70 research outputs found
Learning Arbitrary Statistical Mixtures of Discrete Distributions
We study the problem of learning from unlabeled samples very general
statistical mixture models on large finite sets. Specifically, the model to be
learned, , is a probability distribution over probability
distributions , where each such is a probability distribution over . When we sample from , we do not observe
directly, but only indirectly and in very noisy fashion, by sampling from
repeatedly, independently times from the distribution . The problem is
to infer to high accuracy in transportation (earthmover) distance.
We give the first efficient algorithms for learning this mixture model
without making any restricting assumptions on the structure of the distribution
. We bound the quality of the solution as a function of the size of
the samples and the number of samples used. Our model and results have
applications to a variety of unsupervised learning scenarios, including
learning topic models and collaborative filtering.Comment: 23 pages. Preliminary version in the Proceeding of the 47th ACM
Symposium on the Theory of Computing (STOC15
Stochastic Activation Pruning for Robust Adversarial Defense
Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed strategy for adversarial defense. SAP prunes a random subset of activations (preferentially pruning those with smaller magnitude) and scales up the survivors to compensate. We can apply SAP to pretrained networks, including adversarially trained models, without fine-tuning, providing robustness against adversarial examples. Experiments demonstrate that SAP confers robustness against attacks, increasing accuracy and preserving calibration
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