AISTATS*2012 Invited Speakers

Sir David Cox

Nuffield College, Oxford

Examples will be given of the statistical analysis of data and of the general principles involved. Similarities and distinctions between approaches in the statistical and machine learning-AI literatures will be sketched.

Bio: Sir David Cox was educated at St John's College, Cambridge (MA), and the University of Leeds (PhD). After working in industry, he held academic posts at Cambridge and Birkbeck College, London. In 1966 he became Professor of Statistics, and in 1970 Head of the Mathematics Department, at the Imperial College of Science and Technology. He is a former Warden (1988-94) and an honorary Fellow of Nuffield College, Oxford. He is a Fellow and former Member of Council of the Royal Society and was President of the International Statistical Institute from 1995 to 1997. He holds a number of awards, including honorary Fellowships at St John's College, Cambridge, and the British Academy, the Guy Medal (in Silver and in Gold) from the Royal Statistical Society, and the degree of DSc from a number of universities. He has also been awarded the Weldon Memorial Prize, University of Oxford, and the Kettering Prize and Gold Medal for Cancer Research. He is a Foreign Honorary Member of the US National Academy of Sciences. He was editor of Biometrika from 1966 to 1991.

Rien van de Weygaert

Kapteyn Institute, University of Groningen

Over the past decades a clear paradigm has emerged as large redshift surveys opened the window onto the distribution of matter in our Local Universe: galaxies, intergalactic gas and dark matter exist in a wispy weblike spatial arrangement consisting of dense compact clusters, elongated filaments, and sheetlike walls, amidst large near-empty void regions. The Cosmic Web is the fundamental spatial organization of matter on scales of a few up to a hundred Megaparsec, scales at which the Universe still resides in a state of moderate dynamical evolution.

While the complex intricate structure of the cosmic web contains a wealth of cosmological information, its quantification has remained a major challenge. In this lecture, we describe our effort to measure key topological parameters. To this end, we resort to the homology of the weblike structure, and determine the scale-dependent Betti numbers. For 3-D structures they count the number of components, tunnels and enclosed voids. Out study includes a study of persistence and persistent homology, which entails the conceptual framework for separating scales of a spatial structure. To infer this from the discrete spatial galaxy distribution (or of particles in computer models of cosmic structure formation) we extract the homology from alpha shapes. Alphashapes were introduced by Edelsbrunner to formalize the concept of "shape" for a spatial point dataset. At large value of alpha corresponds to the convex hull of the dataset, while as alpha shrinks the alphashape assumes cavities which may join to form tunnels and voids.

We have studied the alpha complex of the cosmic weblike point patterns, in order to assess the signature of filaments, walls and voids. The physical interpretation of the obtained scale-dependence of Betti numbers is determined from a range of cellular point distributions. The findings from the Voronoi clustering models is used to analyze the outcome of cosmological N-body simulations and the SDSS galaxy redshift survey.

Bio: Rien van de Weygaert studied astronomy and physics at the University of Leiden, where he obtained his PhD cum laude in 1991 on "Voids and the Geometry of Large Scale Structure". Subsequently, he worked as an NSERC fellow at the Canadian Institute of Astrophysics (CITA) in Toronto, Canada and as a research fellow at the Max Planck Institut für Astrophysik in Garching, Germany before taking up a KNAW fellowship at the Kapteyn Astronomical Institute at the University of Groningen. Since 2004 he is professor of cosmological structure formation at the Kapteyn Insitute. His research interests concern cosmology, the large scale Universe and the formation of structure in the Universe, as well as computational geometry and topology and pattern recognition. Within these research subjects he has had a particular interest in the formation and dynamics of the Cosmic Web, the complex network of interconnected filamentary galaxy associations that pervades our universe on scales of tens to hundreds of million lightyears, and the existence and evolution of voids, the large near empty regions in between these structures. For the analysis of this structure, he has been working on a diverse array of tools based on Voronoi and Delaunay tessellations and related geometric concepts, finding that they provide a highly versatile means of tracing the complex structures seen in the Universe. Recently he started to wander into the history of astronomy, via a research project on world's oldest astronomical and mechanical computer, the Antikythera mechanism from ancient Greek times.

Gábor Lugosi

ICREA and Pompeu Fabra University, Barcelona

We consider the problem of finding information in high-dimensional noisy data. Our goal is to understand the possibilities and limitations of such correlation detection problems. The mathematical analysis reveals some interesting phase transitions. We also discuss an interesting connection with random geometric graphs.

Bio: Gábor Lugosi graduated in electrical engineering at the Technical University of Budapest in 1987, and received his Ph.D. from the Hungarian Academy of Sciences in 1991. Since 1996, he has been at the Department of Economics, Pompeu Fabra University. In 2006 he became an ICREA research professor. His research interest includes learning theory, nonparametric statistics, inequalities in probability, random structures, and information theory.