Learning and inference in the presence of corrupted inputs
published: Aug. 20, 2015, recorded: July 2015, views: 1889
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We consider a model where given an uncorrupted input an adversary can corrupt it to one out of $m$ corrupted inputs. We model the classification and inference problems as a zero-sum game between a learner, minimizing the expected error, and an adversary, maximizing the expected error. The value of this game is the optimal error rate achievable. For learning using a limited hypothesis class $\calH$ over corrupted inputs, we give an efficient algorithm that given an uncorrupted sample returns a hypothesis $h\in H$ whose error on adversarially corrupted inputs is near optimal. Our algorithm uses as a blackbox an oracle that solves the ERM problem for the hypothesis class $\calH$. We provide a generalization bound for our setting, showing that for a sufficiently large sample, the performance on the sample and future unseen corrupted inputs will be similar. This gives an efficient learning algorithm for our adversarial setting, based on an ERM oracle. We also consider an inference related setting of the problem, where given a corrupted input, the learner queries the target function on various uncorrupted inputs and generates a prediction regarding the given corrupted input. There is no limitation on the prediction function the learner may generate, so implicitly the hypothesis class includes all possible hypotheses. In this setting we characterize the optimal learner policy as a minimum vertex cover in a given bipartite graph, and the optimal adversary policy as a maximum matching in the same bipartite graph. We design efficient local algorithms for approximating minimum vertex cover in bipartite graphs, which implies an efficient near optimal algorithm for the learner.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !