Applying Winnow to Context-Sensitive Spelling Correction

Multiplicative weight-updating algorithms such as Winnow have been studied extensively in the COLT literature, but only recently have people started to use them in applications. In this paper, we apply a Winnow-based algorithm to a task in natural language: context-sensitive spelling correction. This is the task of fixing spelling errors that happen to result in valid words, such as substituting {\it to\/} for {\it too}, {\it casual\/} for {\it causal}, and so on. Previous approaches to this problem have been statistics-based; we compare Winnow to one of the more successful such approaches, which uses Bayesian classifiers. We find that: (1)~When the standard (heavily-pruned) set of features is used to describe problem instances, Winnow performs comparably to the Bayesian method; (2)~When the full (unpruned) set of features is used, Winnow is able to exploit the new features and convincingly outperform Bayes; and (3)~When a test set is encountered that is dissimilar to the training set, Winnow is better than Bayes at adapting to the unfamiliar test set, using a strategy we will present for combining learning on the training set with unsupervised learning on the (noisy) test set.Comment: 9 page

A Winnow-Based Approach to Context-Sensitive Spelling Correction

A large class of machine-learning problems in natural language require the characterization of linguistic context. Two characteristic properties of such problems are that their feature space is of very high dimensionality, and their target concepts refer to only a small subset of the features in the space. Under such conditions, multiplicative weight-update algorithms such as Winnow have been shown to have exceptionally good theoretical properties. We present an algorithm combining variants of Winnow and weighted-majority voting, and apply it to a problem in the aforementioned class: context-sensitive spelling correction. This is the task of fixing spelling errors that happen to result in valid words, such as substituting "to" for "too", "casual" for "causal", etc. We evaluate our algorithm, WinSpell, by comparing it against BaySpell, a statistics-based method representing the state of the art for this task. We find: (1) When run with a full (unpruned) set of features, WinSpell achieves accuracies significantly higher than BaySpell was able to achieve in either the pruned or unpruned condition; (2) When compared with other systems in the literature, WinSpell exhibits the highest performance; (3) The primary reason that WinSpell outperforms BaySpell is that WinSpell learns a better linear separator; (4) When run on a test set drawn from a different corpus than the training set was drawn from, WinSpell is better able than BaySpell to adapt, using a strategy we will present that combines supervised learning on the training set with unsupervised learning on the (noisy) test set.Comment: To appear in Machine Learning, Special Issue on Natural Language Learning, 1999. 25 page

Decision Making in Uncertain and Changing Environments

We consider an agent who has to repeatedly make choices in an uncertain and changing environment, who has full information of the past, who discounts future payoffs, but who has no prior. We provide a learning algorithm that performs almost as well as the best of a given finite number of experts or benchmark strategies and does so at any point in time, provided the agent is sufficiently patient. The key is to find the appropriate degree of forgetting distant past. Standard learning algorithms that treat recent and distant past equally do not have the sequential epsilon optimality property.Adaptive learning, experts, distribution-free, epsilon-optimality, Hannan regret

Decision making in uncertain and changing environments

We consider an agent who has to repeatedly make choices in an uncertain and changing environment, who has full information of the past, who discounts future payoffs, but who has no prior. We provide a learning algorithm that performs almost as well as the best of a given finite number of experts or benchmark strategies and does so at any point in time, provided the agent is sufficiently patient. The key is to find the appropriate degree of forgetting distant past. Standard learning algorithms that treat recent and distant past equally do not have the sequential epsilon optimality property.Adaptive learning, experts, distribution-free, e-optimality, Hannan regret

Online Learning with an Almost Perfect Expert

We study the multiclass online learning problem where a forecaster makes a sequence of predictions using the advice of $n$ experts. Our main contribution is to analyze the regime where the best expert makes at most $b$ mistakes and to show that when $b = o(\log_4{n})$, the expected number of mistakes made by the optimal forecaster is at most $\log_4{n} + o(\log_4{n})$. We also describe an adversary strategy showing that this bound is tight and that the worst case is attained for binary prediction