Publications

Monographs

  • H.-G. Bartel, H.-J. Mucha, Chapter 2: Incomparability/Inequality Measures and Clustering, in: Partial Order Concepts in Applied Sciences, M. Fattore, R. Brüggemann, eds., Springer International Publishing, New York, 2017, pp. 21--34, (Chapter Published).

  • CH. Bayer, J.G.M. Schoenmakers, Option Pricing in Affine Generalized Merton Models, in: Advanced Modelling in Mathematical Finance -- In Honour of Ernst Eberlein, J. Kallsen, A. Papapantoleon , eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing Switzerland, Cham, 2016, pp. 219--239, (Chapter Published).
    Abstract
    In this article we consider affine generalizations of the Merton jump diffusion model Merton (1976) and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in Belomestny, Kampen, Schoenmakers (2009). We conclude with some numerical examples.

  • P. Friz, P. Gassiat, Geometric Foundations of Rough Paths, in: Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, D. Barilari , U. Boscain , M. Sigalotti, eds., 2 of EMS Series of Lectures in Mathematics, European Mathematical Society, Zurich, Switzerland, 2016, pp. 171--210, (Chapter Published).

Articles in Refereed Journals

  • F. Anker, Ch. Bayer, M. Eigel, M. Ladkau, J. Neumann, J.G.M. Schoenmakers, SDE based regression for random PDEs, SIAM Journal on Scientific Computing, 39 (2017) pp. A1168--A1200.
    Abstract
    A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.

  • F. Anker, Ch. Bayer, M. Eigel, J. Neumann, J.G.M. Schoenmakers, A fully adaptive interpolated stochastic sampling method for linear random PDEs, International Journal for Uncertainty Quantification, 7 (2017) pp. 189--205, DOI 10.1615/Int.J.UncertaintyQuantification.2017019428 .
    Abstract
    A numerical method for the fully adaptive sampling and interpolation of PDE with random data is presented. It is based on the idea that the solution of the PDE with stochastic data can be represented as conditional expectation of a functional of a corresponding stochastic differential equation (SDE). The physical domain is decomposed subject to a non-uniform grid and a classical Euler scheme is employed to approximately solve the SDE at grid vertices. Interpolation with a conforming finite element basis is employed to reconstruct a global solution of the problem. An a posteriori error estimator is introduced which provides a measure of the different error contributions. This facilitates the formulation of an adaptive algorithm to control the overall error by either reducing the stochastic error by locally evaluating more samples, or the approximation error by locally refining the underlying mesh. Numerical examples illustrate the performance of the presented novel method.

  • A. Andresen, V. Spokoiny, Convergence of an alternating maximization procedure, Journal of Machine Learning Research (JMLR). MIT Press, Cambridge, MA. English, English abstracts., 53 (2017) pp. 389--429, DOI 10.1214/15-AIHP720 .

  • A. Anikin, A. Gasnikov, P. Dvurechensky, A. Turin, A. Chernov, Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints, Computational Mathematics and Mathematical Physics, 57 (2017) pp. 1262--1276.

  • H.-G. Bartel, H.-J. Mucha, Seriation und Clusteranalyse von Objekten mit binären Merkmalen, erläutert am Beispiel von Götterdarstellungen des Löwentempels von Musawwarat es Sufra (Sudan), Berliner Beiträge zur Archäometrie, (2017) pp. 21--38.

  • D. Belomestny, H. Mai, J.G.M. Schoenmakers, Generalized Post--Widder inversion formula with application to statistics, Journal of Mathematical Analysis and Applications, 455 (2017) pp. 89--104.
    Abstract
    In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. As an application we consider the problem of statistical inference for variance-mean mixture models. We construct a nonparametric estimator for the mixing density based on the generalized Post-Widder formula, derive bounds for its root mean square error and give a brief numerical example.

  • Y. Nesterov, V. Spokoiny, Random gradient-free minimization of convex functions, Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, 17 (2017) pp. 527--566.
    Abstract
    Summary: In this paper, we prove new complexity bounds for methods of convex optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most nn times more iterations than the standard gradient methods, where nn is the dimension of the space of variables. This conclusion is true for both nonsmooth and smooth problems. For the latter class, we present also an accelerated scheme with the expected rate of convergence O(n2k2)O(n2k2), where kk is the iteration counter. For stochastic optimization, we propose a zero-order scheme and justify its expected rate of convergence O(nk1/2)O(nk1/2). We give also some bounds for the rate of convergence of the random gradient-free methods to stationary points of nonconvex functions, for both smooth and nonsmooth cases. Our theoretical results are supported by preliminary computational experiments.

  • P. Friz, J. Diehl, P. Gassiat, Stochastic control with rough paths, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 75 (2017) pp. 285--315, DOI 10.1007 /s00245-016-9333- 9 .

  • P. Friz, A. Shekhar, General rough integration, Lévy rough paths and a Lévy--Kintchine type formula, The Annals of Probability, 45 (2017) pp. 2707--2765, DOI 10.1214/16- AOP1123 .

  • H.-J. Mucha, Assessment of stability in partitional clustering using resampling techniques, Archives of Data Science Series A, 1 (2017) pp. 21--35, DOI 10.5445/KSP/1000058747/02 .

  • R. Hildebrand, Spectrahedral cones generated by rank 1 matrices, Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering, 64 (2016) pp. 349--397.

  • A. Kalinina, A. Suvorikova, V. Spokoiny, M. Gelfand, Detection of homologous recombination in closely related strains, Journal of Bioinformatics and Computational Biology, 14 (2016) pp. 1641001/1--1641001/12.

  • A. Andresen, V. Spokoiny, Convergence for an alternation maximization procedure, Journal of Machine Learning Research (JMLR). MIT Press, Cambridge, MA. English, English abstracts., 17 (2016) pp. 1--53.

  • D. Belomestny, J.G.M. Schoenmakers, Statistical inference for time-changed Lévy processes via Mellin transform approach, Stochastic Processes and their Applications, 126 (2016) pp. 2092--2122.

  • Z. Brzezniak, F. Flandoli, M. Maurelli, Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity, Archive for Rational Mechanics and Analysis, 221 (2016) pp. 107--142.

  • M. Deppe, K. Tabelow, J. Krämer, J.-G. Tenberge, P. Schiffler, S. Bittner, W. Schwindt, F. Zipp, H. Wiendl, S.G. Meuth, Evidence for early, non-lesional cerebellar damage in patients with multiple sclerosis: DTI measures correlate with disability, atrophy, and disease duration, Multiple Sclerosis Journal, 22 (2016) pp. 73--84, DOI 10.1177/1352458515579439 .

  • P.J.C. Dickinson, R. Hildebrand, Considering copositivity locally, Journal of Mathematical Analysis and Applications, 437 (2016) pp. 1184--1195.

  • J. Diehl, P. Friz, H. Mai, Pathwise stability of likelihood estimators for diffusions via rough paths, The Annals of Applied Probability, 26 (2016) pp. 2169--2192.
    Abstract
    We consider the estimation problem of an unknown drift parameter within classes of non-degenerate diffusion processes. The Maximum Likelihood Estimator (MLE) is analyzed with regard to its pathwise stability properties and robustness towards misspecification in volatility and even the very nature of noise. We construct a version of the estimator based on rough integrals (in the sense of T. Lyons) and present strong evidence that this construction resolves a number of stability issues inherent to the standard MLEs.

  • A. Gasnikov, P. Dvurechensky, V. Spokoiny, P. Stetsyuk, A. Suvorikova, Superposition of the balancing algorithm and the universal gradient method for search of the regularized Wasserstein barycenter and equilibria in multistage transport models, Proceedings of Moscow Institute of Physics and Technology, 8 (2016) pp. 5--24.

  • A.V. Gasnikov, P. Dvurechensky, Y.E. Nesterov, Stochastic gradient methods with inexact oracle, Proceedings of Moscow Institute of Physics and Technology, 8:1 (2016) pp. 41--91.

  • A. Gasnikov, P. Dvurechensky, I. Usmanova, On accelerated randomized methods, Proceedings of Moscow Institute of Physics and Technology, 8:2 (2016) pp. 67--100.

