We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time and polynomial number of samples, assuming that the data is generated by a network in this class. This result covers both parameter estimation for a known network structure and structure learning. It implies as a corollary that we can learn factor graphs for both Bayesian networks and Markov networks of bounded degree, in polynomial time and sample complexity. Unlike maximum likelihood estimation, our method does not require inference in the underlying network, and so applies to networks where inference is intractable. We also show that the error of our learned model degrades gracefully when the generating distribution is not a member of the target class of networks.

A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for variances of other variables and many nonlinear models. The underlying variational Bayesian machinery, providing for fast and robust estimation but being mathematically rather involved, is almost completely hidden from the user thus making it very easy to use the library. The building blocks include Gaussian, rectified Gaussian and mixture-of-Gaussians variables and computational nodes which can be combined rather freely.

We propose a new problem formulation which is similar to, but more informative than, the binary multiple-instance learning problem. In this setting, we are given groups of instances (described by feature vectors) along with estimates of the fraction of positively-labeled instances per group. The task is to learn an instance level classifier from this information. That is, we are trying to estimate the unknown binary labels of individuals from knowledge of group statistics. We propose a principled probabilistic model to solve this problem that accounts for uncertainty in the parameters and in the unknown individual labels. This model is trained with an efficient MCMC algorithm. Its performance is demonstrated on both synthetic and real-world data arising in general object recognition.

We introduce a novel latent grouping model for predicting the relevance of a new document to a user. The model assumes a latent group structure for both users and documents. We compared the model against a state-of-the-art method, the User Rating Profile model, where only users have a latent group structure. We estimate both models by Gibbs sampling. The new method predicts relevance more accurately for new documents that have few known ratings. The reason is that generalization over documents then becomes necessary and hence the twoway grouping is profitable.

We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as well. We show how the various signs translate into order constraints on the network parameters and how isotonic regression can be used to compute order-constrained estimates from the available data. Our experimental results show that taking prior knowledge about the signs of influences into account leads to an improved fit of the true distribution, especially when only a small sample of data is available. Moreover, the computed estimates are guaranteed to be consistent with the specified signs, thereby resulting in a network that is more likely to be accepted by experts in its domain of application.

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.

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.

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.