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Measuring dissimilarity with diffeomorphism invariance
Théophile Cantelobre · Carlo Ciliberto · Benjamin Guedj · Alessandro Rudi

Thu Jul 21 08:30 AM -- 08:35 AM (PDT) @ None

Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nyström sampling. Empirical experiments support the merits of DID.

Author Information

Théophile Cantelobre (Inria)
Théophile Cantelobre

PhD Candidate @ SIERRA Team (Inria Paris & Inria London Programme) I am interested in building machine learning methods that are provably efficient and useful in practice. I am a PhD candidate in Computer Science based in the SIERRA project-team (Inria Paris DI-ENS) and in the Inria London Programme, supervised by Alessandro Rudi and Benjamin Guedj. Before my PhD, I studied Mathematics & Engineering in a dual masters program between Mines ParisTech (Cycle Ingénieur Civil) and Sorbonne Université (M2A) in Paris, France. In the past, I worked on PAC-Bayes guarantess for structured prediction at Inria & UCL, and state estimation for underwater robotics at Schlumberger-Doll Research.

Carlo Ciliberto (University College London)
Benjamin Guedj (Inria and University College London)
Benjamin Guedj

Benjamin Guedj is a tenured research scientist at Inria (France) and a senior research scientist at University College London (UK). His main research areas are statistical learning theory, PAC-Bayes, machine learning and computational statistics. He obtained a PhD in mathematics from Sorbonne Université (formerly Université Pierre et Marie Curie, France) in 2013.

Alessandro Rudi (INRIA, École Normale Supérieure)

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