  • A. Gasnikov, P. Dvurechensky, Y. Dorn, Y. Maximov, Numerical methods for finding equilibrium flow distribution in Beckman and stable dynamics models, Rossiiskaya Akademiya Nauk. Matematicheskoe Modelirovanie, 28 (2016) pp. 40--64.

  • A. Gasnikov, P. Dvurechensky, Stochastic intermediate gradient method for convex optimization problems, Doklady Mathematics. Maik Nauka/Interperiodica Publishing, Moscow. English. Translation of the Mathematics Section of: Doklady Akademii Nauk. (Formerly: Russian Academy of Sciences. Doklady. Mathematics)., 93 (2016) pp. 148--151.

  • G.N. Milstein, J.G.M. Schoenmakers, Uniform approximation of the CIR process via exact simulation at random times, Advances in Applied Probability, 48 (2016) pp. 1095--1116.
    Abstract
    In this paper we uniformly approximate the trajectories of the Cox-Ingersoll-Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact simulation of the CIR dynamics at some deterministic time grid.

  • K. Schildknecht, K. Tabelow, Th. Dickhaus, More specific signal detection in functional magnetic resonance imaging by false discovery rate control for hierarchically structured systems of hypotheses, PLOS ONE, 11 (2016) pp. e0149016/1--e0149016/21, DOI 10.1371/journal.pone.0149016 .

  • H.U. Voss, J.P. Dyke, K. Tabelow, N. Schiff, D. Ballon, Magnetic resonance advection imaging (MRAI) of cerebrovascular pulse dynamics, Journal of Cerebral Blood Flow and Metabolism, pp. , DOI 10.1177/0271678x16651449 .

  • M. Deliano, K. Tabelow, R. König, J. Polzehl, Improving accuracy and temporal resolution of learning curve estimation for within- and across-session analysis, PLOS ONE, 11 (2016) pp. e0157355/1--e0157355/23, DOI 10.1371/journal.pone.0157355 .
    Abstract
    Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. In this approach, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors for single subjects as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from a shuttle-box avoidance experiment with Mongolian gerbils, our approach revealed performance changes occurring at multiple temporal scales within and across training sessions which were otherwise obscured in the conventional analysis. The proper assessment of the behavioral dynamics of learning at a high temporal resolution clarified and extended current descriptions of the process of avoidance learning. It further disambiguated the interpretation of neurophysiological signal changes recorded during training in relation to learning.

  • CH. Bayer, A. Moraes, R. Tempone, P. Villanova, An efficient forward-reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks, Stochastic Analysis and Applications, 34 (2016) pp. 193--231.

  • CH. Bayer, P. Friz, J. Gatheral, Pricing under rough volatility, Quantitative Finance, 16 (2016) pp. 887--904.
    Abstract
    From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum [SSRN 2509457, 2014] previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated volatility. We analyze in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.

  • CH. Bayer, P. Friz, S. Riedel, J.G.M. Schoenmakers, From rough path estimates to multilevel Monte Carlo, SIAM Journal on Numerical Analysis, 54 (2016) pp. 1449--1483.
    Abstract
    Discrete approximations to solutions of stochastic differential equations are well-known to converge with strong rate 1/2. Such rates have played a key-role in Giles' multilevel Monte Carlo method [Giles, Oper. Res. 2008] which gives a substantial reduction of the computational effort necessary for the evaluation of diffusion functionals. In the present article similar results are established for large classes of rough differential equations driven by Gaussian processes (including fractional Brownian motion with H>1/4 as special case).

  • P. Dvurechensky, A. Gasnikov, Stochastic intermediate gradient method for convex problems with inexact stochastic oracle, Journal of Optimization Theory and Applications, 171 (2016) pp. 121--145.

  • P. Friz, B. Gess, A. Gulisashvili, S. Riedel, The Jain--Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory, The Annals of Probability, 44 (2016) pp. 684--738.
    Abstract
    We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11 (1983) 46?57]. This condition is verified in many examples, even in absence of explicit expressions for the covariance or Volterra kernels. Of special interest are random Fourier series, with covariance given as Fourier series itself, and we formulate conditions directly in terms of the Fourier coefficients. We also establish convergence and rates of convergence in rough path metrics of approximations to such random Fourier series. An application to SPDE is given. Our criterion also leads to an embedding result for Cameron?Martin paths and complementary Young regularity (CYR) of the Cameron?Martin space and Gaussian sample paths. CYR is known to imply Malliavin regularity and also Itô-like probabilistic estimates for stochastic integrals (resp., stochastic differential equations) despite their (rough) pathwise construction. At last, we give an application in the context of non-Markovian Hörmander theory.

  • P.K. Friz, P. Gassiat, P.-L. Lions, P.E. Souganidis, Eikonal equations and pathwise solutions to fully non-linear SPDEs, Stochastic Partial Differential Equations. Analysis and Computations, pp. , DOI 10.1007/s40072-016-0087-9 .

  • J. Polzehl, K. Tabelow, Low SNR in diffusion MRI models, Journal of the American Statistical Association, 11 (2016) pp. 1480--1490.
    Abstract
    Noise is a common issue for all magnetic resonance imaging (MRI) techniques such as diffusion MRI and obviously leads to variability of the estimates in any model describing the data. Increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from the true value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasi-likelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate the relevance of the problem using data from the Human Connectome Project.

Contributions to Collected Editions

  • TH. Koprucki, M. Kohlhaase, D. Müller, K. Tabelow, Mathematical models as research data in numerical simulation of opto-electronic devices, in: Numerical Simulation of Optoelectronic Devices (NUSOD), 2017, pp. 225-- 226, DOI 10.1109/NUSOD.2017.8010073 .
    Abstract
    Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the stationary one-dimensional drift-diffusion equations (van Roosbroeck system).

  • M. Kohlhase, Th. Koprucki, D. Müller, K. Tabelow, Mathematical models as research data via flexiformal theory graphs, in: Intelligent Computer Mathematics: 10th International Conference, CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceedings, H. Geuvers, M. England, O. Hasan, F. Rabe , O. Teschke, eds., Springer International Publishing, Cham, 2017, pp. 224--238, DOI 10.1007/978-3-319-62075-6_16 .
    Abstract
    Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution -- to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but non-trivial model: van Roosbroeck's drift-diffusion model for one-dimensional devices. This formalization -- and future extensions -- allows us to support the modeler by e.g. flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating MMS as "research data'' and opens the way towards more MKM services for models.

  • CH. Bayer, H. Oberhauser, Splitting methods for SPDEs: From robustness to financial engineering, optimal control and nonlinear filtering, in: Splitting Methods in Communication, Imaging, Science, and Engineering, R. Glowinski, S.J. Osher, W. Yin, eds., Scientific Computation, Springer International Publishing Switzerland, 2017, pp. 499--539.
    Abstract
    In this survey chapter we give an overview of recent applications of the splitting method to stochastic (partial) differential equations, that is, differential equations that evolve under the influence of noise. We discuss weak and strong approximations schemes. The applications range from the management of risk, financial engineering, optimal control and nonlinear filtering to the viscosity theory of nonlinear SPDEs.

  • H.-J. Mucha, T.M. Gluhak, Finding Groups in Compositional Data - Some Experiments, in: Big data clustering: Data preprocessing, variable selection, and dimension reduction, WIAS Report, 2017, pp. 97--105.
    Abstract
    The talk is concerned with finding groups (clusters) in compositional data, that is nonnegative data with row sums (or column sums, respectively) equal to a constant, usually 1 in case of proportions or 100 in case of percentages. Without loss of generality, the cluster analysis of observations (row points) of compositional data is considered here, where the row profiles contains parts of some whole. Special distance functions between the profiles are proposed. Finally, applications to archaeometry are presented.

  • N. Buzun, A. Suvorikova, V. Spokoiny, Multiscale parametric approach for change point detection, in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, pp. 979--996.

  • A. Anikin, A. Gasnikov, A. Garinov, P. Dvurechensky, V. Semenov, Parallelizable dual methods for searching equilibriums in large-scale mixed traffic assignment problems (in Russian), in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 85--89.

  • L. Bogulubsky, P. Dvurechensky, A. Gasnikov, G. Gusev, Y. Nesterov, A. Raigorodskii, A. Tikhonov, M. Zhukovskii, Learning supervised PageRank with gradient-based and gradient-free optimization methods, in: Advances in Neural Information Processing Systems 29, D.D. Lee, M. Sugiyama, U.V. Luxburg, I. Guyon, R. Garnett, eds., Curran Associates, Inc., 2016, pp. 4907--4915.

  • A. Chernov, P. Dvurechensky, A primal-dual first-order method for minimization problems with linear constraints, in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 41--45.

  • A. Chernov, P. Dvurechensky, A. Gasnikov, Fast primal-dual gradient method for strongly convex minimization problems with linear constraints, in: Discrete Optimization and Operations Research -- 9th International Conference, DOOR 2016, Vladivostok, Russia, September 19--23, 2016, Proceedings, Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, P. Pardalos, eds., 9869 of Theoretical Computer Science and General Issues, Springer International Publishing Switzerland, Cham, 2016, pp. 391--403.

  • J. Dolata, H.-G. Bartel , H.-J. Mucha, Naturwissenschaftliche Charakterisierung, mathematische Einordnung und archäologische Bewertung bislang unbekannter spätantiker römischer Ziegelstempel, in: Archäometrie und Denkmalpflege 2016, S. Greiff, A. Kronz, F. Schlütter, M. Prange, eds., Metalla, Sonderheft 8, Deutsches Bergbau-Museum Bochum, 2016, pp. 144--147.

  • K. Kraus, J. Dolata, T. Schade, H.-J. Mucha, H.-G. Bartel, Werkstoffuntersuchungen an einem barocken Kanal im Mainzer Bleichenviertel, in: Archäometrie und Denkmalpflege 2016, S. Greiff, A. Kronz, F. Schlütter, M. Prange, eds., Metalla, Sonderheft 8, Deutsches Bergbau-Museum Bochum, 2016, pp. 74--77.

  • P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, in: Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016), A. Kononov, I. Bykadorov , O. Khamisov , I. Davydov , P. Kononova , eds., 1623 of CEUR Workshop Proceedings, Technische Universität Aaachen, pp. 584--595.

  • P. Friz, P. Gassiat, Geometric foundations of rough paths, in: Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, Vol. 2, D. Barilari, U. Boscain, M. Sigalotti, eds., EMS Series of Lectures in Mathematics, European Mathematical Society, Zurich, 2016, pp. 171--210.

  • TH. Koprucki, K. Tabelow, Mathematical models: A research data category?, in: Mathematical Software -- ICMS 2016: 5th International Conference, Berlin, Germany, July 11--14, 2016, Proceedings, G.-M. Greuel, Th. Koch, P. Paule, A. Sommese, eds., Lecture Notes in Computer Science, Springer International Publishing AG Switzerland, Cham, 2016, pp. 423--428.
    Abstract
    Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines and application areas. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. In this contribution we propose a holistic approach to research data in MMS by including the mathematical models and discuss the initial requirements for a conceptual data model for this field.

  • H.-J. Mucha, H.-G. Bartel, Bottom-up variable selection in cluster analysis using bootstrapping: A proposal, in: Analysis of Large and Complex Data, A.F.X. Wilhelm, H.A. Kestler, eds., 51 of Studies in Classification, Data Analysis, and Knowledge Organization, Springer International Publishing, Heidelberg et al., 2016, pp. 125--135.

  • H.-J. Mucha, H.-G. Bartel , Ein Vorschlag zur Variablenselektion in der Clusteranalyse mit einer Anwendung auf p-RFA-Daten von bronzezeitlicher Keramik aus Corneşti-Larcuri (Rumänien), in: Archäometrie und Denkmalpflege 2016, S. Greiff, A. Kronz, F. Schlütter, M. Prange, eds., Metalla, Sonderheft 8, Deutsches Bergbau-Museum Bochum, 2016, pp. 136--139.

Preprints, Reports, Technical Reports

  • H.-J. Mucha, Big data clustering: Data preprocessing, variable selection, and dimension reduction, Report no. 29, WIAS, Berlin, 2017, DOI 10.20347/WIAS.REPORT.29 .
    PDF (20 MByte)

  • M. Redmann, Type II balanced truncation for deterministic bilinear control systems, Preprint no. 2425, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2425 .
    Abstract, PDF (248 kByte)
    When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is balanced truncation (BT), a method which has been extensively studied for deterministic linear systems. As so-called type I BT it has already been extended to bilinear equations, an important subclass of nonlinear systems. We provide an alternative generalisation of the linear setting to bilinear systems which is called type II BT. The Gramians that we propose in this context contain information about the control. It turns out that the new approach delivers energy bounds which are not just valid in a small neighbourhood of zero. Furthermore, we provide an ℋ∞-error bound which so far is not known when applying type I BT to bilinear systems.

  • CH. Bayer, P. Friz, A. Gulisashvili, B. Horvath, B. Stemper, Short-time near-the-money skew in rough fractional volatility models, Preprint no. 2406, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2406 .
    Abstract, PDF (450 kByte)
    We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter H < ½. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large deviation results of Forde-Zhang (2017) in a way that allows us to zoom-in around the money while maintaining full analytical tractability. More precisely, this amounts to proving higher order moderate deviation estimates, only recently introduced in the option pricing context. This in turn allows us to push the applicability range of known at-the-money skew approximation formulae from CLT type log-moneyness deviations of order t1=2 (recent works of Alòs, León & Vives and Fukasawa) to the wider moderate deviations regime.

  • V. Avanesov, N. Buzun, Change-point detection in high-dimensional covariance structure, Preprint no. 2404, WIAS, Berlin, 2017.
    Abstract, PDF (383 kByte)
    In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process ? a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality p  n). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.

  • M. Redmann, Type II singular perturbation approximation for linear systems with Lévy noise, Preprint no. 2398, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2398 .
    Abstract, PDF (347 kByte)
    When solving linear stochastic partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is singular perturbation approximation (SPA), a method which has been extensively studied for deterministic systems. As so-called type I SPA it has already been extended to stochastic equations. We provide an alternative generalisation of the deterministic setting to linear systems with Lévy noise which is called type II SPA. It turns out that the ROM from applying type II SPA has better properties than the one of using type I SPA. In this paper, we provide new energy interpretations for stochastic reachability Gramians, show the preservation of mean square stability in the ROM by type II SPA and prove two different error bounds for type II SPA when applied to Lévy driven systems

  • D. Belomestny, J.G.M. Schoenmakers, Projected particle methods for solving McKean--Vlaslov equations, Preprint no. 2341, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2341 .
    Abstract, PDF (320 kByte)
    We study a novel projection-based particle method to the solution of the corresponding McKean-Vlasov equation. Our approach is based on the projection-type estimation of the marginal density of the solution in each time step. The projection-based particle method can profit from additional smoothness of the underlying density and leads in many situation to a significant reduction of numerical complexity compared to kernel density estimation algorithms. We derive strong convergence rates and rates of density estimation. The case of linearly growing coefficients of the McKean-Vlasov equation turns out to be rather challenging and requires some new type of averaging technique. This case is exemplified by explicit solutions to a class of McKean-Vlasov equations with affine drift.

  • M. Redmann, M.A. Freitag, Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems, Preprint no. 2339, WIAS, Berlin, 2016.
    Abstract, PDF (718 kByte)
    When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.

  • R. Hildebrand, J.G.M. Schoenmakers, J. Zhang, F. Dickmann, Regression based duality approach to optimal control with application to hydro electricity storage, Preprint no. 2330, WIAS, Berlin, 2016, DOI 10.5072/WIAS.PREPRINT.2330 .
    Abstract, PDF (341 kByte)
    In this paper we consider the problem of optimal control of stochastic processes. We employ the dual martingale method brought forward in [Brown, Smith, and Sun, 2010]. The martingale constituting the solution of the dual problem is determined by linear regression within a Monte-Carlo approach. We apply the solution algorithm to a model of a hydro electricity storage and production system coupled with a model of the electricity wholesale market.

