# Mathematics of Data Analysis - Oberseminar

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## News

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• 18.10.2016: We restart the seminar with a talk of Michael Sandbichler.

## Dates

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 Monday, 15.01.2018 14:00-15:30 Speaker: Lars Palzer (TUM) Title: TBA Room: 02.08.020

 Monday, 08.01.2018 14:00-15:30 Speaker: Florian Boßmann  (Universität Passau) Title: TBA Room: 02.08.020

 Monday, 18.12.2017 14:00-15:30 Speaker: Andreas Langer  (Universität Stuttgart) Title: TBA Room: 02.08.020

 Monday, 11.12.2017 14:00-15:30 Speaker: Jeff Hogan  (The University of Newcastle, Australia) Title: TBA Room: 02.08.020

 Monday, 27.11.2017 14:00-15:30 Speaker: Prof. W. R. Madych  (University of Connecticut, USA) Title: Spline summability of cardinal sine series and the Bernstein class B_{\pi} Room: 02.08.020

 Friday, 18.08.2017 11:00-12:00 Speaker: Andreas Bluhm, Daniel Stilck Franca (TUM) Title: We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson-Lindenstrauss transforms to produce a smaller SDP whose solution preserves feasibility or approximates the value of the original problem with high probability. These techniques allow to improve both complexity and storage space requirements. They apply to problems in which the Schatten 1-norm of the matrices specifying the SDP and of a solution to the problem is constant in the problem size. Furthermore, we provide some no-go results which clarify the limitations of positive, linear sketches in this setting. Finally, we discuss numerical examples to benchmark our methods. Room: 02.08.011

 Tuesday, 18.07.2017 14:30-16:00 Speaker: Prof. Uwe Kähler  (Universidad de Aveiro, Portugal) Title: In the last two decades one can observe an increased interest in the analysis of discrete structures. One one hand the fact that increased computational power is nowadays available to everybody and that computers can essentially work only with discrete values sparked an increased interest in working with discrete structures. This is true even for persons who are originally unrelated to the field. An outstanding example can be seen in the change of the philosophy of the Finite Element Method. From the classical point of view of being essentially a method for discretization of partial differential equations via a variational formulation the modern approach lifts the problem and, therefore, the finite element modelation directly on to the mesh, resulting in the so-called Finite Element Exterior Calculus. This means that one requires discrete structures which are equivalent to the usual continuous structures. On the other hand, the increased computational power also means that problems in physics which are traditionally modeled by means of continuous analysis are more and more directly studied on the discrete level, the principal example being the Ising model from statistical physics as opposed to the continuous Heisenberg model which has been studied by S. Smirnov and his collaborators using discrete complex analysis. Unfortunately, a higher dimensional analogue of discrete function theories is only in its infancy. In this talk we will present two principal approaches: the classic one based on finite differences as well as a more general version called script geometry. Furthermore, we will present the basic ingredients of a function theory, such as Fischer decomposition and power series as well as discuss potential-theoretical arguments like discrete Cauchy kernels, discrete Hilbert/Riesz-transforms and Hardy spaces. Among possible applications we are going to discuss discrete Riemann boundary value problems and their importance for image processing. Room: 02.08.020

 Thursday, 13.07.2017 10:30-12:00 Speaker: Prof. Hans-Georg Feichtinger  (Universität Wien) Title: The talk describes a surprisingly rich family of function spaces which can be defined on general LCA (locally compact Abelian groups, such as G = R^d). The start point is the Banach Gelfand triple (SO,L2,SO’), consisting of the Segal algebra SO(G) as a space of test functions and the dual space as the minimal resp. maximal space in this family. One of the most attractive (and surprising) facts about this setting, which requires only the use of Banach spaces and their dual spaces, is the existence of a kernel theorem, which extends the classical association of L2-kernels with the family of Hilbert-Schmidt operators. As time permits a number of questions arising from classical analysis and time-frequency analysis resp. Gabor analysis are mentioned. Room: 02.08.020

