Workshop on Statistics in Metric Spaces


The workshop on Statistics in Metric Spaces was held at ENSAE, on October 11, 12 and 13, 2023. It brought together international experts in the joint fields of statistics, optimization, probability theory and geometry. Each participant gave a 45-60 min talk and the range of topics that were covered was broad, tackling modern questions concerning statistical analysis on non-standard spaces.

Victor-Emmanuel Brunel (CREST-ENSAE), Christopher Criscitiello (EPFL), Stephan Huckemann (Georg-August-Universität Göttingen), Alexey Kroshnin (Weierstrass-Institut Für Angewandte Analysis und Stochastik), Kazuhiro Kuwae (Fukuoka University), Tom Nye (Newcastle University), Shin-ichi Ohta (Osaka University), Miklós Pálfia (Corvinus University of Budapest), Pierre Pansu (Université Paris-Saclay), Quentin Paris (HSE University), Xavier Pennec (INRIA), Gabriel Romon (CREST-ENSAE), Jordan Serres (CREST-ENSAE), Austin Stromme (CREST-ENSAE)

 

While available data become more and more rich and complex, it is essential to understand their intrinsic geometry, for instance as a tool of dimensionality reduction or, sometimes, in order to produce interpretable statistical procedures. This, however, also comes at a cost, since these geometries may be non-standard (e.g., non-linear and/or non-smooth geometries), yielding new challenges from the points of view of both statistical and algorithmic analysis.
For instance, directional data lie on spheres or projective spaces. In shape statistics, data are encoded as landmarks on three-dimensional objects, which should be invariant under rigid transformations: Hence, data lie in the quotient of a Euclidean space by a class of rigid transformations. In fact, such quotient spaces are also useful to understand statistical models that arise in econometrics, when a parameter is only identifiable up to some known transformations. Optimal transport theory is based on Wasserstein spaces, which are metric spaces with Riemannian/Finsler-like geometries. In various fields, in particular physics and economics, the geometry provided by optimal transport on sets of probability measures has been shown to be very well adapted to understand general phenomena, such as transportation of goods, or distribution of tasks, capital, etc. In the machine learning community, it has also been recently pointed out that metric trees and hyperbolic spaces, which exhibit negative curvature, are well adapted to encode data with hierarchical structures.

While probability theory is now fairly well understood in smooth, finite dimensional spaces (such as Euclidean spaces and Riemannian manifolds), much less is known in more general metric spaces, exhibiting possible infinite dimension (such as functional spaces), inhomogeneous structure (such as stratified spaces), etc. From a more algorithmic prospective, gradient flows and their discretization in non-smooth spaces are challenging because they require brand new approaches (e.g., new definitions of (sub)-gradients), yet they are essential in order to extend fundamental tools such as gradient descent algorithms to non-standard setups. Even in smooth spaces, the impact of curvature on gradient descent algorithms is still not clearly understood. More generally, the notion of convexity, which is pervasive to probability theory, statistical learning and optimization, and its interplays with curvature, still raise challenging questions.

To summarize, the impact of curvature (or generalized notions of curvature) on measure concentration, on the statistical behavior of learning algorithms and on their computational aspects is a flourishing topic of research that brings together experts in smooth/non-smooth geometry, statistics, probability theory and optimization.

The workshop brought these challenges onto the stage, and yielded fruitful discussions among the participants and the audience, with the goal of entailing future collaborations. We hope that this workshop, on Statistics in Metric Spaces, was the first edition of a long series, that will also spread interest in these rich topics into a broader audience.

2023 ENSAE-ENSAI Days


On September 12 and 13, statisticians from both campuses of CREST (Bruz, ENSAI and Palaiseau, ENSAE) as well as statisticians from INSEE gathered for the Statistical workshop ENSAE-ENSAI at Palaiseau to present their current work. The event was organized by Victor-Emmanuel Brunel, Professor in Statistics ENSAE/CREST and Adrien Saumard, Associate Professor in Statistics ENSAI/CREST.

The primary objective of these meetings between statisticians from ENSAE and ENSAI, as well as statisticians from INSEE, is to enhance exchanges and foster collaborations between the two CREST campuses and INSEE. The event featured participants delivering 30-minute presentations.

Statistical insights from the CREST workshop

On the first day of the workshop, a diverse range of topics in statistics was explored through a series of presentations. Researchers delved into intriguing subjects such as preemption and learning in stochastic scheduling, determinantal sampling designs, and the theoretical perspective and practical solutions related to kernel Stein discrepancy thinning. The day also featured discussions on dynamic modeling of abundance data in ecology, non-parametric intensity estimation of spatial point processes employing random forests, and the complexities of repeated bidding with dynamic value. Additionally, topics like adaptive functional principal components analysis, learning patterns within multivariate functional data, and the concentration of empirical barycenters in non-positively curved metric spaces contributed to a rich and stimulating day of statistical exploration and research.

