Long time no see, Statisfaction!
I’m glad to write about my habilitation entitled Bayesian statistical learning and applications I defended yesterday at Inria Grenoble. This Habilitation à Diriger des Recherches (HDR) is the highest degree issued through a university examination in France. If I am to believe official texts, the HDR recognizes a candidate’s “high scientific level, the originality of approach in a field of science, ability to master a research strategy in a sufficiently broad scientific or technological field and ability to supervise young researchers”. No less! In French academia, HDR is a necessary condition for supervising a Ph.D., being a reviewer for a Ph.D., and applying to prof positions. Part of the process consists of writing a manuscript summarizing the research done since the Ph.D. Mine is organized in three parts:
Chapter 1. Bayesian Nonparametric Mixture Modeling. This chapter is devoted to mixture models that are central to Bayesian nonparametrics. It focusses on BNP mixture models for (i) survival analysis, (ii) image segmentation and (ii) ecotoxicological applications.
Chapter 2. Approximate Bayesian Inference. This chapter is concerned in large parts with computational aspects of Bayesian inference. It describes: (i) conditional approaches in the form of truncation-based approximations for the Pitman–Yor process and for completely random measures, (ii) a marginal approach based on approximations of the predictive distribution of Gibbs-type processes, (iii) an approximate Bayesian computation (ABC) algorithm using the energy distance as data discrepancy.
Chapter 3. Distributional Properties of Statistical and Machine Learning Models. This chapter is concerned with general distributional properties of statistical and machine learning models, including (i) sub-Gaussian and sub-Weibull properties, (ii) a prior analysis of Bayesian neural networks and (iii) theoretical properties of asymmetric copulas.
I defended with Alessandra Guglielmi (Politecnico di Milano), Éric Moulines (École polytechnique & Académie des Sciences), and Yee Whye Teh (University of Oxford & DeepMind) as reviewers, and Stéphane Girard (Inria), Anatoli Juditsky and Adeline Samson (both Université Grenoble Alpes) as examiners. A word cloud made of the authors cited in my manuscript bibliography shows how much my research directions have been shaped during my postdoc in Italy.
I reproduce here the (lengthy) acknowledgments from my manuscript that owes a lot to many people. I am very grateful to Alessandra Guglielmi, Éric Moulines and Yee Whye Teh for agreeing to be rapporteurs. It is an honor and a pleasure to know that one’s work is read and appreciated by researchers we highly think of. Thank you for devoting time to this manuscript, and for traveling to Grenoble in a period full of teachings (and what’s more, the day after a half-marathon for one of you). Alessandra, thank you for agreeing to open the ball with a presentation. Thank you, Adeline Samson, Anatoli Juditsky and Stéphane Girard for agreeing to be part of the jury.
Ghislaine Gayraud and Judith Rousseau, as well as Kerrie Mengersen: you showed me by example during my Ph.D. thesis how much exciting research was, and also and above all, thanks for supporting me in difficult times.
Igor Prünster, thank you for your confidence, and for the opportunity to join the Collegio Carlo Alberto, first in Turin and then in Milan, for a long postdoc made of new collaborations, (species) discoveries, and a new culture. The supervision, leaving a lot of room for autonomy, has allowed me to develop deep links with my colleagues at the Collegio, Antonio Lijoi, Bernardo Nipoti, Guillaume Kon Kam King, Stefano Favaro, Pierpaolo De Blasi, Matteo Ruggiero, Antonio Canale, Bertrand Lods, and Giovanni Pistone.
I thank the Fellowship Selection Committee of the Alan Turing Institute for not ranking me. This allowed me a posteriori to know the Brexit only “from the outside”.
Thank you, Florence Forbes, Stéphane Girard and Jean-Baptiste Durand for your welcome to Inria and for supporting my application, as well as Judith Rousseau, Kerrie Mengersen, Christian Robert, Peter Müller and Igor Prünster. My position at Inria and my collaborations and discussions with you and others in Grenoble, including Emmanuel Barbier, Michel Dojat, Alexis Arnaud, Pablo Mesejo, Jakob Verbeek, Julien Mairal, Maria Laura Delle Monache, Eugenio Cinquemani, Wilfried Thuiller, Sophie Achard, Simon Barthelmé, Michael Blum, Adeline Samson, have allowed me to broaden my interests in statistics: extreme values, copulas, graphic models including Markov fields, deep learning, expectation-propagation (yes Simon, I should program it one day to understand EP) as well as applications in neuroimaging, road traffic, ecology such as joint species distribution models, etc. Jakob, Wilfried, and Eugenio: thank you for having me kindly, but repeatedly, encouraged to take the HDR.
I have had the opportunity to exchange and collaborate with many students over the past two years in Inria, Marta Crispino, Hongliang Lü, Riccardo Corradin, Łukasz Rajkowski, Mariia Vladimirova, Verónica Muñoz Ramírez, Fabien Boux, Caroline Lawless, Aleksandra Malkova, Michał Lewandowski, Daria Bystrova, Giovanni Poggiato, Sharan Yalburgi. I appreciate your dynamism, and I know I’m lucky to have (had) you here at Inria. I also learned a lot in our discussions with the visits of more seniors ones, Bernardo Nipoti (present at Mistis “every other week” thanks to Ulysses, among others), Guillaume Kon Kam King, Olivier Marchal, Rémi Bardenet, Jean-Bernard Salomond, Botond Szabó, Eric Marchand, Robin Ryder, Hien Nguyen, Nicolas Lartillot, Alisa Kirichenko, and Matteo Sesia.
Thank you Stephen Walker, Peter Müller for your welcome to UT Austin in the spring of 2017, these three months have been extremely productive; thank you Matti Vihola, Éric Parent, Didier Fraix-Burnet for your invitations to present Bayesian statistics courses in summer schools, and Richard Nickl, Hanne Kekkonen, Fabrizio Ruggeri, Bernardo Nipoti, Roberto Cassarin, Raffaele Argiento, Pierre Chainais, Alice Cleynen, François Sillion, Kerrie Mengersen, Antonio Lijoi, Matteo Ruggiero, Mame Diarra Fall, Bruno Gaujal, Jim Griffin, Silvia Montagna, Fabrizio Leisen, Jean-François Cœurjolly, Eric Marchand, Rebecca Steorts, Anne-Laure Fougères, Adeline Samson, Bas Kleijn, Sara Wade, Aurore Lavigne, Jean-Bernard Salomond, Célestin Kokonendji, Florence Forbes, Christophe Biernacki, Igor Prünster, Nicolas Chopin, François Caron, Michele Guindani, for your invitations to present at conferences or seminars. Thank you Michele Guindani and Hien Nguyen for offering me to join editorial boards of great journals. Thank you Pierre Jacob, Jérôme Le and Robin Ryder for putting Statisfaction into orbit in 2010 (what, it’s already been nine years?!?). This blog has been an excellent means of expression during my Ph.D. thesis and still is today.
I would particularly like to thank my co-authors, all of whom are already mentioned above, whose texts are included in the HDR manuscript, sometimes without them even knowing. I have learned a lot about your subjects, but above all these joint projects have been unforgettable moments spent together.
Finally, thank you to my family; thank you Christelle, my matching prior (by slightly paraphrasing Xian in his Bayesian Choice), for your constant support; thank you Jeanne and Léonie, our two cherished pseudo-random observations, our beloved chattering starlets who know so well how to take us away from our equations and computer screens and bring us back to real life.
Statisfaction 