 Tuesday, 11.07.2017 14:30-15:30 Speaker: Kiryung Lee (GeorgiaTech) Title: The restricted isometry property (RIP) has been an integral tool in the analysis of various inverse problems with sparsity models. We propose generalized notions of sparsity and provide a unified framework on the RIP for structured measurements, in particular when combined with isotropic group actions. Our results extend the RIP for partial Fourier measurements by Rudelson and Vershynin to a much broader context and provide upper bounds on the number of group structured measurements for the RIP on generalized sparsity models. We illustrate the main results with an infinite dimensional example, where the sparsity represented by a smoothness condition approximates the total variation. We also discuss fast dimensionality reduction on generalized sparsity models. In generalizing models, the sparsity parameter becomes no longer subadditive. Therefore, the RIP does not preserve distances among sparse vectors. We show a weaker version with additive distortion, which is similar to analogous property in 1-bit compressed sensing. This is a joint work with Marius Junge. Room: 02.08.020

 Thursday, 29.06.2017 11:00-12:00 Speaker: Prof. Ahmed I. Zayed  ( De-Paul University, Chicago) Title: In this talk we present the solution of the energy concentration problem for the Fourier transform that was proposed by D. Slepian, H.Landau, and H. Pollak of Bell Labs in the 1960s, and then investigate the solution of a similar problem for the special affine Fourier transformation. Room: 02.08.020

 Tuesday, 21.06.2017 10:30-11:30 Speaker: Timo Klock  (Simula Research Laboratory) Title: Inverse problems of unmixing type arise in many real-life applications such as audio processing or medical image analysis. In such problems additive noise directly affects a sparse signal before being measured through a sampling matrix. Consequently, the noise in the measurement is amplified through the sampling process and the so-called noise folding phenomenon occurs. This amplification worsens the results on support identification by means of "classical'' sparse recovery techniques based on the l1-penalised Lasso functional. Several recent works suggest to apply a multi-penalty framework for a correct modeling and separation of the original signal in such problems. Admittedly, the parameter choice in such multi-penalty functionals becomes more involved compared other single-penalty methods. In this talk, we use multi-penalty regularization for the unmixing problem. It has been shown that the resulting functional can be seen as a parameterised Lasso such that we can solve the multi-penalty minimisation with known techniques for the Lasso. In this spirit, we provide an extension of the Lasso-path algorithm for an efficient calculation of large parts of the multi-penalty solution space without performing extensive grid-searches over regularisation parameters. Finally, by using a naive support selection heuristic based on signal-to-noise ratios, we identify a unique support that is compared to results from conventional sparse recovery techniques. Such experiments confirm improved results of the multi-penalty functional compared to single-penalty counterparts. Room: TBA

 Tuesday, 06.06.2017 14:30-16:00 Speaker: Prof. Stephan Günnemann (TUM) Title: Efficient and Robust Learning with Graphs Room: 02.08.020

 Tuesday, 30.05.2017 14:30-16:00 Speaker: Prof. Felix Krahmer (TUM) Title: In this talk, we will discuss random models with varying degrees of imposed structure for different applications in signal processing and data analysis. First, we will study a matrix factorization problem as motivated by applications in bioinformatics. To establish uniqueness under a random model, we develop new tools in probabilistic combinatorics. Motivated by applications in wireless communication, we consider the problem of simultaneous demixing and deconvolution for randomly embedded signals. We improve upon recent results by Ling and Strohmer, establishing for the first time near-optimal parameter dependence. Lastly, we show near-optimal recovery guarantees for analog-to-digital conversion in combination with compressed sensing for structured random measurement systems. These are joint works with the speaker’s PhD students David James, Dominik Stöger, and Joe-Mei Feng as well as with Matthias Hein (Universität des Saarlandes), Peter Jung (TU Berlin), and Rayan Saab (UC San Diego). Room: 02.06.011

 Thursday, 18.05.2017 09:00-10:00 Speaker: Matthias Beckmann  (Universität Hamburg) Title: This talk concerns the approximation of bivariate functions by using the well- established filtered back projection (FBP) formula from computerized tomography, which allows us to reconstruct a bivariate function from given Radon data. Our aim is to analyse the inherent FBP approximation error which is incurred by the application of a low-pass filter. To this end, we present error estimates in Sobolev spaces of fractional order. The obtained error bounds depend on the bandwidth of the utilized filter, on the flatness of the filter’s window function at the origin, on the smoothness of the target function, and on the order of the considered Sobolev norm. Finally, we prove convergence for the approximate FBP reconstruction in the treated Sobolev norms along with asymptotic convergence rates, as the filter’s bandwidth goes to infinity. The theoretical results are supported by numerical experiments. This talk is based on joint work with Armin Iske. Room: 02.08.011