  • W. Dreyer, P. Friz, P. Gajewski, C. Guhlke, M. Maurelli, Stochastic model for LFP-electrodes, Preprint no. 2329, WIAS, Berlin, 2016.
    Abstract, PDF (1531 kByte)
    In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltagecharge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.

  • CH. Bayer, M. Siebenmorgen, R. Tempone, Smoothing the payoff for efficient computation of basket option prices, Preprint no. 2280, WIAS, Berlin, 2016.
    Abstract, PDF (272 kByte)
    We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 25.

  • R. Hildebrand, Copositive matrices with circulant zero pattern, Preprint no. 2241, WIAS, Berlin, 2016.
    Abstract, PDF (335 kByte)
    Let n be an integer not smaller than 5 and let u1,...,un be nonnegative real n-vectors such that the indices of their positive elements form the sets 1,2,...,n-2,2,3,...,n-1,...,n,1,...,n-3, respectively. Here each index set is obtained from the previous one by a circular shift. The set of copositive forms which vanish on the vectors u1,...,un is a face of the copositive cone. We give an explicit semi-definite description of this face and of its subface consisting of positive semi-definite matrices, and study their properties. If the vectors u1,...,un and their positive multiples exhaust the zero set of an exceptional copositive form belonging to this face, then we call this form regular, otherwise degenerate. We show that degenerate forms are always extremal, and regular forms can be extremal only if n is odd. We construct explicit examples of extremal degenerate forms for any order n, and examples of extremal regular forms for any odd order n. The set of all degenerate forms, i.e., defined by different collections u1,...,un of zeros, is a submanifold of codimension 2n, the set of all regular forms a submanifold of codimension n.

  • V. Avanesov, J. Polzehl, K. Tabelow, Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix, Preprint no. 2229, WIAS, Berlin, 2016.
    Abstract, PDF (522 kByte)
    In this paper we consider the adaptive l1-penalized estimators for the precision matrix in a finite-sample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments.

  • J. Borchardt, P. Mathé, G. Printsypar, Calibration methods for gas turbine performance models, Technical Report no. 16, WIAS, Berlin, 2016, DOI 10.20347/WIAS.TECHREPORT.16 .
    Abstract
    The WIAS software package BOP is used to simulate gas turbine models. In order to make accurate predictions the underlying models need to be calibrated. This study compares different strategies of model calibration. These are the deterministic optimization tools as non-linear least squares (MSO) and the sparsity promoting variant LASSO, but also the probabilistic (Bayesian) calibration. The latter allows for the quantification of the inherent uncertainty, and it gives rise to a surrogate uncertainty measure in the MSO tool. The implementation details are accompanied with a numerical case study, which highlights the advantages and drawbacks of each of the proposed calibration methods.

Talks, Poster

  • A. Suvorikova, Construction of confidence sets in 2-Wasserstein space, Haindorf Seminar 2017, January 24 - 28, 2017, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Hejnice, Czech Republic, January 26, 2017.

  • A. Suvorikova, Construction of non-asymptotic confidence sets in 2-Wasserstein space, Spring School ``Structural Inference'' 2017, Bad Malente, March 5 - 10, 2017.

  • A. Suvorikova, Statistical inference, WIAS-Day, Berlin, February 27 - 28, 2017.

  • N. Buzun, Bootstrap for multiple hypothesis testing, Spring School ``Structural Inference'' 2017, March 5 - 10, 2017, DFG Research Unit FOR 1735 ``Structural Inference in Statistic'', Bad Malente, March 6, 2017.

  • W. Dreyer, J. Fuhrmann, P. Gajewski, C. Guhlke, M. Landstorfer, M. Maurelli, R. Müller, Stochastic model for LiFePO4-electrodes, ModVal14 - 14th Symposium on Fuel Cell and Battery Modeling and Experimental Validation, Karlsruhe, March 2 - 3, 2017.

  • M. Maurelli, Regularization by noise for scalar conservation laws, Stochastic Analysis Day, February 25 - March 3, 2017, Universita' di Pisa, Dipartimento di Matematica, Italy, February 27, 2017.

  • P. Pigato, Estimation of the parameters of a diffusion with discontinuous coefficients, 7th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis, May 18 - 20, 2017, WIAS-Berlin, May 20, 2017.

  • M. Redmann, A regression method to solve parabolic rough PDEs, 7th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis, May 18 - 20, 2017, WIAS-Berlin, May 20, 2017.

  • M. Redmann, A regression method to solve parabolic rough PDEs, Ninth Workshop on Random Dynamical Systems, June 14 - 17, 2017, University of Bielefeld, Department of Mathematics, June 15, 2017.

  • M. Redmann, Type II singular perturbation approximation for linear systems with Levy noise, London Mathematical Society -- EPSRC Durham Symposium: Model Order Reduction, Durham University, Department of Mathematical Sciences, UK, August 14, 2017.

  • CH. Bayer, Numerics for rough volatility models, Ninth Workshop on Random Dynamical Systems, June 14 - 17, 2017, University of Bielefeld, Department of Mathematics, June 14, 2017.

  • CH. Bayer, Smoothing the payoff for efficient computation of basket option prices, Workshop ``Mathematics of Quantitative Finance'', February 26 - March 4, 2017, Mathematisches Forschungsinstitut Oberwolfach.

  • CH. Bayer, Smoothing the payoff for efficient computation of basket options, Workshop on Recent Developments in Numerical Methods with Applications in Statistics and Finance, June 8 - 9, 2017, University of Mannheim, Graduate School of Economics and Social Sciences, June 9, 2017.

  • CH. Bayer, Smoothing the payoff for efficient computation of basket options, Conference on Mathematical Modelling in Finance 2017, August 30 - September 2, 2017, Imperial College London, UK, September 2, 2017.

  • P. Dvurechensky, A unified view on accelerated randomized optimization methods: Coordinate descent, directional search, derivative-free method, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 17 - 19, 2017.

  • P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, Optimization and Statistical Learning, Les Houches, France, April 10 - 14, 2017.

  • P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 17 - 19, 2017.

  • P. Dvurechensky, Gradient method with inexact oracle for non convex optimization, 3rd Applied Mathematics Symposium Münster: Shape, Imaging and Optimization, February 28 - March 3, 2017.

  • P. Friz, A regularity structure for rough volatility, Global Derivates Trading & Risk Management, May 8 - 12, 2017, Barcelona, Spain, May 10, 2017.

  • P. Friz, An application of regularity structures to the analysis of rough volatility, Fractional Brownian Motion and Rough Models, June 8 - 9, 2017, Barcelona Graduate School of Economics, Spain, June 9, 2017.

  • P. Friz, Aspects of rough volatility, The 5th Imperial - ETH Workshop on Mathematical Finance, March 27 - 29, 2017, Imperial College London, Dept of Mathematics, UK, March 27, 2017.

  • P. Friz, General semimartingales and rough paths, Durham Symposium on Stochastic Analysis, July 10 - 20, 2017, Durham University, Department of Mathematical Sciences, Durham, UK, July 13, 2017.

  • P. Friz, Geometric aspects in pathwise stochastic analysis, High Risk High Gain - Groundbreaking Research in Berlin, Technische Universität Berlin, Stabsstelle Presse, July 20, 2017.

  • A. Koziuk, Bootstrap for the regression problem with instrumental variables, Haindorf Seminar 2017, January 24 - 28, 2017, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Hejnice, Czech Republic, January 26, 2017.

  • P. Mathé, Bayesian inverse problems with non-commuting operators, Statistical Foundations of Uncertainty Quantification for Inverse Problems Workshop, June 19 - 22, 2017, University of Cambridge, Center for Mathematical Sciences, UK, June 21, 2017.

  • P. Mathé, Complexity of supervised learning, ibc-paris2017 : Information Based Complexity, High-Dimensional Problems, March 14 - 15, 2017, Institut Henri Poincaré, Paris, France, March 15, 2017.

