Robust Inference and Local Algorithms

We introduce a new feature to inference and learning which we call robustness. By robustness we intuitively model the case that the observation of the learner might be corrupted. We survey a new and novel approach to model such possible corruption as a zero-sum game between an adversary that selects the corruption and a leaner that predict the correct label. The corruption of the observations is done in a worse-case setting, by an adversary, where the main restriction is that the adversary is limited to use one of a fixed know class of modification functions. The main focus in this line of research is on efficient algorithms both for the inference setting and for the learning setting. In order to be efficient in the dimension of the domain, one cannot hope to inspect all the possible inputs. For this, we have to invoke local computation algorithms, that inspect only a logarithmic fraction of the domain per query.