 Tuesday, 16.05.2017 14:30-16:00 Speaker: Benedikt Diederichs (Universität Hamburg) Title: Prony's problem - estimating the frequencies of an exponential sum - and its higher dimensional analogs have attracted a lot of attention in recent years. A somewhat neglected question is whether this problem is well-posed. In this talk, some results in this direction will be presented. The most important techniques we need are e cient estimates of certain exponential sums. Inci- dentally, they can be used to improve classic estimates of the condition numbers of matrices arising when one interpolates with a positive definite kernel. If time permits, we will discuss this connection. This talk is based on joint work with Armin Iske. Room: 02.08.020

 Tuesday, 09.05.2017 14:30-16:00 Speaker: Markus Stachl (TUM) Title: The flow of motorized vehicles through urban road networks is known to be one of the main reasons for high pollution in metropolitan areas. So far little scientific research has been spent on the effects of coordinated traffic lights on emissions. In our approach to simulate traffic flow through a network of roads we resort to a well-posed macroscopic conservation law coupled with a one-dimensional pollution model. Model Predictive Control (MPC) is used as a responsive optimization technique to manage the movement of cars close to junctions, mirroring the use of traffic signals. On basis of an exemplaric road network in Munich we show that by optimizing traffic dynamics in this manner a decrease in CO-emissions by 5-10% can be achieved. Room: 02.08.020

 Tuesday, 02.05.2017 14:30-16:00 Speaker: Frank Filbir  (Helmholtz Zentrum München) Title: We develop constructive algorithms to represent functions defined on a metric measure space within a prescribed accuracy. The constructions can be based on either spectral information or scattered samples of the target function. Our algorithmic scheme is asymptotically optimal in the sense of nonlinear n-widths and asymptotically optimal up to a logarithmic factor with respect to the metric entropy. The talk is based on joint work with Martin Ehler, University of Vienna. Room: 02.08.020

 Tuesday, 04.04.2017 10:30-11:30 Speaker: Thomas Fink  (Universität Passau) Title: In various fields of image analysis, determining the precise geometry of occurent edges, e.g. the contour of an object, is a crucial task. Especially the curvature of an edge is of great practical relevance. In this talk, we introduce an extension of the continuous shearlet transform which additionally utilizes shears of higher order. This extension, called the Taylorlet transform, allows for a detection of the position and orientation, as well as the curvature and other higher order geometric information of edges. Furthermore, we introduce novel vanishing moment conditions of the form $$\int_{\mathbb{R}} g \left( \pm t^k \right) t^m dt$$. We will show that Taylorlets fulfilling such conditions enable a more robust detection of the geometric edge features. Room: 02.10.011

 Tuesday, 28.03.2017 10:30-11:30 Speaker: Dr. Ilaria Lucardesi  (École des Mines de Nancy) Title: The two most studied elliptic PDEs are probably the torsion problem, also known as St-Venant problem, and the Dirichlet eigenvalue problem. For these classical problems, many estimates and qualitative properties have been obtained, see for example works by P\'olya, Szeg\"o, Schiffer, Payne, Hersch, Bandle, and many others. In this seminar I present some recent results about upper and lower bounds of two shape functionals involving the maximum of the torsion function: I consider the ratio $T(Omega)\lambda_1(Omega) Omega$ and the product $M(Omega)\lambda_1(Omega)$, where $Omega$ is bounded open set with finite Lebesgue measure $Omega$, $T(\Omega)$ denotes the torsion, and $\lambda_1(\Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets. Room: 02.12.020

 Wednesday, 01.03.2017 11:00-12:00 Speaker: Patrick van Meurs  (Kanazawa University) Title: The starting point is a 2D model for the dynamics of n dislocations, which are modelled as point particles with a positive or negative ’charge’. In the celebrated engineering paper by Groma and Balogh in 1999, the limit passage n → ∞ of these dislocation dynamics is performed in a statistical mechanics framework, which relies on a phenomenological closure assumption. In my talk, I present how to pass rigorously to the limit n → ∞ by using the theory of Wasserstein gradient flows and using advanced functional analysis on the weak form of the evolution equation. Interestingly, our conclusion for the limiting dynamics of the dislocation density differs from the conclusion in the paper by Groma and Balogh. Room: 02.08.011