The second day of the workshop continued to offer a diverse array of statistical topics and insights. Researchers engaged in discussions about scalable and hyper-parameter-free covariate shift adaptation through a conditional sampling approach, contributing to the field’s adaptability and scalability. Another session explored risk-aware bandits with implications for improving crop management practices, bridging statistical methods with real-world applications. The day also delved into “Topics on methodology for official statistics,” providing valuable insights into the methodological considerations for producing authoritative statistical information. In addition, there were discussions on “Learning the smoothness of weakly dependent functional time series,” a crucial topic in understanding data patterns. Lastly, the finite-sample performance of the maximum likelihood estimator in logistic regression was explored, shedding light on the practical applications of statistical techniques in this context. The second day continued to enrich the workshop with a broad spectrum of statistical research and its real-world implications.

CREST: a collaboration between Bruz (ENSAI) and Palaiseau (ENSAE Paris) campuses

The recent statistics workshop held at ENSAE Paris exemplified the collaborative spirit between our campuses in Bruz at ENSAI and Palaiseau. This event provided researchers from both locations with a unique opportunity to connect, share ideas, and contribute to the advancement of statistical research. It underscored the enduring commitment to knowledge exchange and academic synergy that characterizes the partnership between our two campuses.

2023 France-Berkeley Fund: 2 recipients from the CREST


The France-Berkeley Fund

Established in 1993 as a partnership with the French Ministry of Foreign Affairs, the France-Berkeley Fund (FBF) promotes and supports scholarly exchange in all disciplines between faculty and research scientists at the University of California and their counterparts in France.

Through its annual grant competition, the FBF provides seed money for innovative, bi-national collaborations. The Fund’s core mission is to advance research of the highest caliber, to foster interdisciplinary inquiry, to encourage new partnerships, and to promote lasting institutional and intellectual cooperation between France and the United States.

2023-2024 Call: 2 CREST recipients

For the 2023-2024 call, 2 projects have been submitted and are getting funded:

• Decentralizing divorces
A project developed by Matias Nunez (CREST, CNRS Research fellow) and his counterpart Federico Echenique, Professor of Economics and Social Sciences at UC Berkeley.

Abstract:
This project focuses on the development of practical applications of mechanism design, a branch of economics concerned with developing well-functioning institutions that ensure efficient and fair outcomes. In particular, we will focus on legal settings where two persons need to reach an agreement while their preferences are misaligned. Examples are dissolution of partnerships, allocation of rights and duties among conflicting agents, and divorces. While a judge, legal experts and lengthy bargaining procedures are often needed in practice, we plan to develop economic tools to appraise reasonable compromises, reducing both cost and time.

• Towards Local, Distribution-Free and Efficient Guarantees in Aggregation and Statistical Learning
A project developed by Jaouad Mourtada (CREST, ENSAE Paris) and his counterpart Nikita Zhivotovskiy, Assistant Professor in Statistics at UC Berkeley.

Description:
Statistical learning theory is dedicated to the analysis of procedures for learning based on data. The general aim is to understand what guarantees on the prediction accuracy can be obtained, under which conditions and by which procedures. It can inform the design of sound and robust methods, that can withstand corruption in the data or departure from an idealized posited model, without sacrificing accuracy or efficiency in more favorable situations. In particular, the problem of aggregation can be formulated as follows: given a class of predictors and a sample, form a new predictor that is guaranteed to have an accuracy approaching that of the best predictor within the class, up to an error that should be as small as possible.
This problem can be cast in several settings and has been investigated through various angles in Statistics and Computer Science. While the topic is classical, it has seen a renewed interest through (for instance) the recent direction of robust statistical learning, which raises the question of the most general conditions under which a good accuracy can be achieved. Despite important progress, several important and basic questions have remained unanswered in the literature, which we aim to study.

CREST, a multidisciplinary laboratory


On June 19, 2023, CREST organized a day dedicated to doctoral students was held.

At this event, doctoral students from the 4 research divisions (economics, sociology, finance-insurance and statistics) were able to exchange ideas with their colleagues and present their areas of research.

Multidisciplinarity…

CREST favors an interdisciplinary approach to tackling complex issues. This synergy between different areas of expertise enriches research and provides innovative perspectives in a variety of fields such as the sociology of work, public economics, green finance, political economy, statistical analysis of networks and many others.

Thanks to this multidisciplinary approach, the CREST laboratory fosters fruitful collaborations between researchers from different backgrounds, encouraging the emergence of innovative solutions to contemporary societal challenges.

Fields of research by division

… At all levels

CREST maintains a wide range of academic and industrial partnerships beyond its core themes. These enriching interdisciplinary collaborations help to provide innovative solutions and tackle complex challenges in a wide range of sectors. CREST works with financial institutions (Caisse des dépôts et consignation, La Banque Postale Asset Management, HSBC AM) and public institutions (Ile de France region) to examine the determinants and impacts of integrating environmental, social and governance issues into investment decisions or to assess their climate and sustainable finance action plans (City of Paris, Ile de France region).

