We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials, with a prediction to be made in each, and the goal of the learner is to make few mistakes. We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well, but the learner does not know which one. A simple and effective method, based on weighted voting, is introduced for constructing a compound algorithm in such a circumstance. We call this method the Weighted Majority Algorithm. We show that this algorithm is robust in the presence of errors in the data. We discuss various versions of the Weighted Majority Algorithm and prove mistake bounds for them that are closely related to the mistake bounds of the best algorithms of the pool. For example, given a sequence of trials, if there is an algorithm in the pool A that makes at most m mistakes then the Weighted Majority Algorithm will make at most c(log jAj + m) mi...

this paper, we concentrate on linear predictors . To any vector u 2 R

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.

Abstract. We generalize the recent relative loss bounds for on-line algorithms where the additional loss of the algorithm on the whole sequence of examples over the loss of the best expert is bounded. The generalization allows the sequence to be partitioned into segments, and the goal is to bound the additional loss of the algorithm over the sum of the losses of the best experts for each segment. This is to model situations in which the examples change and different experts are best for certain segments of the sequence of examples. In the single segment case, the additional loss is proportional to log n, where n is the number of experts and the constant of proportionality depends on the loss function. Our algorithms do not produce the best partition; however the loss bound shows that our predictions are close to those of the best partition. When the number of segments is k +1and the sequence is of length ℓ, we can bound the additional loss of our algorithm over the best partition by O(k log n + k log(ℓ/k)). For the case when the loss per trial is bounded by one, we obtain an algorithm whose additional loss over the loss of the best partition is independent of the length of the sequence. The additional loss becomes O(k log n + k log(L/k)), where L is the loss of the best partition with k +1segments. Our algorithms for tracking the predictions of the best expert are simple adaptations of Vovk’s original algorithm for the single best expert case. As in the original algorithms, we keep one weight per expert, and spend O(1) time per weight in each trial.

We address the problem of deciding when to spin down the disk of a mobile computer in order to extend battery life. Since one of the most critical resources in mobile computing environments is battery life, good energy conservation methods can dramatically increase the utility of mobile systems. We use a simple and efficient algorithm based on machine learning techniques that has excellent performance in practice. Our experimental results are based on traces collected from HP C2474s disks. Using this data, the algorithm outperforms several algorithms that are theoretically optimal in under various worst-case assumptions, as well as the best fixed time-out strategy. In particular, the algorithm reduces the power consumption of the disk to about half (depending on the disk's properties) of the energy consumed by a one minute fixed time-out. Since the algorithm adapts to usage patterns, it uses as little as 88% of the energy consumed by the best fixed time-out computed in retrospect. 1 In...

This paper describes experimental results on using Winnow and Weighted-Majority based algorithms on a real-world calendar scheduling domain. These two algorithms have been highly studied in the theoretical machine learning literature. We show here that these algorithms can be quite competitive practically, outperforming the decision-tree approach currently in use in the Calendar Apprentice system in terms of both accuracy and speed. One of the contributions of this paper is a new variant on the Winnow algorithm (used in the experiments) that is especially suited to conditions with stringvalued classifications, and we give a theoretical analysis of its performance. In addition we show how Winnow can be applied to achieve a good accuracy/coverage tradeoff and explore issues that arise such as concept drift. We also provide an analysis of a policy for discarding predictors in Weighted-Majority that allows it to speed up as it learns. Keywords: Winnow, Weighted-Majority, Multiplicative alg...

In this paper we study a Bayesian or average-case model of concept learning with a twofold goal: to provide more precise characterizations of learning curve (sample complexity) behavior that depend on properties of both the prior distribution over concepts and the sequence of instances seen by the learner, and to smoothly unite in a common framework the popular statistical physics and VC dimension theories of learning curves. To achieve this, we undertake a systematic investigation and comparison of two fundamental quantities in learning and information theory: the probability of an incorrect prediction for an optimal learning algorithm, and the Shannon information gain. This study leads to a new understanding of the sample complexity of learning in several existing models. 1 Introduction Consider a simple concept learning model in which the learner attempts to infer an unknown target concept f , chosen from a known concept class F of f0; 1g-valued functions over an instance space X....

In many real-world domains, supervised learning requires a large number of training examples. In this paper, we describe an active learning method that uses a committee of learners to reduce the number of training examples required for learning. Our approach is similar to the Query by Committee framework, where disagreement among the committee members on the predicted label for the input part of the example is used to signal the need for knowing the actual value of the label. Our experiments are conducted in the text categorization domain, which is characterized by a large number of features, many ofwhich are irrelevant. We report here on experiments using a committee of Winnowbased learners and demonstrate that this approach can reduce the number of labeled training examples required over that used by a single Winnow learner by 1-2 orders of magnitude. 1.

To Mom, Dad, and Susan, for their support and encouragement.

. Littlestone developed a simple deterministic on-line learning algorithm for learning k-literal disjunctions. This algorithm (called Winnow) keeps one weight for each of the n variables and does multiplicative updates to its weights. We develop a randomized version of Winnow and prove bounds for an adaptation of the algorithm for the case when the disjunction may change over time. In this case a possible target disjunction schedule T is a sequence of disjunctions (one per trial) and the shift size is the total number of literals that are added/removed from the disjunctions as one progresses through the sequence. We develop an algorithm that predicts nearly as well as the best disjunction schedule for an arbitrary sequence of examples. This algorithm that allows us to track the predictions of the best disjunction is hardly more complex than the original version. However the amortized analysis needed for obtaining worst-case mistake bounds requires new techniques. In some cases our low...