, parameter and structure learning, etc. In this paper, we propose an efficient algorithm for updating the structure of an existing lifted network with incremental changes to the evidence. This allows us to construct the lifted network once for the initial inference problem, and amortize the cost over the subsequent problems. Experiments on video segmentation and viral marketing problems show that the algorithm greatly reduces the cost of inference without affecting the quality of the solutions.

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.

Mini-Bucket Elimination (MBE) is a well-known approximation algorithm deriving lower and upper bounds on quantities of interest over graphical models. It relies on a procedure that partitions a set of functions, called bucket, into smaller subsets, called mini-buckets. The method has been used with a single partitioning heuristic throughout, so the impact of the partitioning algorithm on the quality of the generated bound has never been investigated. This paper addresses this issue by presenting a framework within which partitioning strategies can be described, analyzed and compared. We derive a new class of partitioning heuristics from first-principles geared for likelihood queries, demonstrate their impact on a number of benchmarks for probabilistic reasoning and show that the results are competitive (often superior) to state-of-the-art bounding schemes.

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.

Different solvers for computationally difficult problems such as satisfiability (SAT) perform best on different instances. Algorithm portfolios exploit this phenomenon by predicting solvers' performance on specific problem instances, then shifting computational resources to the solvers that appear best suited. This paper develops a new approach to the problem of making such performance predictions: natural generative models of solver behavior. Two are proposed, both following from an assumption that problem instances cluster into latent classes: a mixture of multinomial distributions, and a mixture of Dirichlet compound multinomial distributions. The latter model extends the former to capture burstiness, the tendency of solver outcomes to recur. These models are integrated into an algorithm portfolio architecture and used to run standard SAT solvers on competition benchmarks. This approach is found competitive with the most prominent existing portfolio, SATzilla, which relies on domain-specific, hand-selected problem features; the latent class models, in contrast, use minimal domain knowledge. Their success suggests that these models can lead to more powerful and more general algorithm portfolio methods.

This paper presents the Topic-Aspect Model (TAM), a Bayesian mixture model which jointly discovers topics and aspects. We broadly define an aspect of a document as a characteristic that spans the document, such as an underlying theme or perspective. Unlike previous models which cluster words by topic or aspect, our model can generate token assignments in both of these dimensions, rather than assuming words come from only one of two orthogonal models. We present two applications of the model. First, we model a corpus of computational linguistics abstracts, and find that the scientific topics identified in the data tend to include both a computational aspect and a linguistic aspect. For example, the computational aspect of GRAMMAR emphasizes parsing, whereas the linguistic aspect focuses on formal languages. Secondly, we show that the model can capture different viewpoints on a variety of topics in a corpus of editorials about the Israeli-Palestinian conflict. We show both qualitative and quantitative improvements in TAM over two other state-of-the-art topic models.

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.