These interdisciplinary partnerships demonstrate CREST’s commitment to tackling contemporary challenges by mobilizing a wide range of knowledge and expertise.

Doctoral studies at CREST 

Working in the CREST laboratory, doctoral students benefit from a stimulating environment, conducive to the exchange ideas and collaboration with researchers from a variety of backgrounds. This diversity of approaches fosters the acquisition of cross-disciplinary skills and enables doctoral students to develop a holistic vision of their field of study, strengthening their ability to conduct innovative research and meet the challenges of tomorrow.

2023 France-Berkeley Fund: 2 CREST recipients


The France-Berkeley Fund

Established in 1993 as a partnership with the French Ministry of Foreign Affairs, the France-Berkeley Fund (FBF) promotes and supports scholarly exchange in all disciplines between faculty and research scientists at the University of California and their counterparts in France.

Through its annual grant competition, the FBF provides seed money for innovative, bi-national collaborations. The Fund’s core mission is to advance research of the highest caliber, to foster interdisciplinary inquiry, to encourage new partnerships, and to promote lasting institutional and intellectual cooperation between France and the United States.

2023-2024 Call: 2 CREST recipients

For the 2023-2024 call, 2 projects have been submitted and are getting funded:

• Decentralizing divorces
A project developed by Matias Nunez (CREST, CNRS Research fellow) and his counterpart Federico Echenique, Professor of Economics and Social Sciences at UC Berkeley.

Abstract:
This project focuses on the development of practical applications of mechanism design, a branch of economics concerned with developing well-functioning institutions that ensure efficient and fair outcomes. In particular, we will focus on legal settings where two persons need to reach an agreement while their preferences are misaligned. Examples are dissolution of partnerships, allocation of rights and duties among conflicting agents, and divorces. While a judge, legal experts and lengthy bargaining procedures are often needed in practice, we plan to develop economic tools to appraise reasonable compromises, reducing both cost and time.

• Towards Local, Distribution-Free and Efficient Guarantees in Aggregation and Statistical Learning
A project developed by Jaouad Mourtada (CREST, ENSAE Paris) and his counterpart Nikita Zhivotovskiy, Assistant Professor in Statistics at UC Berkeley.

Description:
Statistical learning theory is dedicated to the analysis of procedures for learning based on data. The general aim is to understand what guarantees on the prediction accuracy can be obtained, under which conditions and by which procedures. It can inform the design of sound and robust methods, that can withstand corruption in the data or departure from an idealized posited model, without sacrificing accuracy or efficiency in more favorable situations. In particular, the problem of aggregation can be formulated as follows: given a class of predictors and a sample, form a new predictor that is guaranteed to have an accuracy approaching that of the best predictor within the class, up to an error that should be as small as possible.
This problem can be cast in several settings and has been investigated through various angles in Statistics and Computer Science. While the topic is classical, it has seen a renewed interest through (for instance) the recent direction of robust statistical learning, which raises the question of the most general conditions under which a good accuracy can be achieved. Despite important progress, several important and basic questions have remained unanswered in the literature, which we aim to study.

CREST, a multidisciplinary laboratory


On June 19, 2023, CREST organized a day dedicated to doctoral students was held.

At this event, doctoral students from the 4 research divisions (economics, sociology, finance-insurance and statistics) were able to exchange ideas with their colleagues and present their areas of research.

Multidisciplinarity…

CREST favors an interdisciplinary approach to tackling complex issues. This synergy between different areas of expertise enriches research and provides innovative perspectives in a variety of fields such as the sociology of work, public economics, green finance, political economy, statistical analysis of networks and many others.

Thanks to this multidisciplinary approach, the CREST laboratory fosters fruitful collaborations between researchers from different backgrounds, encouraging the emergence of innovative solutions to contemporary societal challenges

Fields of research by division

… At all levels

CREST maintains a wide range of academic and industrial partnerships beyond its core themes. These enriching interdisciplinary collaborations help to provide innovative solutions and tackle complex challenges in a wide range of sectors. CREST works with financial institutions (Caisse des dépôts et consignation, La Banque Postale Asset Management, HSBC AM) and public institutions (Ile de France region) to examine the determinants and impacts of integrating environmental, social and governance issues into investment decisions or to assess their climate and sustainable finance action plans (City of Paris, Ile de France region).

These interdisciplinary partnerships demonstrate CREST’s commitment to tackling contemporary challenges by mobilizing a wide range of knowledge and expertise.

Doctoral studies at CREST 

Working in the CREST laboratory, doctoral students benefit from a stimulating environment, conducive to the exchange ideas and collaboration with researchers from a variety of backgrounds. This diversity of approaches fosters the acquisition of cross-disciplinary skills and enables doctoral students to develop a holistic vision of their field of study, strengthening their ability to conduct innovative research and meet the challenges of tomorrow.

Bayes Comp 2023 15-17 March


Nicolas Chopin will give a presentation on March 15 at the third edition of the conference of the Bayesian Computation Section of the International Society for Bayesian Analysis