 Tuesday, 07.02.2017 16:00-17:00 Speaker: Kiryung Lee  (Georgia Tech) Title: Multichannel blind deconvolution resolves unknown input signal from multiple channel outputs with unknown impulse responses. It is often easier to estimate only the unknown channel impulse responses when they are modeled with only few parameters. This is the case with channel estimation problems in wireless communications and underwater acoustics. In particular with FIR models, various reconstruction methods based on statistics of the input signal and/or the commutativity of the convolution operator have been proposed with algebraic performance guarantees in 1990s. However, these guarantees are restricted to the case where the observations are noise-free or the input has infinite length. In fact, with finitely many noisy observations, the empirical performance of these classical methods deteriorates dramatically as the length of observation decreases. This weakness restricts their utility in estimating time-varying channels. Motivated from the observation that parametric models with few parameters can be embedded into low-dimensional subspaces, we propose modifications on the classical methods leveraging these subspace models. Our proposed method provides significant improvement over the original method in terms of providing stable estimates from finitely many noisy measurements. Furthermore, using recently developed tools in applied probability, we derive rigorous performance guarantees under certain random subspace models. We verify that the numerical results are aligned with our theory through Monte Carlo simulations. Furthermore, we also verify the empirical success in a realistic setup of channel delay estimation. Finally, we extend the methods and theory to the sparsity case and present corresponding theoretic and numerical results. This is the joint work with Felix Krahmer and Justin Romberg. Room: 02.12.020

 Tuesday, 31.01.2017 16:00-17:00 Speaker: Stefano Almi (TUM) Title: The aim of this talk is to present a variational model of the quasi-static evolution of hydraulic crack in the general framework of rate-independent processes. Room: 02.06.020

 Tuesday, 24.01.2017 16:00-17:30 Speaker: Marco Morandotti   (TUM) Title: In this talk I will present the theory of structured deformations. Starting from the original formulation by Del Piero and Owen, I will move to the variational formulation proposed by Choksi and Fonseca, to conclude with some recent results regarding relaxation of non-convex energies. I will also present some examples and explicit formulas as an application to specific surface energies. Room: 02.06.020

 Tuesday, 17.01.2017 10:30-12:00 Speaker: Giacomo Albi   (TUM) Title: In this talk I will review some basic results in the modeling and control of multi-agent system. The prototype problem will account a large system of interacting agents, whose dynamics are influenced by a policy maker acting in order to enforce a desired behavior. Different examples will be shown: from opinion-formation processes to crowd-safety management. From the mathematical view-point, this situation can be described by means of a mean-field optimal control problem, governing the dynamics of the probability distribution of the agent population. In order to deal numerically with the high-dimensionality and the non-linearities of this type of problems, I will introduce a novel approximating hierarchy of sub-optimal controls based on a stochastic-Boltzmann approach, whose computation requires a moderate computational effort compared with standard direct approaches. I will compare the behavior of the control hierarchy with respect to the solution of the optimal control problem. Several numerical examples will show the effectiveness of the proposed strategies. Room: 02.10.011

 Tuesday, 10.01.2017 10:30-12:00 Speaker: Prof. Dr. Sergei Pereverzyev  (RICAM Linz) Title: We discuss the parameter choice in learning algorithms generated by general regularization scheme. In contrast to classical deterministic regularization, the performance of regularized learning algorithms is influenced not only by the smoothness of a target function, but also by the capacity of a regularization space. In supervised learning both the smoothness and the capacity are intrinsically unknown. Therefore, we are interested in a posteriori regularization parameter choice rules and propose a new form of the balancing principle. We provide the analysis of the proposed rule and demonstrate its advantages in simulations. Joint research with Peter Mathe (WIAS-Berlin) and Shuai Lu (Fudan University, Shanghai). Room: 02.10.011

