In typical classification tasks, we seek a function which assigns a label to a single object. Kernel-based approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ability to use high-dimensional feature spaces, and from their strong theoretical guarantees. However, many real-world tasks involve sequential, spatial, or structured data, where multiple labels must be assigned. Existing kernel-based methods ignore structure in the problem, assigning labels independently to each object, losing much useful information. Conversely, probabilistic graphical models, such as Markov networks, can represent correlations between labels, by exploiting problem structure, but cannot handle high-dimensional feature spaces, and lack strong theoretical generalization guarantees. In this paper, we present a new framework that combines the advantages of both approaches: Maximum margin Markov (M 3) networks incorporate both kernels, which efficiently deal with high-dimensional features, and the ability to capture correlations in structured data. We present an efficient algorithm for learning M 3 networks based on a compact quadratic program formulation. We provide a new theoretical bound for generalization in structured domains. Experiments on the task of handwritten character recognition and collective hypertext classification demonstrate very significant gains over previous approaches. 1

Learning general functional dependencies is one of the main goals in machine learning. Recent progress in kernel-based methods has focused on designing flexible and powerful input representations. This paper addresses the complementary issue of problems involving complex outputs suchas multiple dependent output variables and structured output spaces. We propose to generalize multiclass Support Vector Machine learning in a formulation that involves features extracted jointly from inputs and outputs. The resulting optimization problem is solved efficiently by a cutting plane algorithm that exploits the sparseness and structural decomposition of the problem. We demonstrate the versatility and effectiveness of our method on problems ranging from supervised grammar learning and named-entity recognition, to taxonomic text classification and sequence alignment. 1.

Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order to accomplish this, we propose to appropriately generalize the well-known notion of a separation margin and derive a corresponding maximum-margin formulation. While this leads to a quadratic program with a potentially prohibitive, i.e. exponential, number of constraints, we present a cutting plane algorithm that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains involving different types of output spaces emphasize the breadth and generality of our approach.

We present a family of margin based online learning algorithms for various prediction tasks. In particular we derive and analyze algorithms for binary and multiclass categorization, regression, uniclass prediction and sequence prediction. The update steps of our different algorithms are all based on analytical solutions to simple constrained optimization problems. This unified view allows us to prove worst-case loss bounds for the different algorithms and for the various decision problems based on a single lemma. Our bounds on the cumulative loss of the algorithms are relative to the smallest loss that can be attained by any fixed hypothesis, and as such are applicable to both realizable and unrealizable settings. We demonstrate some of the merits of the proposed algorithms in a series of experiments with synthetic and real data sets.

We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification—for example, achieving a test error rate of 1.3 % on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification. 1

In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarity-score between each prototype and the input instance and then sets the predicted label to be the index of the prototype achieving the highest similarity. To design and analyze the learning algorithms in this paper we introduce the notion of ultraconservativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarity-scores which are higher than the score of the correct label's prototype. We start by describing a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarity-scores. We then discuss a specific online algorithm that seeks a set of prototypes which have a small norm. The resulting algorithm, which we term MIRA (for Margin Infused Relaxed Algorithm) is ultraconservative as well. We derive mistake bounds for all the algorithms and provide further analysis of MIRA using a generalized notion of the margin for multiclass problems.

We consider visual category recognition in the framework of measuring similarities, or equivalently perceptual distances, to prototype examples of categories. This approach is quite flexible, and permits recognition based on color, texture, and particularly shape, in a homogeneous framework. While nearest neighbor classifiers are natural in this setting, they suffer from the problem of high variance (in bias-variance decomposition) in the case of limited sampling. Alternatively, one could use support vector machines but they involve time-consuming optimization and computation of pairwise distances. We propose a hybrid of these two methods which deals naturally with the multiclass setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice. The basic idea is to find close neighbors to a query sample and train a local support vector machine that preserves the distance function on the collection of neighbors. Our method can be applied to large, multiclass data sets for which it outperforms nearest neighbor and support vector machines, and remains efficient when the problem becomes intractable for support vector machines. A wide variety of distance functions can be used and our experiments show state-of-the-art performance on a number of benchmark data sets for shape and texture classification (MNIST, USPS, CUReT) and object recognition (Caltech-101). On Caltech-101 we achieved a correct classification rate of 59.05%(±0.56%) at 15 training images per class, and 66.23%(±0.48%) at 30 training images. 1.

2 Everything Old Is New Again: A Fresh Look at Historical

We discuss the problem of ranking instances with the use of a “large margin ” principle. We introduce two main approaches: the first is the “fixed margin ” policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for different margins where the sum of margins is maximized. This approach is shown to reduce to-SVM when the number of classes. Both approaches are optimal in size of where is the total number of training examples. Experiments performed on visual classification and “collaborative filtering ” show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification. 1

A fundamental problem in statistical parsing is the choice of criteria and algorithms used to estimate the parameters in a model. The predominant approach in computational linguistics has been to use a parametric model with some variant of maximum-likelihood estimation. The assumptions under which maximum-likelihood estimation is justified are arguably quite strong. This paper discusses the statistical theory underlying various parameter-estimation methods, and gives algorithms which depend on alternatives to (smoothed) maximumlikelihood estimation. We first give an overview of results from statistical learning theory. We then show how important concepts from the classification literature -- specifically, generalization results based on margins on training data -- can be derived for parsing models. Finally, we describe parameter estimation algorithms which are motivated by these generalization bounds.