A one day conference at IHP
Room 314.
Researchers should send an email with affiliation for registration to
doukhan"at"cyu.fr,
A confirmation is necessary since the room is for 34 persons and a meal and a cocktail will be offered:
Registered researchers.
Program
- 9:00-10:00 Reception and Opening Gérard Bénarous (Courant Institute, NY)
- 10:00 Steffen Grünewälder (Newcastle University, UK).
- 11:00-12:00 Donatas Surgailis (Vilnius University).
- 12:00-13:00 Adam Jakubowski (Nicolas Copernic University, Torun).
- Cocktail Lunch
- 14:30-15:30 Tommaso Proietti (Rome Tor Vergata).
- 15:30-16:30 Victor de la Pena (Columbia, New York).
- 16:30-17:30 Mathieu Rosenbaum (Polytechnique, Palaiseau).
- 17:30-19:30 Cocktail
Link to this event on IHP site.
Abstracts
- Victor de la Pena.
Sharp Complete Decoupling: Old and New Results.
Traditional decoupling inequalities replace dependent random variables by ''conditional'' independent random variables. In contrast complete decoupling inequalities compare dependent variables to completely independent random variables.- Steffen Grünewälder. Large scale statistics.
Let {d_{𝑖}, 𝑖 = 1, ..., 𝑛} be a sequence of dependent random variables. Let also {y_{𝑖}, 𝑖 = 1, ..., 𝑛} be a sequence of independent variables where for each 𝑖, d_{𝑖} and y_{𝑖} have the same marginal distributions.
Since E d_{𝑖} = E y_{𝑖}, linearity of expectations leads to the complete decoupling equality
E sum d_{𝑖} = E sum y_{𝑖}.
A natural question arises: How far can one extend this phenomenon?
It turns out that Complete Decoupling ''inequalities'' are valid (up to constants) to the case of Concave and Convex functions of sums of dependent variables .
In this talk I will present several sharp complete decoupling inequalities for sums and maximums as well as some of their applications.
In ecology you often have to deal with large amounts of data and classical methods like Support Vector Machines (SVMs), which are often used for analysing ecological data, are unable to profit from such large amounts of data. In this talk I’ll discuss an approach for compressing the empirical measure in the context of finite dimensional reproducing kernel Hilbert spaces. In this context, the empirical measure is contained within a natural convex set and can be approximated using convex optimization methods. Such an approximation gives, under certain conditions, rise to a small coreset of data points which allows methods like SVMs to process significantly larger data sets without loss in predictive quality. A key quantity that controls how large such a coreset has to be is the size of the largest ball around the empirical measure that is contained within the empirical convex set. I will give a high-level overview of how high probability lower bounds on the size of such a ball can be derived before discussing how these approaches can be adapted to common statistical problems like regression.
- Adam Jakubowski. Multivariate phantom distributions.
The notion of a phantom distribution function was introduced by O’Brien (1987). The theory of phantom distribution functions was developed in [2] and perfected in [1]. In the present lecture we first essentially extend the notion of the extremal index by defining the lower and the upper extremal indices. Then we provide an example of a stationary sequence with continuous phantom distribution function for which both indices are non-zero and different. This example shows another advantage of the techniques based on phantom distribution functions over the classical approach involving the extremal index. Motivated by such arguments we develop the corresponding theory for stationary random vectors. The obtained notion is more complicated than in the one-dimensional case, but still tractable numerically. This is a joint work with Thomas Mikosch, Igor Rodionov and Natalia Soja-Kukiela.
[1] P. Doukhan, A. Jakubowski and G. Lang, Phantom distribution functions for some stationary sequences, Extremes, 18 (2015), 697—725.
[2] A. Jakubowski, An asymptotic independent representation in limit theorems for maxima of nonstationary random sequences, Ann. Probab., 21 (1993), 819—830.
- Tommaso Proietti. Another Look at Dependence: the Most Predictable Aspects of Time Series.
Serial dependence and predictability are two sides of the same coin. The literature has considered alternative measures of these two fundamental concepts. In this paper we aim at distilling the most predictable aspect of a univariate time series, i.e., the one for which predictability is optimized. Our target measure is the mutual information between past and future of a random process, a broad measure of predictability that takes into account all future forecast horizons, rather than focusing on the one-step-ahead prediction error mean square error. The first most predictable aspect is defined as the measurable transformation of the series for which the mutual information between past and future is a maximum. The proposed transformation arises from of the linear combination of a set of basis functions localized at the quantiles of the unconditional distribution of the process. The mutual information is estimated as a function of the sample partial autocorrelations, by a semiparametric method which estimates an infinite sum by a regularized finite sum. The second most predictable aspect can also be defined, subject to suitable orthogonality restrictions. We also investigate the use of the most predictable aspect for testing the null of no predictability. Preprint.
Keywords:Mutual information, Nonlinear dependence, Canonical Analysis.
- Mathieu Rosenbaum . From earthquakes to understanding
financial risks via football:
around statistical modeling by Hawkes processes.
The purpose of this talk is to illustrate the relevance and flexibility of Hawkes processes as a modeling tool for many statistical problems. We will show in particular how these have made it possible to revisit our understanding of the dynamics of risks in finance and to create new, more effective quantitative management approaches. We will also discuss their use for the analysis of sports data in the context of the construction of performance metrics.
- Donatas Surgailis.
Scaling limits of nonlinear functions of random grain model
with application to Burgers' equation.
We study scaling limits of nonlinear functions G of random grain model X on R^{d} with long-range dependence and marginal Poisson distribution. Following Kaj et al. (2007) we assume that the intensity M of the underlying Poisson process of grains increases together with the scaling parameter λ as M = λ^{γ}, for some γ > 0. The results are applicable to the Boolean model and exponential G and rely on an expansion of G in Charlier polynomials and a generalization of Mehler's formula. Application to solution of Burgers' equation with initial aggregated random grain data is discussed.