One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill-climbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easy-to-implement method for addressing this task. Our approach is based on the well-known fact that the best network (of bounded in-degree) consistent with a given node ordering can be found very efficiently. We therefore propose a search not over the space of structures, but over the space of orderings, selecting for each ordering the best network consistent with it. This search space is much smaller, makes more global search steps, has a lower branching factor, and avoids costly acyclicity checks. We present results for this algorithm on both synthetic and real data sets, evaluating both the score of the network found and in the running time. We show that ordering-based search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement.

Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three calibration methods for correcting this distortion: Platt Scaling, Isotonic Regression, and Logistic Correction. We also experiment with boosting using log-loss instead of the usual exponential loss. Experiments show that Logistic Correction and boosting with log-loss work well when boosting weak models such as decision stumps, but yield poor performance when boosting more complex models such as full decision trees. Platt Scaling and Isotonic Regression, however, significantly improve the probabilities predicted by

When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e.g., Clark & Matwin's work with the CN2 rule learning algorithm). We show how to interpret knowledge of qualitative influences, and in particular of monotonicities, as constraints on probability distributions, and to incorporate this knowledge into Bayesian network learning algorithms. We show that this yields improved accuracy, particularly with very small training sets (e.g. less than 10 examples).

We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed models such as LDA for similar tasks, but bears significant difference in inference/learning cost tradeoffs, latent topic representations, and topic mixing mechanisms. In particular, our model facilitates efficient inference and robust topic mixing, and potentially provides high flexibilities in modeling the latent topic spaces. A contrastive divergence and a variational algorithm are derived for learning. We specialized our model to a dual-wing harmonium for captioned images, incorporating a multivariate Poisson for word-counts and a multivariate Gaussian for color histogram. We present empirical results on the applications of this model to classification, retrieval and image annotation on news video collections, and we report an extensive comparison with various extant models.

In this paper, we present an algorithm for minimizing the difference between two submodular functions using a variational framework which is based on (an extension of) the concave-convex procedure [17]. Because several commonly used metrics in machine learning, like mutual information and conditional mutual information, are submodular, the problem of minimizing the difference of two submodular problems arises naturally in many machine learning applications. Two such applications are learning discriminatively structured graphical models and feature selection under computational complexity constraints. A commonly used metric for measuring discriminative capacity is the EAR measure which is the difference between two conditional mutual information terms. Feature selection taking complexity considerations into account also fall into this framework because both the information that a set of features provide and the cost of computing and using the features can be modeled as submodular functions. This problem is NP-hard, and we give a polynomial time heuristic for it. We also present results on synthetic data to show that classifiers based on discriminative graphical models using this algorithm can significantly outperform classifiers based on generative graphical models.

We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that does not depend on the states of POMDP. This function is the conditional mean of the true value function that depends on the states. We show that the critic can be implemented using temporal difference (TD) methods with linear function approximations, and the analytical results on TD and Actor-Critic can be transfered to this case. Although Actor-Critic algorithms have been used extensively in Markov decision processes (MDP), up to now they have not been proposed for POMDP as an alternative to the earlier proposal GPOMDP algorithm, an actor-only method. Furthermore, we show that the same idea applies to semi-Markov problems with a subset of finite-state controllers.

This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesian-minded method that employs the Imprecise Dirichlet Model to generate set-valued estimates.

Markov Decision Processes (MDPs) are widely popular in Artificial Intelligence for modeling sequential decision-making scenarios with probabilistic dynamics. They are the framework of choice when designing an intelligent agent that needs to act for long periods of time in an environment where its actions could have uncertain outcomes. MDPs are actively researched in two related subareas of AI, probabilistic planning and reinforcement learning. Probabilistic planning assumes known models for the agent's goals and domain dynamics, and focuses on determining how the agent should behave to achieve its objectives. On the other hand, reinforcement learning additionally learns these models based on the feedback the agent gets from the environment.

In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by "surrogate models" such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the Expected Improvement criterion (Jones et al. 1998), we show that this ensemble is particularly effective when the simulator is ill-behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application.

We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimating the mixture components, and our output is a tree-mixture model which serves as a good approximation to the underlying graphical model mixture. Our method is efficient when the union graph, which is the union of the Markov graphs of the mixture components, has sparse vertex separators between any pair of observed variables. This includes tree mixtures and mixtures of bounded degree graphs. For such models, we prove that our method correctly recovers the union graph structure and the tree structures corresponding to maximum-likelihood tree approximations of the mixture components. The sample and computational complexities of our method scale as $\poly(p, r)$, for an $r$-component mixture of $p$-variate graphical models. We further extend our results to the case when the union graph has sparse local separators between any pair of observed variables, such as mixtures of locally tree-like graphs, and the mixture components are in the regime of correlation decay.