A new on-line learning algorithm which minimizes a statistical de(cid:173) pendency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual in(cid:173) formation (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of the sources. The Gram-Charlier expansion instead of the Edgeworth expansion is used in evaluating the MI. The natural gradient approach is used to minimize the MI.

There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order, given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a two-stage approach in which one first learns by conventional means a preference Junction, of the form PREF( u, v), which indicates whether it is advisable to rank u before v. New instances are then ordered so as to maximize agreements with the learned preference func(cid:173) tion. We show that the problem of finding the ordering that agrees best with a preference function is NP-complete, even under very restrictive assumptions. Nevertheless, we describe a simple greedy algorithm that is guaranteed to find a good approximation.

We study online learning in Boolean domains using kernels which cap- ture feature expansions equivalent to using conjunctions over basic fea- tures. We demonstrate a tradeoff between the computational efficiency with which these kernels can be computed and the generalization abil- ity of the resulting classifier. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Percep- tron algorithm over an exponential number of conjunctions; however we also prove that using such kernels the Perceptron algorithm can make an exponential number of mistakes even when learning simple func- tions. We also consider an analogous use of kernel functions to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions.

In this paper we show that on-line algorithms for classification and re- gression can be naturally used to obtain hypotheses with good data- dependent tail bounds on their risk. Our results are proven without re- quiring complicated concentration-of-measure arguments and they hold for arbitrary on-line learning algorithms. Furthermore, when applied to concrete on-line algorithms, our results yield tail bounds that in many cases are comparable or better than the best known bounds.

In this paper we show that online algorithms for classification and regression canbe naturally used to obtain hypotheses with good datadependent tailbounds on their risk. Our results are proven without requiring complicated concentration-of-measure arguments and they hold for arbitrary online learning algorithms. Furthermore, when applied to concrete online algorithms, our results yield tail bounds that in many cases are comparable or better than the best known bounds.