3 years ago

Approximate Newton-based statistical inference using only stochastic gradients.

Liu Liu, Tianyang Li, Constantine Caramanis, Anastasios Kyrillidis

We present a novel inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a Hessian-vector product from first-order information. In theory, our method efficiently computes the statistical error covariance in $M$-estimation, both for unregularized convex learning problems and high-dimensional LASSO regression, without using exact second order information, or resampling the entire data set. In practice, we demonstrate the effectiveness of our framework on large-scale machine learning problems, that go even beyond convexity: as a highlight, our work can be used to detect certain adversarial attacks on neural networks.

Publisher URL: http://arxiv.org/abs/1805.08920

DOI: arXiv:1805.08920v1

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