Retrieval tasks typically require a ranking of items given a query. Collaborative filtering tasks, on the other hand, learn to model user's preferences over items. In this paper we study the joint problem of recommending items to a user with respect to a given query, which is a surprisingly common task. This setup differs from the standard collaborative filtering one in that we are given a query x user x item tensor for training instead of the more traditional user x item matrix. Compared to document retrieval we do have a query, but we may or may not have content features (we will consider both cases) and we can also take account of the user's profile. We introduce a factorized model for this new task that optimizes the top-ranked items returned for the given query and user. We report empirical results where it outperforms several baselines.

Binary linear classification operates as follows: obtain a new instance, determine a set of real-valued features, form their weighted combination, and output a label which is positive iff this combination is nonnegative. The interpretability, empirical performance, and theoretical depth of this scheme have all contributed to its continued popularity (Freund and Schapire, 1997, Friedman et al., 2000, Caruana and Niculescu-Mizil, 2006). In order to obtain the coefficients in the above weighting, convex optimization is typically employed. Specifically, rather than just trying to pick the weighting which makes the fewest mistakes over a finite sample -- which is computationally intractable -- consider instead paying attention to the amount by which these combinations clear the zero threshold, a quantity called the margin. Applying a convex penalty to these margins yields a convex optimization procedure, specifically one which can be specialized into both logistic regression and AdaBoost.

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients. The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinatedescent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.

This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Shift nonparametric clustering algorithm. The experiments highlight the properties of the new model and demonstrate that infinite models can be simple, elegant and practical.

Exemplar-based clustering methods have been shown to produce state-of-the-art results on a number of synthetic and real-world clustering problems. They are appealing because they offer computational benefits over latent-mean models and can handle arbitrary pairwise similarity measures between data points. However, when trying to recover underlying structure in clustering problems, tailored similarity measures are often not enough; we also desire control over the distribution of cluster sizes. Priors such as Dirichlet process priors allow the number of clusters to be unspecified while expressing priors over data partitions. To our knowledge, they have not been applied to exemplar-based models. We show how to incorporate priors, including Dirichlet process priors, into the recently introduced affinity propagation algorithm. We develop an efficient maxproduct belief propagation algorithm for our new model and demonstrate experimentally how the expanded range of clustering priors allows us to better recover true clusterings in situations where we have some information about the generating process.

Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for applications based on subject matter. Drawing on ideas from graphical models and phylogenetics, we describe a non-exchangeable prior for a class of nonparametric latent feature models that is nearly as efficient computationally as its exchangeable counterpart. Our model is applicable to the general setting in which the dependencies between objects can be expressed using a tree, where edge lengths indicate the strength of relationships. We demonstrate an application to modeling probabilistic choice.

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang 2006]. Alternatively, one might bootstrap the resampled estimator of the generalization error to form a confidence set. Unfortunately, these methods do not reliably provide sets of the desired confidence. The poor performance appears to be due to the lack of smoothness of the generalization error as a function of the learned classifier. This results in a non-normal distribution of the estimated generalization error. We construct a confidence set for the generalization error by use of a smooth upper bound on the deviation between the resampled estimate and generalization error. The confidence set is formed by bootstrapping this upper bound. In cases in which the approximation class for the classifier can be represented as a parametric additive model, we provide a computationally efficient algorithm. This method exhibits superior performance across a series of test and simulated data sets.

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inference. The latent likelihood of the data and its gradients are computable in closed form via Tutte's directed matrix tree theorem using determinants and inverses of the out-Laplacian. This novel likelihood subsumes iid likelihood, is exchangeable and yields efficient unsupervised and semi-supervised learning algorithms. In addition to handling taxonomy and phylogenetic datasets the out-tree assumption performs surprisingly well as a semi-parametric density estimator on standard iid datasets. Experiments with unsupervised and semisupervised learning are shown on various UCI and taxonomy datasets.

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning - maximizing entropy with moment matching constraints - and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piecewise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.

We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small sub-problems. The challenge in variable decomposition algorithms is the identification of a subproblem (the active set of variables) that yields the largest improvement. We analyze the limitations of existing methods and cast the active set selection into a zero-norm constrained optimization problem that we solve using greedy methods. By directly estimating the decrease in the objective function, we obtain not only efficient approximate solutions for GBCD, but we are also able to demonstrate that the method is globally convergent. Empirical comparisons against competing dense methods like Conjugate Gradient or SMO show that GBCD is an order of magnitude faster. Comparisons against sparse GP methods show that GBCD is both accurate and capable of handling datasets of 100,000 samples or more.