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Poster
Analyzing the Robustness of Nearest Neighbors to Adversarial Examples
Yizhen Wang · Somesh Jha · Kamalika Chaudhuri

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #68
in Posters Fri »

Motivated by safety-critical applications, test-time attacks on classifiers via adversarial examples has recently received a great deal of attention. However, there is a general lack of understanding on why adversarial examples arise; whether they originate due to inherent properties of data or due to lack of training samples remains ill-understood. In this work, we introduce a theoretical framework analogous to bias-variance theory for understanding these effects. We use our framework to analyze the robustness of a canonical non-parametric classifier – the k-nearest neighbors. Our analysis shows that its robustness properties depend critically on the value of k – the classifier may be inherently non-robust for small k, but its robustness approaches that of the Bayes Optimal classifier for fast-growing k. We propose a novel modified 1-nearest neighbor classifier, and guarantee its robustness in the large sample limit. Our experiments suggest that this classifier may have good robustness properties even for reasonable data set sizes.

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Author Information

Yizhen Wang (UCSD)
Somesh Jha (University of Wisconsin, Madison)
Kamalika Chaudhuri (University of California at San Diego)

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