Learning by transduction

We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object /classification are generated by an i.i.d. process from a continuous probability distribution. Our method is a modification of Vapnik's support-vector machine; its main novelty is that it gives not only the prediction itself but also a practicable measure of the evidence found in support of that prediction. We also describe a procedure for assigning degrees of confidence to predictions made by the support vector machine. Some experimental results are presented, and possible extensions of the algorithms are discussed. 1 THE PROBLEM Suppose labeled points (x i ; y i ) (i = 1; 2; : : :), where x i 2 IR n (our objects are specified by n real-valued attributes) and y i 2 f\\Gamma1; 1g, are generated independently from an unknown (but the same for all points) probability distribution. We are given l points x i , i = 1; : : : ; l, toge...