I am working in the Empirical Inference group as a Ph.D. student associated with the International Max Planck Research School for Intelligent Systems (IMPRS-IS). Currently I have two main research interests.
Theoretical questions in machine learning, with a particular focus in deep learning. Specifically I am using techniques from topics like "concentration inequalities", "optimal transport" and "tropical geometry" to provide a better theoretical understanding of so called "adversarial examples". Adversarial examples are specifically crafted modifications of real inputs (images, sounds, etc) that humans find indistinguishable from the original, but that are consistently misclassified by our programs. For example an image of a panda will be correctly classified but adding an imperceptible noise to it will lead the algorithm to classify it as a potato (Here it is possible to find a quick survey).
The intersection between machine learning and bayesian statistics, in particular variational methods. Together with Isabel Valera we are investigating how to improve variational techniques, like variational autoencoders (VAE). We are following two main approaches, first trying to develop better priors and second extend the VAE to the case of heterogeneous data.
Machine Learning Deep Learning Mathematics Statistical Learning Theory Bayesian Statistics
Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems