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Unfortunately, it is known that many classes of problems can be learned with adversarial manipulation of an epsilon-fraction of the training data. See for examp
by j2kun 9y ago
Unfortunately, it is known that many classes of problems can be learned with adversarial manipulation of an epsilon-fraction of the training data. See for example the paper "PAC learning with nasty noise," though there are many other adversarial noise models in which resilience can be proven (though proving it even for a specific concept class would be enough to prove it wrong that "all machine learning systems are vulnerable").
- LolWolf 9y agoBut the claim the paper is making fits perfectly with the above: > On the negative side, we prove that no algorithm can achieve accuracy of ε < 2η in learning any non-trivial class of functions. Though this is for a very particular type of adversary which has a lot more power than I'm claiming. In my case, though, I'm strengthening the side that the adversary has a very large number (e.g. infinite, as my claim "N->infty") of possible examples in the training set to be eps-close to. --- Rereading the above: Sorry, I'm not quite sure I understood your point! Are you claiming that there is such a model which is resilient to adversarial examples, and also has a large number of parameters relative to the hypothesis class size? (e.g. say VC dimension?) In that case, my claim would be definitely false, but I have yet to see such a paper (if you have a reference, I'd love to check it out!)