This is the Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, which was held in Bellevue, WA, August 11-15, 2013

This is the Proceedings of the First Conference on Uncertainty in Artificial Intelligence, which was held in Los Angeles, CA, July 10-12, 1985

Many applications in translational medicine require the understanding of how diseases progress through the accumulation of persistent events. Specialized Bayesian networks called monotonic progression networks offer a statistical framework for modeling this sort of phenomenon. Current machine learning tools to reconstruct Bayesian networks from data are powerful but not suited to progression models. We combine the technological advances in machine learning with a rigorous philosophical theory of causation to produce Polaris, a scalable algorithm for learning progression networks that accounts for causal or biological noise as well as logical relations among genetic events, making the resulting models easy to interpret qualitatively. We tested Polaris on synthetically generated data and showed that it outperforms a widely used machine learning algorithm and approaches the performance of the competing special-purpose, albeit clairvoyant algorithm that is given a priori information about the model parameters. We also prove that under certain rather mild conditions, Polaris is guaranteed to converge for sufficiently large sample sizes. Finally, we applied Polaris to point mutation and copy number variation data in Prostate cancer from The Cancer Genome Atlas (TCGA) and found that there are likely three distinct progressions, one major androgen driven progression, one major non-androgen driven progression, and one novel minor androgen driven progression.

In group decision making (GDM) problems fuzzy preference relations (FPR) are widely used for representing decision makers' opinions on the set of alternatives. In order to avoid misleading solutions, the study of consistency and consensus has become a very important aspect. This article presents a simulated annealing (SA) based soft computing approach to optimize the consistency/consensus level (CCL) of a complete fuzzy preference relation in order to solve a GDM problem. Consistency level indicates as expert's preference quality and consensus level measures the degree of agreement among experts' opinions. This study also suggests the set of experts for the necessary modifications in their prescribed preference structures without intervention of any moderator.

A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is minimized through the hierarchical design. The method is further extended to joint modeling of continuous measurements and survival events. The baseline hazard, covariate and joint effects are conveniently modeled in this hierarchical structure. The estimation and inference are implemented in fully Bayesian framework using the objective and shrinkage priors. In simulation studies, this model shows robustness in latent estimation, correlation detection and high accuracy in forecasting. The model is illustrated with medical monitoring data from cystic fibrosis (CF) patients. Estimation and forecasts are obtained in the measurement of lung function and records of acute respiratory events. Keyword: Extrapolation, Joint Model, Longitudinal Model, Hierarchical Gaussian Process, Cystic Fibrosis, Medical Monitoring

We consider the problem of maximizing a real-valued continuous function $f$ using a Bayesian approach. Since the early work of Jonas Mockus and Antanas \v{Z}ilinskas in the 70's, the problem of optimization is usually formulated by considering the loss function $\max f - M_n$ (where $M_n$ denotes the best function value observed after $n$ evaluations of $f$). This loss function puts emphasis on the value of the maximum, at the expense of the location of the maximizer. In the special case of a one-step Bayes-optimal strategy, it leads to the classical Expected Improvement (EI) sampling criterion. This is a special case of a Stepwise Uncertainty Reduction (SUR) strategy, where the risk associated to a certain uncertainty measure (here, the expected loss) on the quantity of interest is minimized at each step of the algorithm. In this article, assuming that $f$ is defined over a measure space $(\mathbb{X}, \lambda)$, we propose to consider instead the integral loss function $\int_{\mathbb{X}} (f - M_n)_{+}\, d\lambda$, and we show that this leads, in the case of a Gaussian process prior, to a new numerically tractable sampling criterion that we call $\rm EI^2$ (for Expected Integrated Expected Improvement). A numerical experiment illustrates that a SUR strategy based on this new sampling criterion reduces the error on both the value and the location of the maximizer faster than the EI-based strategy.

In the big data era, scalability has become a crucial requirement for any useful computational model. Probabilistic graphical models are very useful for mining and discovering data insights, but they are not scalable enough to be suitable for big data problems. Bayesian Networks particularly demonstrate this limitation when their data is represented using few random variables while each random variable has a massive set of values. With hierarchical data - data that is arranged in a treelike structure with several levels - one would expect to see hundreds of thousands or millions of values distributed over even just a small number of levels. When modeling this kind of hierarchical data across large data sets, Bayesian networks become infeasible for representing the probability distributions for the following reasons: i) Each level represents a single random variable with hundreds of thousands of values, ii) The number of levels is usually small, so there are also few random variables, and iii) The structure of the network is predefined since the dependency is modeled top-down from each parent to each of its child nodes, so the network would contain a single linear path for the random variables from each parent to each child node. In this paper we present a scalable probabilistic graphical model to overcome these limitations for massive hierarchical data. We believe the proposed model will lead to an easily-scalable, more readable, and expressive implementation for problems that require probabilistic-based solutions for massive amounts of hierarchical data. We successfully applied this model to solve two different challenging probabilistic-based problems on massive hierarchical data sets for different domains, namely, bioinformatics and latent semantic discovery over search logs.

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in LBP's for Potts models influence our hyperparameter estimation procedures.

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a near optimal rate is achieved without any strong convexity of the observation. Moreover, we show that the method has adaptivity to the unknown rank of the true tensor, that is, the near optimal rate depending on the true rank is achieved even if it is not known a priori.

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate inference based on message-passing algorithms, on the other hand, can lead to unstable and biased estimation in loopy graphical models. In this paper, we propose a general framework for distributed estimation based on a maximum marginal likelihood (MML) approach. This approach computes local parameter estimates by maximizing marginal likelihoods defined with respect to data collected from local neighborhoods. Due to the non-convexity of the MML problem, we introduce and solve a convex relaxation. The local estimates are then combined into a global estimate without the need for iterative message-passing between neighborhoods. The proposed algorithm is naturally parallelizable and computationally efficient, thereby making it suitable for high-dimensional problems. In the classical regime where the number of variables $p$ is fixed and the number of samples $T$ increases to infinity, the proposed estimator is shown to be asymptotically consistent and to improve monotonically as the local neighborhood size increases. In the high-dimensional scaling regime where both $p$ and $T$ increase to infinity, the convergence rate to the true parameters is derived and is seen to be comparable to centralized maximum likelihood estimation. Extensive numerical experiments demonstrate the improved performance of the two-hop version of the proposed estimator, which suffices to almost close the gap to the centralized maximum likelihood estimator at a reduced computational cost.