  • P. Mathé, Tikhonov regularization with oversmoothing penalty, 7th German Polish Conference on Optimization (GPCO 2017), Mathematical Research and Conference Center (MRCC) of IM PAN, Będlewo, Poland.

  • J. Polzehl, Connectivity networks in neuroscience - construction and analysis, Summer School 2017: Probabilistic and statistical methods for networks, August 21 - 22, 2017, Berlin Mathematical School (BMS).

  • J. Polzehl, Toward in-vivo histology of the brain, Neuro-Statisstics: the interface between Neuroscience, University of Minnesoata, School of Statistics (IRSA), Minneapolis, USA, May 5, 2017.

  • J.G.M. Schoenmakers, Projected particle methods for solving McKean-Vlasov SDEs, Dynstoch 2017, April 5 - 7, 2017, Universität Siegen, Department Mathematik, Fachgruppe Stochastik, April 6, 2017.

  • V. Spokoiny, Adaptive nonparametric clustering, Optimization and Statistical Learning, Les Houches, France, April 10 - 14, 2017.

  • V. Spokoiny, Adaptive nonparametric clustering, Statistical Recovery of Discrete, Geometric and Invariant Structures, March 21 - 24, 2017, Mathematisches Forschungsinstitut Oberwolfach, March 24, 2017.

  • V. Spokoiny, Gaussian approximation for a probability of a ball, Seminar Structural Learning, Russian Academy of Sciences, Kharkevich Institute for Information Transmission Problems, PreMoLab, Moscow, Russian Federation, June 5, 2017.

  • V. Spokoiny, Gaussian approximiation of the squared norm of a high dimensional vector, Structure Learning Seminar, Russian Academy of Sciences, Kharkevich Institute for Information Transmission Problems, PreMoLab, Russian Federation, May 18, 2017.

  • V. Spokoiny, Nonparametric estimation: parametric view, Advanced statistical methods, February 7 - 22, 2017, Independent University of Moscow, Russian Federation.

  • V. Spokoiny, Subset selection using the smallest accepted rule, Structure Learning Seminar, Russian Academy of Sciences, Kharkevich Institute for Information Transmission Problems, PreMoLab, Moscow, Russian Federation, April 6, 2017.

  • K. Tabelow, Ch. D'alonzo, L. Ruthotto, M.F. Callaghan, N. Weiskopf, J. Polzehl, S. Mohammadi, Removing the estimation bias due to the noise floor in multi-parameter maps, The International Society for Magnetic Resonance in Medicine (ISMRM) 25th Annual Meeting /& Exhibition, Honolulu, USA, April 22 - 27, 2017.

  • K. Tabelow, Ch. D'alonzo, J. Polzehl, Toward in-vivo histology of the brain, 2nd Leibniz MMs Days2017, Hannover, February 22 - 24, 2017.

  • K. Tabelow, High resolution MRI by variance and bias reduction, IBS Channel Network Conference 2017, April 24 - 26, 2017, Hasselt Univeristy, Diepenbeek, Belgium, April 25, 2017.

  • K. Tabelow, MRI data models at low SNR, 2nd Leibniz MMs Days2017, February 22 - 24, 2017, Leibniz Informationszentrum Technik und Naturwissenschaften Technische Informationsbibliothek, Hannover, February 24, 2017, DOI 10.5446/21910 .

  • K. Tabelow, To smooth or not to smooth in fMRI, Cognitive Neuroscience Seminar, Universitätsklinikum Hamburg-Eppendorf, Institut für Computational Neuroscience, April 4, 2017.

  • A. Suvorikova, Bootstrap confidence sets for Wasserstein barycenters, Meeting in Mathematical Statistics 2016 ``Advances in Nonparametric and High-dimensional Statistics'', December 12 - 16, 2016, Fréjus, France, December 16, 2016.

  • A. Suvorikova, Bootstrap procedure in the space of Gaussian measures, Information Technology and Systems 2016, September 25 - 30, 2016, Russian Academy of Sciences, Institute for Information Transmission Problems, St. Petersburg.

  • A. Suvorikova, Multiscale change point detection, Georg-August-Universität Göttingen, Institut für Mathematische Stochastik, November 9, 2016.

  • M. Zhilova, Choosing the number of samples in a Monte Carlo simulation using bootstrap, Workshop on Applied Statistics 2016, March 10 - 11, 2016, Technische Universität Dresden, Institut für Wirtschaft & Verkehr, March 10, 2016.

  • M. Zhilova, Some new non-asymptotic results about accuracy of the weighted bootstrap, Stochastics Seminar, Georgia Institute of Technology, School of Mathematics, Atlanta, USA, April 28, 2016.

  • N. Buzun, Multiplier bootstrap for change point detection, Mathematical Statistics and Inverse Problems, February 8 - 12, 2016, Faculté des Sciences de Luminy, France, February 11, 2016.

  • N. Buzun, Multiplier bootstrap for change point detection, Spring School ``Structural Inference 2016", March 13 - 18, 2016, DFG Forschergruppe FOR 1735, Lübeck, Germany, March 14, 2016.

  • R. Hildebrand, Barriers on symmetric cones, Bridging Gaps: The CORE@50 Conference, May 23 - 25, 2016, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, May 23, 2016.

  • R. Hildebrand, Canonical barriers on convex cones, Oberseminar Geometrische Analysis, Johann Wolfgang Goethe-Universität Frankfurt am Main, Fachbereich Mathematik, April 26, 2016.

  • R. Hildebrand, Periodic discrete dynamical systems and copositive matrices with circulant zero patterns, Optimization Without Borders, February 7 - 12, 2016, Les Houches, France, February 11, 2016.

  • R. Hildebrand, Periodic discrete dynamical systems and copositive matrices with circulant zero patterns, International Conference on Optimization: SIGOPT 2016, April 6 - 8, 2016, Universität Trier, Fachbereich Mathematik, April 6, 2016.

  • M. Maurelli, Enhanced Sanov theorem and large deviations for interacting particles, Workshop ``Rough Paths, Regularity Structures and Related Topics'', May 1 - 7, 2016, Mathematisches Forschungsinstitut Oberwolfach, May 5, 2016.

  • M. Maurelli, Enhanced Sanov theorem and robust propagation of chaos, Berlin--Leipzig Workshop in Analysis and Stochastics, April 13 - 15, 2016, Max Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, April 13, 2016.

  • M. Maurelli, Regularization by noise for continuity equation via Young drivers, Stochastic Partial Differential Equations and Applications, May 30 - June 2, 2016, Centro Internazionale per la Ricerca Matematica (CIRM), Levico, Italy, May 30, 2016.

  • M. Maurelli, Regularization by noise for linear SPDE's, Oberseminar Analysis -- Probability, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, January 26, 2016.

  • M. Maurelli, Regularization by noise for scalar conservation laws, Workshop Stochastic Analysis of Dynamical Systems, Sochastic Control and Games, October 24 - 26, 2016, University of Leeds, Faculty of Maths & Physical Science, UK, October 24, 2016.

  • M. Maurelli, Regularization by noise for scalar conservation laws, Mathematical Finance and Stochastic Analysis Seminars, University of York, UK, October 26, 2016.

  • M. Maurelli, Regularization by noise for stochastic scalar conservation laws, The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 41 ``Stochastic Partial Differential Equations'', July 1 - 5, 2016, The American Institute of Mathematical Science, Orlando (Florida), USA, July 4, 2016.

  • M. Maurelli, Regularization by noise for transport-type equations via stochastic exponentials, Workshop in Stochastic Analysis, June 28 - 30, 2016, Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica, Campinas, Brazil, June 29, 2016.

  • M. Maurelli , P. Gajewski, Stochastic methods for lithium-ion batteries, Matheon Center Days, April 11, 2016.

  • M. Redmann, Low order approximations to linear SPDEs with Lévy noise, 5th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis, August 12 - 15, 2016, WIAS Berlin /& TU Berlin, August 12, 2016.

  • M. Redmann, Model reduction for stochastic differential equations, Stochastic Analysis Seminar, University of Oxford, Mathematical Institute, UK, October 31, 2016.

