Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Statistical tests are at the heart of many scientific tasks. To validate their hypotheses, researchers in medical and social sciences use individuals' data. The sensitivity of participants' data requires the design of statistical tests that ensure the privacy of the individuals in the most efficient way. In this paper, we use the framework of property testing to design algorithms to test the properties of the distribution that the data is drawn from with respect to differential privacy. In particular, we investigate testing two fundamental properties of distributions: (1) testing the equivalence of two distributions when we have unequal numbers of samples from the two distributions.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse PCA. We give the first practically viable robust estimators for these problems. In more detail, our algorithms are sample and computationally efficient and achieve near-optimal robustness guarantees. In contrast to prior provable algorithms which relied on the ellipsoid method, our algorithms use spectral techniques to iteratively remove outliers from the dataset. Our experimental evaluation on synthetic data shows that our algorithms are scalable and significantly outperform a range of previous approaches, nearly matching the best error rate without corruptions.

Statistical tests are at the heart of many scientific tasks. To validate their hypotheses, researchers in medical and social sciences use individuals' data. The sensitivity of participants' data requires the design of statistical tests that ensure the privacy of the individuals in the most efficient way. In this paper, we use the framework of property testing to design algorithms to test the properties of the distribution that the data is drawn from with respect to differential privacy. In particular, we investigate testing two fundamental properties of distributions: (1) testing the equivalence of two distributions when we have unequal numbers of samples from the two distributions.

We consider the problem of computing the maximum likelihood multivariate logconcave distribution for a set of points.

We propose the first reduction-based approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth [8], by reducing the problem to achieving typical switching regret. Specifically, for the classical expert problem with K actions and T rounds, using our framework we develop various algorithms with a regret bound of order O( T (S ln T + n ln K)) compared to any sequence of experts with S 1 switches among n min{S, K} distinct experts. In addition, by plugging specific adaptive algorithms into our framework we also achieve the best of both stochastic and adversarial environments simultaneously.