A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs. Complex notions of similar(cid:173) ity appear necessary for cognitive models and applications, while simple notions of similarity form a tractable basis for current computational ap(cid:173) proaches to classification. We explore the nature of this dichotomy and why it calls for new approaches to well-studied problems in learning. We begin this process by demonstrating new computational methods for supervised learning that can handle complex notions of similarity.

Clustering and prediction of sets of curves is an important problem in many areas of science and engineering. It is often the case that curves tend to be misaligned from each other in a continuous manner, either in space (across the measurements) or in time. We develop a probabilistic framework that allows for joint clustering and continuous alignment of sets of curves in curve space (as opposed to a fixed-dimensional feature- vector space). The proposed methodology integrates new probabilistic alignment models with model-based curve clustering algorithms. The probabilistic approach allows for the derivation of consistent EM learn- ing algorithms for the joint clustering-alignment problem. Experimental results are shown for alignment of human growth data, and joint cluster- ing and alignment of gene expression time-course data.

Lasso regression tends to assign zero weights to most irrelevant or redundant features, and hence is a promising technique for feature selection. Its limitation, however, is that it only offers solutions to linear models. Kernel machines with feature scaling techniques have been studied for feature selection with non-linear models. However, such approaches require to solve hard non-convex optimization problems. This paper proposes a new approach named the Feature Vector Machine (FVM). It reformulates the standard Lasso regression into a form isomorphic to SVM, and this form can be easily extended for feature selection with non-linear models by introducing kernels defined on feature vectors.

We present a simple and scalable algorithm for large-margin estima- tion of structured models, including an important class of Markov net- works and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gra- dient and projection calculations. The projection step can be solved us- ing combinatorial algorithms for min-cost quadratic flow. This makes the approach an efficient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.

The Maximum Margin Planning (MMP) (Ratliff et al., 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher appear to be lower cost (with a lossscaled margin) than any other policy for a given planning domain. We provide a novel approach, M M P B O O S T, based on the functional gradient descent view of boosting (Mason et al., 1999; Friedman, 1999a) that extends MMP by "boosting" in new features. This approach uses simple binary classification or regression to improve performance of MMP imitation learning, and naturally extends to the class of structured maximum margin prediction problems.

In this paper, we formalize multi-instance multi-label learning, where each train- ing example is associated with not only multiple instances but also multiple class labels. Such a problem can occur in many real-world tasks, e.g. an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways. We analyze the relationship between multi-instance multi-label learning and the learning frameworks of traditional supervised learning, multi- instance learning and multi-label learning. Then, we propose the MIMLBOOST and MIMLSVM algorithms which achieve good performance in an application to scene classification.

Motivated by recent developments in manifold-valued regression we propose a family of nonparametric kernel-smoothing estimators with metric-space valued output including a robust median type estimator and the classical Frechet mean. Depending on the choice of the output space and the chosen metric the estimator reduces to partially well-known procedures for multi-class classification, multivariate regression in Euclidean space, regression with manifold-valued output and even some cases of structured output learning. In this paper we focus on the case of regression with manifold-valued input and output. We show pointwise and Bayes consistency for all estimators in the family for the case of manifold-valued output and illustrate the robustness properties of the estimator with experiments.

In this paper we propose an approximated learning framework for large scale graphical models and derive message passing algorithms for learning their parameters efficiently. We first relate CRFs and structured SVMs and show that in the CRF's primal a variant of the log-partition function, known as soft-max, smoothly approximates the hinge loss function of structured SVMs. We then propose an intuitive approximation for structured prediction problems using Fenchel duality based on a local entropy approximation that computes the exact gradients of the approximated problem and is guaranteed to converge. Unlike existing approaches, this allow us to learn graphical models with cycles and very large number of parameters efficiently. We demonstrate the effectiveness of our approach in an image denoising task.

In discriminative machine learning one is interested in training a system to optimize a certain desired measure of performance, or loss. In binary classification one typically tries to minimizes the error rate. But in structured prediction each task often has its own measure of performance such as the BLEU score in machine translation or the intersection-over-union score in PASCAL segmentation. The most common approaches to structured prediction, structural SVMs and CRFs, do not minimize the task loss: the former minimizes a surrogate loss with no guarantees for task loss and the latter minimizes log loss independent of task loss. The main contribution of this paper is a theorem stating that a certain perceptron-like learning rule, involving features vectors derived from loss-adjusted inference, directly corresponds to the gradient of task loss.

The multi-armed bandit (MAB) setting is a useful abstraction of many online learning tasks which focuses on the trade-off between exploration and exploitation. In this setting, an online algorithm has a fixed set of alternatives ("arms"), and in each round it selects one arm and then observes the corresponding reward. While the case of small number of arms is by now well-understood, a lot of recent work has focused on multi-armed bandits with (infinitely) many arms, where one needs to assume extra structure in order to make the problem tractable. In particular, in the Lipschitz MAB problem there is an underlying similarity metric space, known to the algorithm, such that any two arms that are close in this metric space have similar payoffs. In this paper we consider the more realistic scenario in which the metric space is implicit -- it is defined by the available structure but not revealed to the algorithm directly.