  • B. Stemper, MOTM option pricing under rough volatility, 6th Berlin--Oxford Meeting, December 8 - 10, 2016, University of Oxford, Mathematics Department, UK, December 10, 2016.

  • L. Bogolubsky, P. Dvurechensky, A. Gasnikov, G. Gusev, Y. Nesterov, A.M. Raigorodskii , A. Tikhonov, M. Zhukovskii, Learning supervised PageRank with gradient-based and gradient-free optimization methods, The Thirtieth Annual Conference on Neural Information Processing Systems (NIPS), Barcelona, Spain, December 4 - 10, 2016.

  • K. Kraus, J. Dolata, T. Schade, H.-J. Mucha, H.-G. Bartel, Werkstoffuntersuchungen an einem barocken Kanal im Mainzer Bleichenviertel, Jahrestagung Archäometrie und Denkmalpflege 2016, Göttingen, September 27 - October 1, 2016.

  • CH. Bayer, Pricing under rough volatility, Stochastic Analysis and Mathematical Finance -- A Fruitful Partnership, May 22 - 27, 2016, Banff International Research Station for Mathematical Innovation and Discovery, Oaxaca, Mexico, May 24, 2016.

  • CH. Bayer, Pricing under rough volatility, Statistics for Differential Equations driven by Rough Paths, September 7 - 8, 2016, University of Warwick, Centre for Research in Statistical Methodology, Coventry, UK, September 7, 2016.

  • CH. Bayer, Pricing under rough volatility, Vienna Congress on Mathematical Finance -- VCMF 2016, September 12 - 14, 2016, Vienna University of Economics and Business, Austria, September 12, 2016.

  • CH. Bayer, Pricing under rough volatility, Czech, Slovenian, Austrian, Slovak and Catalan Mathematical Societies Joint Meeting 2016, September 20 - 23, 2016, Societat Catalana de Matemàtiques, Institut d'Estudis Catalans, Barcelona, Spain, September 20, 2016.

  • CH. Bayer, SDE based regression for random PDEs, Workshop ``Rough Paths, Regularity Structures and Related Topics'', May 1 - 7, 2016, Mathematisches Forschungsinstitut Oberwolfach, May 3, 2016.

  • CH. Bayer, Short dated option prices under rough volatility, Rough Volatility Meeting, October 7 - 8, 2016, Imperial College London, Department of Mathmatics, UK, October 7, 2016.

  • CH. Bayer, The forward-reverse method for conditional Markov processes, Bayes in Paris, École Nationale de la Statistique et de l'Administration Économique, Paris, France, January 28, 2016.

  • CH. Bayer , Short dated option pricing under rough volatility, Bachelier seminar, École Polytechnique CNRS, Centre de Mathématiques Appliquées, Palaiseau, France, December 16, 2016.

  • CH. Bayer , Smoothing the payoff for efficient computation of basket option, Stochastik Seminar, Technische Universität Wien, Institut für Stochastik und Wirtschaftsmathematik, Austria, December 1, 2016.

  • CH. Bayer , Smoothing the payoff for efficient computation of basket option, Seminar, École Polytechnique CNRS, Centre de Mathématiques Appliquées, Palaiseau, France, December 12, 2016.

  • P. Dvurechensky, Accelerated primal-dual gradient method for composite optimization with unknown smoothness parameter, VIII Moscow International Conference on Operations Research (ORM2016), November 18 - 21, 2016, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation, October 19, 2016.

  • P. Dvurechensky, Accelerated primal-dual gradient method for linearly constrained minimization Problems, VII International Conference Optimization and Applications, September 25 - 28, 2016, Montenegrin Academy of Sciences and Arts, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Sciences, University of Evora, Portugal, Moscow Institute of Physics and Technology, Russiate of Physics and Technology, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Science, Petrovac, Montenegro, September 26, 2016.

  • P. Dvurechensky, Gradient and gradient-free methods for pagerank algorithm learning, Workshop on Modern Statistics and Optimization, February 23 - 24, 2016, Russian Academy of Sciences, Institute for Information Transmission Problems, Moscow, Russian Federation, February 24, 2016.

  • P. Dvurechensky, Random gradient-free methods for web-page ranking model learning, 30th annual conference of the Belgian Operational Research Society, January 27 - 29, 2016, Louvain-la-Neuve, Belgium, January 28, 2016.

  • P. Friz, A regularity structure for rough volatility, Stochastic Analysis, Rough Paths, Geometry, January 7 - 9, 2016, Imperial College London, UK, January 7, 2016.

  • P. Friz, From rough paths to regularity structures and back, Colloquium, November 8 - 12, 2016, Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain, November 8, 2016.

  • P. Friz, Malliavin calculus for regularity structures: The case of gPAM, Stochastic Partial Differential Equations and Related Fields, October 10 - 14, 2016, Universität Bielefeld, Fakultät für Mathematik, October 13, 2016.

  • P. Friz, Option pricing in the moderate deviations regime, At the Frontiers of Quantitative Finance, June 27 - 30, 2016, University of Edinburgh, UK, June 28, 2016.

  • P. Friz, Option pricing in the moderate deviations regime, Vienna Congress on Mathematical Finance -- VCMF 2016, September 12 - 14, 2016, Vienna University of Economics and Business, Austria, September 12, 2016.

  • P. Friz, Signatures, rough paths and probability, Stochastics and Finance Seminar, University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Netherlands, October 18, 2016.

  • P. Friz, Support theorem for singular SPDEs: The case of gPAM, Stochastic Partial Differential Equations and Applications, May 29 - June 3, 2016, Centro Internazionale per la Ricerca Matematica (CIRM), Levico, Italy, May 31, 2016.

  • P. Friz, Support theorem for the (generalized) parabolic Anderson model, Stochastic Partial Differential Equations, May 16 - 20, 2016, Stony Brook University, Simons Center for Geometry and Physics, USA, May 18, 2016.

  • P. Friz, The enhanced Sanov theorem and propagation of chaos, Probabilistic Models -- From Discrete to Continuous, March 29 - April 2, 2016, University of Warwick, Mathematics Institute, UK, March 31, 2016.

  • P. Mathé, Bayes methods within the BOP project, Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics, WIAS Berlin, May 17, 2016.

  • P. Mathé, Complexity of linear ill-posed problems in Hilbert space, IBC on the 70th anniversary of Henryk Wozniakowski, August 29 - September 2, 2016, Banach Center, Bedlewo, Poland, August 31, 2016.

  • P. Mathé, Complexity of linear ill-posed problems in Hilbert space, Chemnitz Symposium on Inverse Problems, September 22 - 23, 2016, Technische Universität Chemnitz, Fakultät für Mathematik, September 22, 2016.

  • P. Mathé, Discrepancy based model selection in statistical inverse problems, Mathematical Statistics and Inverse Problems, February 8 - 12, 2016, Centre International de Rencontres Mathématiques (CIRM), Luminy, France, February 11, 2016.

  • H.-J. Mucha, Big Data Clustering Based on Fast Pre-Clustering, Fourth Joint Statistical Meeting of the Deutsche Arbeitsgemeinschaft Statistik - Statistics under one Umbrella, March 14 - 18, 2016, Georg-August-Universität Göttingen, March 16, 2016.

  • H.-J. Mucha, Big data clustering: Is subsampling better than fast pre-clustering?, 5th German-Japanese Workshop, September 11 - 13, 2016, Wissenschaftszentrum Schloss Reisensburg, Günzburg, September 13, 2016.

  • H.-J. Mucha, Ein Vorschlag zur Variablenselektion in der Clusteranalyse mit einer Anwendung auf p-RFA-Daten von bronzezeitlicher Keramik aus Corneşti-Larcuri (Rumänien), Jahrestagung Archäometrie und Denkmalpflege 2016, September 27 - October 1, 2016, AK Archäometrie und Denkmalpflege der DMG, Göttingen, September 29, 2016.

  • H.-J. Mucha, Finding groups in compositional data - some experiments, AG DANK Herbsttagung 2016, November 18 - 19, 2016, WIAS Berlin, November 19, 2016.

