In this paper we show how to extract a hypothesis with small risk from the ensemble of hypotheses generated by an arbitrary on-line learning algorithm run on an i.i.d. sample of data. Using a simple large deviation argument, we prove tight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic M_n associated with the on-line performance of the ensemble. Via sharp pointwise bounds on M_n, we then obtain risk tail bounds for kernel Perceptron algorithms in terms of the spectrum of the empirical kernel matrix. These bounds reveal that the linear hypotheses found via our approach achieve optimal trade-offs between hinge loss and margin size over the class of all linear functions, an issue that was left open by previous results. A distinctive feature of our approach is that the key tools for our analysis come from the model of prediction of individual sequences; i.e., a model making no probabilistic assumptions on the source generating the data. In fact, these tools turn out to be so powerful that we only need very elementary statistical facts to obtain our final risk bounds.

On the generalization ability of on-line learning algorithms / N. Cesa-Bianchi, A. Conconi, C. Gentile. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - 50:9(2004), pp. 2050-2057. [10.1109/TIT.2004.833339]

On the generalization ability of on-line learning algorithms

N. Cesa-Bianchi
Primo
;
A. Conconi
Secondo
;
2004

Abstract

In this paper we show how to extract a hypothesis with small risk from the ensemble of hypotheses generated by an arbitrary on-line learning algorithm run on an i.i.d. sample of data. Using a simple large deviation argument, we prove tight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic M_n associated with the on-line performance of the ensemble. Via sharp pointwise bounds on M_n, we then obtain risk tail bounds for kernel Perceptron algorithms in terms of the spectrum of the empirical kernel matrix. These bounds reveal that the linear hypotheses found via our approach achieve optimal trade-offs between hinge loss and margin size over the class of all linear functions, an issue that was left open by previous results. A distinctive feature of our approach is that the key tools for our analysis come from the model of prediction of individual sequences; i.e., a model making no probabilistic assumptions on the source generating the data. In fact, these tools turn out to be so powerful that we only need very elementary statistical facts to obtain our final risk bounds.
Settore INF/01 - Informatica
2004
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/141718
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