In this paper, we present an efficient way of performing stepwise selection in the class of decomposable models. The main contribution of the paper is a simple characterization of the edges that canbe added to a decomposable model while keeping the resulting model decomposable and an efficient algorithm for enumerating all such edges for a given model in essentially O(1) time per edge. We also discuss how backward selection can be performed efficiently using our data structures.We also analyze the complexity of the complete stepwise selection procedure, including the complexity of choosing which of the eligible dges to add to (or delete from) the current model, with the aim ofminimizing the Kullback-Leibler distance of the resulting model from the saturated model for the data.

DAG models with hidden variables present many difficulties that are absent when all nodes are observed. In particular, fully observed DAG models are identified and correspond to well-defined sets of distributions, whereas this is not true if nodes are unobserved. In this paper we characterize exactly the set of distributions given by a class of Gaussian models with one-dimensional latent variables. These models relate two blocks of observed variables, modeling only the crosscovariance matrix. We describe the relation of this model to the singular value decomposition of the cross-covariance matrix. We show that, although the model is underidentified, useful information may be extracted. We further consider an alternative parameterization in which one latent variable is associated with each block. Our analysis leads to some novel covariance equivalence results for Gaussian hidden variable models.

It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than with respect to the standard marginal likelihood criterion. However, for most Bayesian network models, computing the supervised marginal likelihood score takes exponential time with respect to the amount of observed data. In this paper, we consider diagnostic Bayesian network classifiers where the significant model parameters represent conditional distributions for the class variable, given the values of the predictor variables, in which case the supervised marginal likelihood can be computed in linear time with respect to the data. As the number of model parameters grows in this case exponentially with respect to the number of predictors, we focus on simple diagnostic models where the number of relevant predictors is small, and suggest two approaches for applying this type of models in classification. The first approach is based on mixtures of simple diagnostic models, while in the second approach we apply the small predictor sets of the simple diagnostic models for augmenting the Naive Bayes classifier.

Some high-dimensional data.sets can be modelled by assuming that there are many different linear constraints, each of which is Frequently Approximately Satisfied (FAS) by the data. The probability of a data vector under the model is then proportional to the product of the probabilities of its constraint violations. We describe three methods of learning products of constraints using a heavy-tailed probability distribution for the violations.

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features of the data. We solve this problem by introducing more sophisticated MCMC algorithms. One of these algorithms is a mixture of two MCMC kernels: a random walk Metropolis kernel and a blockMetropolis-Hastings (MH) kernel with a variational approximation as proposaldistribution. The MH kernel allows one to locate regions of high probability efficiently. The Metropolis kernel allows us to explore the vicinity of these regions. This algorithm outperforms variationalapproximations because it yields slightly better estimates of the mean and considerably better estimates of higher moments, such as covariances. It also outperforms standard MCMC algorithms because it locates theregions of high probability quickly, thus speeding up convergence. We demonstrate this algorithm on the problem of Bayesian parameter estimation for logistic (sigmoid) belief networks.

This paper investigates domain generalization: How to take knowledge acquired from an arbitrary number of related domains and apply it to previously unseen domains? We propose Domain-Invariant Component Analysis (DICA), a kernel-based optimization algorithm that learns an invariant transformation by minimizing the dissimilarity across domains, whilst preserving the functional relationship between input and output variables. A learning-theoretic analysis shows that reducing dissimilarity improves the expected generalization ability of classifiers on new domains, motivating the proposed algorithm. Experimental results on synthetic and real-world datasets demonstrate that DICA successfully learns invariant features and improves classifier performance in practice.

Cascade classifiers are widely used in real-time object detection. Different from conventional classifiers that are designed for a low overall classification error rate, a classifier in each node of the cascade is required to achieve an extremely high detection rate and moderate false positive rate. Although there are a few reported methods addressing this requirement in the context of object detection, there is no principled feature selection method that explicitly takes into account this asymmetric node learning objective. We provide such an algorithm here. We show that a special case of the biased minimax probability machine has the same formulation as the linear asymmetric classifier (LAC) of Wu et al (2005). We then design a new boosting algorithm that directly optimizes the cost function of LAC. The resulting totally-corrective boosting algorithm is implemented by the column generation technique in convex optimization. Experimental results on object detection verify the effectiveness of the proposed boosting algorithm as a node classifier in cascade object detection, and show performance better than that of the current state-of-the-art.

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.

Efficient planning plays a crucial role in model-based reinforcement learning. Traditionally, the main planning operation is a full backup based on the current estimates of the successor states. Consequently, its computation time is proportional to the number of successor states. In this paper, we introduce a new planning backup that uses only the current value of a single successor state and has a computation time independent of the number of successor states. This new backup, which we call a small backup, opens the door to a new class of model-based reinforcement learning methods that exhibit much finer control over their planning process than traditional methods. We empirically demonstrate that this increased flexibility allows for more efficient planning by showing that an implementation of prioritized sweeping based on small backups achieves a substantial performance improvement over classical implementations.

We treat collaborative filtering as a univariate time series problem: given a user's previous votes, predict the next vote. We describe two families of methods for transforming data to encode time order in ways amenable to off-the-shelf classification and density estimation tools. Using a decision-tree learning tool and two real-world data sets, we compare the results of these approaches to the results of collaborative filtering without ordering information. The improvements in both predictive accuracy and in recommendation quality that we realize advocate the use of predictive algorithms exploiting the temporal order of data.