  • H.-J. Mucha, Naturwissenschaftliche Charakterisierung, mathematische Einordnung und archäologische Bewertung bislang unbekannter spätantiker römischer Ziegelstempel, Jahrestagung Archäometrie und Denkmalpflege 2016, September 27 - October 1, 2016, AK Archäometrie und Denkmalpflege der DMG, Göttingen, September 29, 2016.

  • J. Polzehl, Assessing dynamics in learning experiments, Novel Statistical Methods in Neuroscience, June 22 - 24, 2016, Otto-von-Guericke-Universität Magdeburg, Institut für Mathematische Stochastik, June 22, 2016.

  • J. Polzehl, Modeling high resolution MRI: Statistical issues, Mathematical and Statistical Challenges in Neuroimaging Data Analysis, January 31 - February 5, 2016, Banff International Research Station (BIRS), Banff, Canada, February 1, 2016.

  • J. Polzehl, R in statistical neuroscience research, 1st Leibniz MMS Days, January 27 - 29, 2016, WIAS, January 27, 2016.

  • J.G.M. Schoenmakers, Financial Mathematics, The 9th Summer School in Financial Mathematics 2016, February 18 - 20, 2016, African Institute for Mathematical Sciences South Africa (AIMS), Cape Town.

  • J.G.M. Schoenmakers, Uniform approximation methods for the C.I.R. process, Stochastic Seminar, Charles University, Prague, Czech Republic, April 6, 2016.

  • J.G.M. Schoenmakers, Uniform approximation of the Cox--Ingersoll--Ross process, Frontiers in Stochastic Modelling for Finance, February 2 - 6, 2016, Università degli Studi di Padova, Padua, Italy, February 5, 2016.

  • V. Spokoiny, Adaptive weights clustering, 2nd International Scientific Conference ``Science of the Future'', September 20 - 23, 2016, The Ministry of Science and Education of the Russian Federation, Kazan, September 21, 2016.

  • V. Spokoiny, Adaptive weights clustering, Mathematisches Kolloquium, Universität Ulm, Institut für Analysis, November 18, 2016.

  • V. Spokoiny, Clustering using adaptive weights, Information Technology and Systems 2016, September 26, 2016, Russian Academy of Sciences, Institute for Information Transmission Problems, St. Petersburg, September 26, 2016.

  • V. Spokoiny, Clustering using adaptive weights, The 3rd Professor Day Academic Conference, December 19 - 20, 2016, Huawei Research Centre (RRC), Moscow, Russian Federation, December 19, 2016.

  • V. Spokoiny, Clustering using adaptive weights, Yandex, Moscow, Russian Federation, October 28, 2016.

  • V. Spokoiny, Deviation bounds for quadratic forms with applications, Monash Probability Conference in Honor of Robert Liptser's 80th Birthday, April 25 - 29, 2016, Monash University, School of Mathematical Sciences, Prato, Italy, April 27, 2016.

  • V. Spokoiny, Gradient and gradient-free methods for pagerank algorithm learning, Workshop on Modern Statistics and Optimization, February 23 - 24, 2016, Russian Academy of Sciences, Institute for Information Transmission Problems, Moscow, Russian Federation.

  • V. Spokoiny, Inference for Structural Nonparametrics, Open Access: urlhttp://www.mathnet.ru/php/conference.phtml?option_lang=eng&eventID=25&confid=872, February 15 - March 1, 2016, Independent University of Moscow (IUM), Russian Federation.

  • V. Spokoiny, Inference for structured regression, Meeting in Mathematical Statistics 2016 ``Advances in Nonparametric and High-dimensional Statistics'', December 12 - 16, 2016, Fréjus, France, December 15, 2016.

  • V. Spokoiny, Self-normalized deviation bound for a martingale, Modern Problems of Stochastic Analysis and Statistics, May 29 - June 2, 2016, Higher School of Economics, International Laboratory of Stochastic Analysis and its Applications, Moscow, Russian Federation, May 31, 2016.

  • K. Tabelow, V. Avanesov, M. Deliano, R. König, A. Brechmann, J. Polzehl, Assessing dynamics in learning experiments, Challenges in Computational Neuroscience: Transition Workshop, Research Triangle Park, North Carolina, USA, May 4 - 6, 2016.

  • K. Tabelow, Ch. D'alonzo, J. Polzehl, M.F. Callaghan, L. Ruthotto, N. Weiskopf, S. Mohammadi, How to achieve very high resolution quantitative MRI at 3T?, 22th Annual Meeting of the Organization of Human Brain Mapping (OHBM 2016), Geneva, Switzerland, June 26 - 30, 2016.

  • K. Tabelow, Adaptive smoothing in quantitative imaging, In-vivo histology/VBQ meeting, Max Planck Institute for Human Cognitinve and Brain Sciences, Leipzig, April 13, 2016.

  • K. Tabelow, Denoising brain images: A clinical need and a mathematical idea, Leibniz-Kolleg for Young Researchers: Challenges and Chances of Interdisciplinary Research, November 9 - 11, 2016, Leibniz-Gemeinschaft, Berlin, November 9, 2016.

  • K. Tabelow, Functional magnetic resonance imaging: Processing large dataset, AG DANK Autumn Meeting 2016, November 18 - 19, 2016, Gesellschaft für Klassifikation, Arbeitsgruppe ``Datenanalyse und Numerische Klassifikation'', WIAS Berlin, November 18, 2016.

  • K. Tabelow, Mathematical models: A research data category?, The 5th International Congress on Mathematical Software, July 11 - 14, 2016, Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), July 13, 2016.

External Preprints

  • L.T. Ding, P. Mathé, Minimax rates for statistical inverse problems under general source conditions, Preprint no. arXiv:1707.01706, Cornell University Library, arXiv.org, 2017.
    Abstract
    We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to the seminal study by D. L. Donoho, R. C. Liu, and B. MacGibbon, it Minimax risk over hyperrectangles, and implications, Ann.  Statist. 18, 1990. These authors highlighted the special role of the truncated series estimator, and for such estimators the risk can explicitly be given. We provide several examples, indicating results for statistical estimation in ill-posed problems in Hilbert space.

  • J. Ebert, V. Spokoiny, A. Suvorikova , Construction of non-asymptotic confidence sets in 2-Wasserstein space, Preprint no. arXiv:1703.03658, Cornell University Library, arXiv.org, 2017.
    Abstract
    In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies on probability measures that have commuting covariance matrices and belong to the same scatter-location family: we proof the validity of a bootstrap procedure that allows to compute confidence sets and critical values for a Wasserstein-based two-sample test.

  • B. Gess, M. Maurelli, Well-posedness by noise for scalar conservation laws, Preprint no. arXiv:1701.05393, Cornell University Library, arXiv.org, 2017.
    Abstract
    We consider stochastic scalar conservation laws with spatially inhomogeneous flux. The regularity of the flux function with respect to its spatial variable is assumed to be low, so that entropy solutions are not necessarily unique in the corresponding deterministic scalar conservation law. We prove that perturbing the system by noise leads to well-posedness.

  • F. Götze, A. Naumov, V. Spokoiny, V. Ulyanov, Gaussian comparison and anti-concentration inequalities for norms of Gaussian random elements, Preprint no. arXiv:1708.08663, Cornell University Library, arXiv.org, 2017.
    Abstract
    We derive the bounds on the Kolmogorov distance between probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimensional-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements. We are also interested in the anti-concentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. All bounds are sharp and cannot be improved in general. We provide a list of motivation examples and applications for the derived results as well.

  • A. Naumov, V. Spokoiny, V. Ulyanov, Bootstrap confidence sets for spectral projectors of sample covariance, Preprint no. arXiv:1703.00871, Cornell University Library, arXiv.org, 2017.
    Abstract
    Let X1,?,Xn be i.i.d. sample in ?p with zero mean and the covariance matrix ?. The problem of recovering the projector onto an eigenspace of ? from these observations naturally arises in many applications. Recent technique from [Koltchinskii, Lounici, 2015] helps to study the asymptotic distribution of the distance in the Frobenius norm ?Pr?P?r?2 between the true projector Pr on the subspace of the r-th eigenvalue and its empirical counterpart P?r in terms of the effective rank of ?. This paper offers a bootstrap procedure for building sharp confidence sets for the true projector Pr from the given data. This procedure does not rely on the asymptotic distribution of ?Pr?P?r?2 and its moments. It could be applied for small or moderate sample size n and large dimension p. The main result states the validity of the proposed procedure for finite samples with an explicit error bound for the error of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high-dimensional spaces. Numeric results confirm a good performance of the method in realistic examples.

