Background
The concept of entropy has played a central role in information theory since it was introduced in a seminal paper of Shannon. It turns out that many common statistical distributions maximise entropy subject to different constraints. For instance, among densities on the real line with a fixed variance, the normal density maximises the entropy, while the uniform density achieves the maximal entropy among distributions supported on the unit interval. These beautiful properties have led to many important statistical applications of the estimation of entropy, e.g. in goodnessoffit testing, independent component analysis, image registration problems and many other areas. Moreover, the entropy functional has many close cousins, including the family of Renyi entropies, relative entropy (or KullbackLeibler divergence), mutual information and many others, which have all applications in a suite of diverse scientific fields. For example, empirical estimation of mutual information is a commonlyused primitive for machine learning applications such as fitting graphical models, as well as for understanding spike train analysis in neuroscience. Thus it is sometimes convenient, from a statistical point of view, to regard entropy as a special case of a class of nonlinear functionals.
Many different estimators of entropy have been proposed in the literature over the last 30 years or so, including methods based on sample spacings, histograms, kernel density estimates and nearest neighbours. However, this area has seen a surge of activity in the last couple of years, as researchers are starting to understand conditions under which we can hope to achieve minimax optimal rates of estimation, or even efficient estimation. These developments are less widely known than they should be, however, and further research is also required to provide a reliable set of methods for practitioners.
Workshop Description
The aim of this workshop is to bring together researchers from a range of backgrounds to present the latest work on the estimation of entropy and other functionals. Recent progress in the area has been made by researchers in a variety of fields, and we aim to foster a sense of community and collaboration across different disciplines.
All talks will be held in the Centre for Mathematical Sciences in Cambridge, UK, and will take place September 911, 2019.
Funding
We are grateful to the Peter Whittle Fund for support with this workshop.
Organisers
 Tom Berrett, Statistical Laboratory, University of Cambridge
 Nikolai Leonenko, School of Mathematics, Cardiff University
 Richard Lockhart, Department of Statistics and Actuarial Science, Simon Fraser University
 Richard Samworth, Statistical Laboratory, University of Cambridge
 Yihong Wu, Department of Statistics and Data Science, Yale University
Confirmed Speakers
 Tom Berrett
University of Cambridge
 Alex Carpentier
OttovonGuerickeUniversität Magdeburg
 Ismael Castillo
Sorbonne Université
 Olivier Collier
Université ParisNanterre  Chao Gao
University of Chicago
 Varun Jog
University of WisconsinMadison  Ioannis Kontoyiannis
University of Cambridge  PoLing Loh
University of WisconsinMadison  Alon Orlitsky
University of California San Diego  Mathew Penrose
University of Bath
 Yury Polyanskiy
Massachusetts Institute of Technology  Barnabás Póczos
Carnegie Mellon University  Judith Rousseau
University of Oxford  Zhiyi Zhang
University of North Carolina at Charlotte
Registration

Speakers and other participants should register for the workshop here.
Programme

The plan is for participants to arrive on the evening of Sunday 8th September. Talks will begin on the Monday morning and will finish before lunch on the Wednesday. There will be a workshop dinner in St John's College on the Monday evening. A detailed programme will be made available nearer the time.
Accommodation

Invited speakers will be staying at Murray Edwards College, which is a fiveminute walk from the Centre for Mathematical Sciences. Other participants may search for accommodation here.
Practical Information
Useful information on how to get to the Centre for Mathematical Sciences can be found here, and information on how to get to Cambridge can be found here.