Koby Crammer

Online Large-Margin Training of Dependency Parsers

We present an effective training algorithm for linearly-scored dependency parsers that implements online large-margin multi-class training (Crammer and Singer, 2003; Crammer et al., 2003) on top of efficient parsing techniques for dependency trees (Eisner, 1996). The trained parsers achieve a competitive dependency accuracy for both English and Czech with no language specific enhancements.

On the Learnability and Design of Output Codes for Multiclass Problems

Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problems. For the design problem of discrete codes, which have been used extensively in previous works, we present mostly negative results. We then introduce the notion of continuous codes and cast the design problem of continuous codes as a constrained optimization problem. We describe three optimization problems corresponding to three different norms of the code matrix. Interestingly, for the l2 norm our formalism results in a quadratic program whose dual does not depend on the length of the code. A special case of our formalism provides a multiclass scheme for building support vector machines which can be solved efficiently. We give a time and space efficient algorithm for solving the quadratic program. We describe preliminary experiments with synthetic data show that our algorithm is often two orders of magnitude faster than standard quadratic programming packages. We conclude with the generalization properties of the algorithm.

A theory of learning from different domains

Discriminative learning methods for classification perform well when training and test data are drawn from the same distribution. Often, however, we have plentiful labeled training data from a source domain but wish to learn a classifier which performs well on a target domain with a different distribution and little or no labeled training data. In this work we investigate two questions. First, under what conditions can a classifier trained from source data be expected to perform well on target data? Second, given a small amount of labeled target data, how should we combine it during training with the large amount of labeled source data to achieve the lowest target error at test time?We address the first question by bounding a classifier’s target error in terms of its source error and the divergence between the two domains. We give a classifier-induced divergence measure that can be estimated from finite, unlabeled samples from the domains. Under the assumption that there exists some hypothesis that performs well in both domains, we show that this quantity together with the empirical source error characterize the target error of a source-trained classifier.We answer the second question by bounding the target error of a model which minimizes a convex combination of the empirical source and target errors. Previous theoretical work has considered minimizing just the source error, just the target error, or weighting instances from the two domains equally. We show how to choose the optimal combination of source and target error as a function of the divergence, the sample sizes of both domains, and the complexity of the hypothesis class. The resulting bound generalizes the previously studied cases and is always at least as tight as a bound which considers minimizing only the target error or an equal weighting of source and target errors.

Confidence-weighted linear classification

We introduce confidence-weighted linear classifiers, which add parameter confidence information to linear classifiers. Online learners in this setting update both classifier parameters and the estimate of their confidence. The particular online algorithms we study here maintain a Gaussian distribution over parameter vectors and update the mean and covariance of the distribution with each instance. Empirical evaluation on a range of NLP tasks show that our algorithm improves over other state of the art online and batch methods, learns faster in the online setting, and lends itself to better classifier combination after parallel training.

Adaptive Regularization of Weight Vectors

We present AROW, an online learning algorithm for binary and multiclass problems that combines large margin training, confidence weighting, and the capacity to handle non-separable data. AROW performs adaptive regularization of the prediction function upon seeing each new instance, allowing it to perform especially well in the presence of label noise. We derive mistake bounds for the binary and multiclass settings that are similar in form to the second order perceptron bound. Our bounds do not assume separability. We also relate our algorithm to recent confidence-weighted online learning techniques. Empirical evaluations show that AROW achieves state-of-the-art performance on a wide range of binary and multiclass tasks, as well as robustness in the face of non-separable data.

New Regularized Algorithms for Transductive Learning

We propose a new graph-based label propagation algorithm for transductive learning. Each example is associated with a vertex in an undirected graph and a weighted edge between two vertices represents similarity between the two corresponding example. We build on Adsorption, a recently proposed algorithm and analyze its properties. We then state our learning algorithm as a convex optimization problem over multi-label assignments and derive an efficient algorithm to solve this problem. We state the conditions under which our algorithm is guaranteed to converge. We provide experimental evidence on various real-world datasets demonstrating the effectiveness of our algorithm over other algorithms for such problems. We also show that our algorithm can be extended to incorporate additional prior information, and demonstrate it with classifying data where the labels are not mutually exclusive.

Ultraconservative Online Algorithms for Multiclass Problems

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 ultracon-servativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarity-scores which are higher than the score of the correct labels 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.

Global Discriminative Learning for Higher-Accuracy Computational Gene Prediction

Most ab initio gene predictors use a probabilistic sequence model, typically a hidden Markov model, to combine separately trained models of genomic signals and content. By combining separate models of relevant genomic features, such gene predictors can exploit small training sets and incomplete annotations, and can be trained fairly efficiently. However, that type of piecewise training does not optimize prediction accuracy and has difficulty in accounting for statistical dependencies among different parts of the gene model. With genomic information being created at an ever-increasing rate, it is worth investigating alternative approaches in which many different types of genomic evidence, with complex statistical dependencies, can be integrated by discriminative learning to maximize annotation accuracy. Among discriminative learning methods, large-margin classifiers have become prominent because of the success of support vector machines (SVM) in many classification tasks. We describe CRAIG, a new program for ab initio gene prediction based on a conditional random field model with semi-Markov structure that is trained with an online large-margin algorithm related to multiclass SVMs. Our experiments on benchmark vertebrate datasets and on regions from the ENCODE project show significant improvements in prediction accuracy over published gene predictors that use intrinsic features only, particularly at the gene level and on genes with long introns.

Flexible Text Segmentation with Structured Multilabel Classification

Many language processing tasks can be reduced to breaking the text into segments with prescribed properties. Such tasks include sentence splitting, tokenization, named-entity extraction, and chunking. We present a new model of text segmentation based on ideas from multilabel classification. Using this model, we can naturally represent segmentation problems involving overlapping and non-contiguous segments. We evaluate the model on entity extraction and noun-phrase chunking and show that it is more accurate for overlapping and non-contiguous segments, but it still performs well on simpler data sets for which sequential tagging has been the best method.

Multi-Class Confidence Weighted Algorithms

The recently introduced online confidence-weighted (CW) learning algorithm for binary classification performs well on many binary NLP tasks. However, for multi-class problems CW learning updates and inference cannot be computed analytically or solved as convex optimization problems as they are in the binary case. We derive learning algorithms for the multi-class CW setting and provide extensive evaluation using nine NLP datasets, including three derived from the recently released New York Times corpus. Our best algorithm out-performs state-of-the-art online and batch methods on eight of the nine tasks. We also show that the confidence information maintained during learning yields useful probabilistic information at test time.