  • CH. Bayer, P. Friz, A. Gulisashvili, B. Horvath, B. Stemper, Short-time near-the-money skew in rough fractional volatility models, Preprint no. arXiv:1703.05132, Cornell University Library, arXiv.org, 2017.
    Abstract
    We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter H<1/2. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large deviation results of Forde-Zhang (2017) in a way that allows us to zoom-in around the money while maintaining full analytical tractability. More precisely, this amounts to proving higher order moderate deviation estimates, only recently introduced in the option pricing context. This in turn allows us to push the applicability range of known at-the-money skew approximation formulae from CLT type log-moneyness deviations of order t1/2 (recent works of Alòs, León & Vives and Fukasawa) to the wider moderate deviations regime.

  • P. Dvurechensky, A. Gasnikov, A. Lagunovskaya, Parallel algorithms and probability of large deviation for stochastic optimization problems, Preprint no. arXiv:1701.01830, Cornell University Library, arXiv.org, .
    Abstract
    We consider convex stochastic optimization problems under different assumptions on the properties of available stochastic subgradient. It is known that, if the value of the objective function is available, one can obtain, in parallel, several independent approximate solutions in terms of the objective residual expectation. Then, choosing the solution with the minimum function value, one can control the probability of large deviation of the objective residual. On the contrary, in this short paper, we address the situation, when the value of the objective function is unavailable or is too expensive to calculate. Under "`light-tail"' assumption for stochastic subgradient and in general case with moderate large deviation probability, we show that parallelization combined with averaging gives bounds for probability of large deviation similar to a serial method. Thus, in these cases, one can benefit from parallel computations and reduce the computational time without loss in the solution quality.

  • P. Dvurechensky, A. Gasnikov, A. Tiurin, Randomized similar triangles method: A unifying framework for accelerated randomized optimization methods (Coordinate Descent, Directional Search, Derivative-Free Method), Preprint no. arXiv:1707.08486, Cornell University Library, arXiv.org, 2017.
    Abstract
    In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework, which allows to construct different types of accelerated randomized methods for such problems and to prove convergence rate theorems for them. We focus on accelerated random block-coordinate descent, accelerated random directional search, accelerated random derivative-free method and, using our framework, provide their versions for problems with inexact oracle information. Our contribution also includes accelerated random block-coordinate descent with inexact oracle and entropy proximal setup as well as derivative-free version of this method.

  • P. Dvurechensky, S. Omelchenko, A. Tiurin, Adaptive similar triangles method: A stable alternative to sinkhorn's algorithm for regularized optimal transport, Preprint no. arXiv:1706.07622, Cornell University Library, arXiv.org, 2017.
    Abstract
    In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization problem with linear equality constraints and objective given as a sum of an entropy regularizer and a linear function. It is known that the state-of-the-art solvers for this problem, which are based on Sinkhorn's method (also known as RSA or balancing method), can fail to work, when the entropy-regularization parameter is small. We consider the above optimization problem as a particular instance of a general strongly convex optimization problem with linear constraints. We propose a new algorithm to solve this general class of problems. Our approach is based on the transition to the dual problem. First, we introduce a new accelerated gradient method with adaptive choice of gradient's Lipschitz constant. Then, we apply this method to the dual problem and show, how to reconstruct an approximate solution to the primal problem with provable convergence rate. We prove the rate O(1/k2), k being the iteration counter, both for the absolute value of the primal objective residual and constraints infeasibility. Our method has similar to Sinkhorn's method complexity of each iteration, but is faster and more stable numerically, when the regularization parameter is small. We illustrate the advantage of our method by numerical experiments for the two mentioned applications. We show that there exists a threshold, such that, when the regularization parameter is smaller than this threshold, our method outperforms the Sinkhorn's method in terms of computation time.

  • P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, Preprint no. arXiv:1703.09180, Cornell University Library, arXiv.org, 2017.
    Abstract
    In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"' convex part. Informally speaking, oracle inexactness means that, for the "`hard"' part, at any point we can approximately calculate the value of the function and construct a quadratic function, which approximately bounds this function from above. We give several examples of such inexactness: smooth non-convex functions with inexact Hölder-continuous gradient, functions given by auxiliary uniformly concave maximization problem, which can be solved only approximately. For the introduced class of problems, we propose a gradient-type method, which allows to use different proximal setup to adapt to geometry of the feasible set, adaptively chooses controlled oracle error, allows for inexact proximal mapping. We provide convergence rate for our method in terms of the norm of generalized gradient mapping and show that, in the case of inexact Hölder-continuous gradient, our method is universal with respect to Hölder parameters of the problem. Finally, in a particular case, we show that small value of the norm of generalized gradient mapping at a point means that a necessary condition of local minimum approximately holds at that point.

  • P. Mathé, B. Hofmann, Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales, Preprint no. arXiv:1705.03289, Cornell University Library, arXiv.org, 2017.

  • V. Avanesov, N. Buzun , Change-point detection in high-dimensional covariance structure, Preprint no. arXiv:1610.03783, Cornell University Library, arXiv.org, 2016.
    Abstract
    In this paper we introduce a novel approach for an important problem of change point detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which has applications many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure requiring a proper choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Multiscale nature of the approach allows for a trade-off between sensitivity of change-point detection and localization of it. The approach can be naturally used in an on-line setting. A simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming competing approaches.

  • L. Bogolubsky, P. Dvurechensky, A. Gasnikov, G. Gusev, Y. Nesterov, A. Raigorodskii, A. Tikhonov, M. Zhukovskii, Learning supervised PageRank with gradient-based and gradient-free optimization methods, Preprint no. arXiv:1603.00717, Cornell University Library, arXiv.org, 2016.

  • S. Bürger, P. Mathé, Discretized Lavrent'ev regularization for the autoconvolution equation, Preprint no. arXiv:1604.03275, Cornell University Library, arXiv.org, 2016.

  • A. Chernov, P. Dvurechensky, A. Gasnikov, Fast primal-dual gradient method for strongly convex minimization problems with linear constraints, Preprint no. arXiv:1605.02970, Cornell University Library, arXiv.org, 2016.

  • J.-D. Deuschel, P. Friz, M. Maurelli, M. Slowik, The enhanced Sanov theorem and propagation of chaos, Preprint no. arxiv:1602.08043, Cornell University Library, arXiv.org, 2016.

  • S. Lu, P. Mathé, S. Pereverzyev, Balancing principle in supervised learning for a general regularization scheme, Preprint no. 2016-38, RICAM Reports, Johann Radon Institute for Computational and Applied Mathematics, 2016.

  • R. Plato, P. Mathé, B. Hofmann, Optimal rates for Lavrentiev regularization with adjoint source conditions, Preprint no. 03, Technische Universität Chemnitz, Fakultät für Mathematik, 2016.
    Abstract
    There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or its adjoint. Previous analysis revealed different convergence rates, and their optimality was unclear, specifically for adjoint source conditions. Based on the fundamental study by T. Kato, it Fractional powers of dissipative operators. J. Math. Soc. Japan, 13(3):247--274, 1961, we establish power type convergence rates for this case. By measuring the optimality of such rates in terms on limit orders we exhibit optimality properties of the convergence rates, for general accretive operators under direct and adjoint source conditions, but also for the subclass of nonnegative selfadjoint operators.

  • P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, Preprint no. arXiv:1606.08988, Cornell University Library, arXiv.org, 2016.
    Abstract
    In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

  • P. Mathé, S. Pereverzyev, Complexity of linear ill-posed problems in Hilbert space, Preprint no. 2016-09, RICAM Reports, Johann Radon Institute for Computational and Applied Mathematics, 2016.