No abstract

Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.

When applying machine learning in safety-critical systems, a reliable assessment of the uncertainy of a classifier is required. However, deep neural networks are known to produce highly overconfident predictions on out-of-distribution (OOD) data and even if trained to be non-confident on OOD data one can still adversarially manipulate OOD data so that the classifer again assigns high confidence to the manipulated samples. In this paper we propose a novel method where from first principles we combine a certifiable OOD detector with a standard classifier into an OOD aware classifier. In this way we achieve the best of two worlds: certifiably adversarially robust OOD detection, even for OOD samples close to the in-distribution, without loss in prediction accuracy and close to state-of-the-art OOD detection performance for non-manipulated OOD data. Moreover, due to the particular construction our classifier provably avoids the asymptotic overconfidence problem of standard neural networks.

Neural networks have led to major improvements in image classification but suffer from being non-robust to adversarial changes, unreliable uncertainty estimates on out-distribution samples and their inscrutable black-box decisions. In this work we propose RATIO, a training procedure for Robustness via Adversarial Training on In-and Outdistribution, which leads to robust models with reliable and robust confidence estimates on the out-distribution. RATIO has similar generative properties to adversarial training so that visual counterfactuals produce class specific features. While adversarial training comes at the price of lower clean accuracy, RATIO achieves state-of-the-art l2-adversarial robustness on CIFAR10 and maintains better clean accuracy.

I want to thank my parents for their endless support in this and all my previous adventures. I am thankful to my girlfriend Camila and to her family for helping me through the many challenges I encountered on this sometimes bumpy path. I thank my adviser Diego Trancanelli for having me as his student and for his helpful advice. I want to thank Edoardo Vescovi who helped me understand many concepts that I would not have grasped without him and motivated me greatly with his seemingly limitless work ethic. I am also thankful to have spent my time together with a great group of peers: Gabriel, Daniel, Felipe, Leo, Márcia and Caio. I also want to thank João Penedones and Miguel Paulos for their very helpful discussions and their patience when answering my questions. Of course, I want to give special thanks to the DAAD who made my entire stay in Brazil and therefore this dissertation possible.