We present a new algorithm for domain adaptation improving upon a discrepancy minimization algorithm previously shown to outperform a number of algorithms for this task. Unlike many previous algorithms for domain adaptation, our algorithm does not consist of a fixed reweighting of the losses over the training sample. We show that our algorithm benefits from a solid theoretical foundation and more favorable learning bounds than discrepancy minimization. We present a detailed description of our algorithm and give several efficient solutions for solving its optimization problem. We also report the results of several experiments showing that it outperforms discrepancy minimization.

Abstract. We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our bounds are always tighter and in some cases substantially improve upon previous ones based on the L1 distance. We also present a generalization of the standard on-line to batch conversion to the drifting scenario in terms of the discrepancy and arbitrary convex combinations of hypotheses. We introduce a new algorithm exploiting these learning guarantees, which we show can be formulated as a simple QP. Finally, we report the results of preliminary experiments demonstrating the benefits of this algorithm.

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We present a differentially private algorithm for releasing the sequence of k elements with the highest counts from a data domain of d elements. The algorithm is a "joint" instance of the exponential mechanism, and its output space consists of all O(d k ) length-k sequences. Our main contribution is a method to sample this exponential mechanism in time O(dk log(k) + d log(d)) and space O(dk). Experiments show that this approach outperforms existing pure differential privacy methods and improves upon even approximate differential privacy methods for moderate k.