Learning Probabilistic Linear-Threshold Classifiers via Selective Sampling

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In this paper we investigate selective sampling, a learning model where the learner observes a sequence of i.i.d. unlabeled instances each time deciding whether to query the label of the current instance. We assume that labels are binary and stochastically related to instances via a linear probabilistic function whose coefficients are arbitrary and unknown. We then introduce a new selective sampling rule and show that its expected regret (with respect to the classifier knowing the underlying linear function and observing the label realization after each prediction) grows not much faster than the number of sampled labels. Furthermore, under additional assumptions on the true margin distribution, we prove that the number of sampled labels grows only logarithmically in the number of observed instances. Experiments carried out on a text categorization problem show that: (1) our selective sampling algorithm performs better than the Perceptron algorithm even when the latter is given the true label after each classification; (2) when allowed to observe the true label after each classification, the performance of our algorithm remains the same. Finally, we note that by expressing our selective sampling rule in dual variables we can learn nonlinear probabilistic functions via the kernel machinery.