Modeling Moscow Institute of Physics and Technology
Workshop on Modern Statistics and Optimization
The workshop will be arranged at the Institute for Information Transmission Problems RAS, Moscow.
Organizers: V. Konakov, E. Mammen, V. Spokoiny
Local organizers: M. Chuyashkin, Yu. Dorn
Registration link http://goo.gl/forms/3DhSkS4Usd
Full program will be anounced later.
Two mini-course will be given at the Workshop.
Alexey Naumov (The Chinese University of Hong Kong, The Institute for Information Transmission Problems RAS and Lomonosov Moscow State University)
Mini-course: Recent developments in Random Matrix Theory
Since the pioneering work of E. Wigner published in 1955 Random Matrix Theory (RMT) became one the most popular mathematical disciplines.
Within the space of 60 years RMT has found its numerous applications in different areas of pure and applied mathematics, physics, biology and financial theory. In my short course I will be mostly interested in Wigner’s semicircle law in macroscopic and microscopic regimes and universality of local eigenvalues statistics. I will give an overview of some classical results and discuss recent developments appeared in the last 10 years. My talk will be partially based on joint results with F. Götze and A. Tikhomirov.
Marc Hoffmann (CREST)
Mini-course: Statistical analysis of transport-fragmentation models
10:00 - 11:30 Mark Hoffmann. Lecture – 1.
11:30 - 12:00 break
12:00 - 13:00 Plenary lecture by Enno Mammen
13:00 - 13:30 Evgeny Burnaev
Abstract: As contemporary software-intensive systems reach increasingly large scale, it is imperative that failure detection schemes be developed to help prevent costly system downtimes. A promising direction towards the construction of such schemes is the exploitation of easily available measurements of system performance characteristics such as average number of processed requests and queue size per time unit. In this work, we investigate a holistic methodology for detection of abrupt changes in time series data in the presence of quasi-seasonal trends and long-range dependence with a focus on failure detection in computer systems. We propose a trend estimation method enjoying optimality properties in the presence of long-range dependent noise to estimate what is considered “normal” system behaviour. To detect change-points and anomalies, we develop an approach based on the ensembles of “weak” detectors. We demonstrate the performance of the proposed change-point detection scheme using an artificial dataset, the publicly available Abilene dataset as well as the proprietary geoinformation system dataset.
13:30 - 14:30
14:30 - 16:00 Alexey Naumov. Lecture – 1.
16:00 - 16:30 break
16:30 - 17:00 Nikita Zhivotovskiy.
A new local complexity measure in classification
Abstract: We perform a refined analysis of the empirical risk minimization algorithm. We discuss a new complexity measure, based on fixed points of the certain empirical entropy.
17:00 - 17:30
Orthogonal series density estimation: lower bounds
In this talk I discuss the problem of constructing minimax lower bounds for the Sobolev balls corresponding to orthonormal systems of Laguerre and Hermite types.
17:30 - 18:00 Stefan Richter
Cross validation for linear locally stationary processes
For specific models such as the time varying autoregressive process
it is possible to describe the evolution of the entire process with a finite set of parameter curves.
We assume that the locally stationary time series model is known, but the parameter curves are not.
For estimation of the curves we use nonparametric kernel-type maximum likelihood estimates which depend on a smoothing parameter (bandwidth).
To the best of our knowledge the theoretical behaviour of data adaptive bandwidth choice methods for such estimates
has not been considered in the literature. We propose an adaptive bandwidth choice via cross validation,
and show that it is asymptotically optimal in a specific sense with respect to a Kullback-Leibler-type distance measure.
10:00 - 11:30 Mark Hoffmann. Lecture – 2.
11:30 - 12:00 break
12:00 – 12:30
Fedor Goncharov, Maxim Panov and Vladimir Spokoiny
Prior Impact in Bernstein-von Mises theorem
Abstract: In this work we investigate the Bernstein-von Mises phenomenon in nonparametric models with Gaussian priors.
The main results describe the accuracy of Gaussian approximation of the posterior distribution in terms of the so called effective dimension.
We also show the applicability of these results to density estimation and consider estimation of non-linear functionals of density.
12:30 - 13:00 Alexander Gasnikov
Huge-scale optimization: how can we use sparsity with randomization?
Abstract: In the talk we consider classical problem Ax = b and different (regulirized) relaxations of this problem. We reformulate this problem as a convex optimization problem (there are different ways to do it) and after that we investigate different approaches to solve this problem: randomized mirror descent, sum randomization method, accelearated random coordinate descent method and its dual variant etc. The main questions we will try to answer: how this randomized methods allows us to use sprasity of A?
In the second part of the talk we generalize the rezults mentioned above to sum type and max type functions with implicit affine-sparse structure.
13:00 - 14:00 Launch
14:00 - 15:30 Alexey Naumov. Lecture – 2.
15:30 - 16:00 break
16:00 - 16:30 Paris Quentin
16:30 - 17:00 Vladimir Panov
Statistical inference for fractional Levy processes and related models
17:00 - 17:30 Pavel Dvurechensky
Gradient and gradient-free methods for pagerank algorithm learning.
Abstract: In this talk we consider a web page ranking model based on markov chain. Transition probabilities in this model depend on unknown parameters which are to be found using experts information about pages relevance to a user query. The learning problem is stated as an optimization problem. We discuss two approaches for solution of this problem: random gradient-free and full gradient. We also study rate of convergence and memory amount which is needed for the proposed algorithms. This a joint work with L. Bogolubsky, A. Gasnikov, G. Gusev, Y. Nesterov, A. Raigorodskii, A. Tikhonov, M. Zhukovskii.
17:30 - 18:00 Konstantin Mishenko
Oracle inequality for offset Rademacher penalization
In the framework of statistical learning with square loss, we consider a penalty based on the offset Rademacher process. We prove oracle inequality for this model selection procedure, which provides us with fast rates of convergence.