Learning problems in the text processing domain often map the text to a space whose dimensions are the measured features of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both the learned concepts and the instances reside very sparsely in the feature space, and (c) a high variation in the number of active features in an instance. In this work we study three mistake-driven learning algorithms for a typical task of this nature -- text categorization. We argue that these algorithms -- which categorize documents by learning a linear separator in the feature space -- have a few properties that make them ideal for this domain. We then show that a quantum leap in performance is achieved when we further modify the algorithms to better address some of the specific characteristics of the domain. In particular, we demonstrate (1) how variation in document length can be tolerated by either normalizing feature weights or by using negative weights, (2) the positive effect of applying a threshold range in training, (3) alternatives in considering feature frequency, and (4) the benefits of discarding features while training. Overall, we present an algorithm, a variation of Littlestone's Winnow, which performs significantly better than any other algorithm tested on this task using a similar feature set.
The methods that are most similar to our techniques are the on-line algorithms used in @cite_16 and @cite_10 . In the first, two algorithms, a multiplicative update and additive update algorithms suggested in @cite_5 are evaluated in the domain, and are shown to perform somewhat better than Rocchio's algorithm. While both these works make use of multiplicative update algorithms, as we do, there are two major differences between those studies and the current one. First, there are some important technical differences between the algorithms used. Second, the algorithms we study here are mistake-driven; they update the weight vector only when a mistake is made, and not after every example seen. The Experts algorithm studied in @cite_10 is very similar to a basic version of the algorithm which we study here. The way we treat the negative weights is different, though, and significantly more efficient, especially in sparse domains (see ). Cohen and Singer experiment also, using the same algorithm, with more complex features (sparse n-grams) and show that, as expected, it yields better results.
@cite_5 @cite_16 @cite_10
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In most kernel based online learning algorithms, when an incoming instance is misclassified, it will be added into the pool of support vectors and assigned with a weight, which often remains unchanged during the rest of the learning process. This is clearly insufficient since when a new support vector is added, we generally expect the weights of the other existing support vectors to be updated in order to reflect the influence of the added support vector. In this paper, we propose a new online learning method, termed Double Updating Online Learning, or DUOL for short, that explicitly addresses this problem. Instead of only assigning a fixed weight to the misclassified example received at the current trial, the proposed online learning algorithm also tries to update the weight for one of the existing support vectors. We show that the mistake bound can be improved by the proposed online learning method. We conduct an extensive set of empirical evaluations for both binary and multi-class online learning tasks. The experimental results show that the proposed technique is considerably more effective than the state-of-the-art online learning algorithms. The source code is available to public at http: www.cais.ntu.edu.sg chhoi DUOL . In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction model to a general decision-theoretic setting. We show that the multiplicative weight-update Littlestone?Warmuth rule can be adapted to this model, yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multiple-outcome prediction, repeated games, and prediction of points in Rn. In the second part of the paper we apply the multiplicative weight-update technique to derive a new boosting algorithm. This boosting algorithm does not require any prior knowledge about the performance of the weak learning algorithm. We also study generalizations of the new boosting algorithm to the problem of learning functions whose range, rather than being binary, is an arbitrary finite set or a bounded segment of the real line. We consider two algorithm for on-line prediction based on a linear model. The algorithms are the well-known Gradient Descent (GD) algorithm and a new algorithm, which we call EG(+ -). They both maintain a weight vector using simple updates. For the GD algorithm, the update is based on subtracting the gradient of the squared error made on a prediction. The EG(+ -) algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively. We present worst-case loss bounds for EG(+ -) and compare them to previously known bounds for the GD algorithm. The bounds suggest that the losses of the algorithms are in general incomparable, but EG(+ -) has a much smaller loss if only a few components of the input are relevant for the predictions. We have performed experiments, which show that our worst-case upper bounds are quite tight already on simple artificial data. We describe and analyze an online algorithm for supervised learning of pseudo-metrics. The algorithm receives pairs of instances and predicts their similarity according to a pseudo-metric. The pseudo-metrics we use are quadratic forms parameterized by positive semi-definite matrices. The core of the algorithm is an update rule that is based on successive projections onto the positive semi-definite cone and onto half-space constraints imposed by the examples. We describe an efficient procedure for performing these projections, derive a worst case mistake bound on the similarity predictions, and discuss a dual version of the algorithm in which it is simple to incorporate kernel operators. The online algorithm also serves as a building block for deriving a large-margin batch algorithm. We demonstrate the merits of the proposed approach by conducting experiments on MNIST dataset and on document filtering.