 Tuesday, 20.12.2016 11:00-12:00 Speaker: David James   (Göttingen) Title: In this talk, we investigate subspaces spanned by biased random vectors. The underlying random model is motivated by applications in computational biology, where one aims at computing a low-rank matrix factorization involving a binary factor. In a random model with adjustable expected sparsity of the binary factor, we show for a large class of random binary factors that the corresponding factorization problem is uniquely solvable with high probability. In data analysis, such uniqueness results are of particular interest; ambiguous solutions often lack interpretability and do not give an insight into the structure of the underlying data. For proving uniqueness in this random model, small ball probability estimates are a key ingredient. Since to the best of our knowledge, there are no such estimate suitable for our application, we prove an extension of the famous Lemma of Littlewood and Offord. Hereby, we also discover a connection between the matrix factorization problem at hand and the notion of Sperner families. Room: 02.10.011

 Tuesday, 29.11.2016 16:00-17:00 Speaker: Christian Kümmerle, Juliane Sigl (TUM) Title: We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of recovering a low-rank matrix from incomplete linear observations. Unlike in previous IRLS approaches for the problem, we exploit the information in the column as well as in the row space of the iterates, using so-called harmonic mean weight matrices. Our non-convex algorithm exhibits local convergence guarantees comparable to previous IRLS algorithms for generic random measurement operators with a number of measurements in the optimal order. Additionally, we prove that the exhibited rate of convergence is superlinear, which is unprecedented even for other iterative approaches for the low-rank recovery problem. Our theoretical findings align very well with our numerical experiments, which also suggest that convergence to non-global minimizers is not an issue and that the proposed algorithm needs fewer measurements for successful recovery than any other algorithm proposed in the literature. Room: 02.12.020

 Tuesday, 22.11.2016 16:00-17:00 Speaker: Young-Pil Choi  (TUM) Title: The jargon "flocking" denotes the phenomenon in which self-propelled individuals using only limited environmental information and simple rules organize into an ordered motion. In this talk, we study the Cucker-Smale flocking model which is a type of Newtonian equations. We first present the large-time behavior of solutions and discuss modified Cucker-Smale models that address several drawbacks of the original model. In the second part, we deal with the rigorous derivation of kinetic Cucker-Smale type equations when sharp sensitivity regions are considered. Room: 02.12.020

Tuesday, 15.11.2016
Speaker: Kristof Schröder  (Helmholtz Zentrum München)
Title:
We will look at the possibility of recovering a sum of Dirac measures on the rotation group SO(3) from its low degree moments with respect to Wigner-D functions only. Topics in the talk will cover theoretical results for recovery guarantee and algorithmic aspects of the problem.
Room: 02.10.011

Tuesday, 08.11.2016
Speaker: Jakob Geppert (Göttingen)
Title: Improved convergence guarantees for Sparse Power Factorization
Room: 02.10.011

Tuesday, 25.10.2016
Speaker: Matthias Wissel (TUM)
Title:
We will propose a time-dependent nonhomogeneous Markov model for predicting free parking spaces in urban areas. We therefore will describe the formalized general setting that reflects the real world environment we work in when concerned with parking prediction. Also, issues concerning the matter of availability of the right kind of data will be addressed. Then, the parameter estimation based on a given data set will be of particular interest. To this end, an extended framework of empirical risk minimization for matrix-valued functions and the use of matrix-valued reproducing kernel Hilbert spaces to approximate the time-dependent generator of the Markov process will be introduced. Finally, we want to give an outlook on further research possibilities in this field with a focus on a purely data driven approach.
Room: 02.10.011

Tuesday, 18.10.2016
Speaker: Michael Sandbichler (TUM)
Title:
Efficient data representation is a core aspect of modern signal processing, for example sparsity of data has been very efficiently used in compressed sensing in order to improve the required minimal number of measurements. We will look at a 'dual' version of sparsity, namely Analysis cosparsity and provide new sequential algorithms to find Analysis Operators which sparsify a given class of signals.
Room: 02.10.011

## Contact

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Person E-Mail Office
Organizer   Massimo Fornasier  massimo.fornasierma.tum.de   MI 02.10.058
Organizer   Felix Krahmer  felix.krahmertum.de   MI 02.10.039
Contact Person   Dominik Stöger   dominik.stoegerma.tum.de MI 02.10.054

-- DominikStoeger - 15 May 2016