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Mathematics of Data Analysis - Oberseminar

Dates

Google calendar of the Oberseminar

Summer semester 2018

Monday, 09.07.2018 14:00-15:30
Speaker: Filipe Goulart Cabral (Federal University of Rio de Janeiro and Operador Nacional do Sistema Elétrico)
Title:
The goal of this talk is to discuss convex optimization methods for non-convex stochastic optimization problems. We aim to present, in a unified way, two results which lie in the core of widely used algorithms for non-convex programming: the classical Balas’s Theorem about the convex hull of union of polyhedra, and the more recent “Blessing of Binary” theorem from Zou, Ahmed and Sun, proving strong duality for stochastic programming with purely binary state variables. A geometrical formulation will be introduced, interpreting both results by means of Cartesian products and projections. This geometrical intuition will be used for describing new models that are amenable to this theory.
Room: 03.10.011

Thursday, 28.06.2018 12:30-14:00
Speaker: José Matias (Instituto Superior Técnico, Lisboa)
Title:
We extend to the abstract A-framework some existence theorems for differential inclusion problems with Dirichlet boundary conditions.
Joint work with Ana Cristina Barroso (FCT/UL) and Pedro Miguel Santos (IST/UL).
Room: 02.08.011

Monday, 25.06.2018 14:00-15:30
Speaker: Elvira Zappale (Università di Salerno)
Title:
Some recent results dealing with optimal design problems for energies which describe composite materials, mixed materials and Ogden ones will be presented.
Room: 03.10.011

Monday, 18.06.2018 14:45-15:30
Speaker: Michael Rauchensteiner (TUM)
Title:
We consider compositions of weighted sums of ridge functions, which are closely related to two layer feed-forward neural networks. The goal is the recovery of the ridge directions under mild smoothness assumptions of the function and for quasi-orthogonal ridge directions.
The reconstruction can be divided into two steps. First, the identification of a matrix space spanned by the symmetric tensor products of the ridge directions. This space is approximated by evaluating the Hessian of the function on random points of the sphere and applying a dimension reduction on the span of the Hessians. Secondly, the recovery of the ridge directions expressed as rank-1 matrices by solving a non-linear program on the intersection of the reduced matrix space with the unit Frobenius sphere.
The primary focus of my presentation is the analysis of the involved matrix spaces. We give bounds on the concentration of the span of the Hessians, that hold with high probability. This concentration is essential and enables us to apply the dimension reduction. This is complemented by numerical results for two-layer neural networks with sigmoidal activation functions.
Room: 03.10.011

Monday, 18.06.2018 14:00-14:45
Speaker: Judith Wewerka (TUM)
Title:
Solving underdetermined linear systems of equations by l^1-regularization is a common approach. The amount of regularization is controlled by a regularization parameter. Even though there exist various techniques for choosing this parameter, it is still a relevant challenge. In this thesis, a data-driven approach is proposed, which is neither relying on knowledge of the solution nor on the noise level.
The idea is to estimate the regularization parameter of LASSO by a greedy solution computed by OMP.
We give explicit error bounds for the vectors reconstructed by the different algorithms and show theoretically that by an optimal choice of the regularization parameter LASSO and OMP can achieve the same error. The numerical results are even more promising: we find scenarios where LASSO, with an estimated parameter, outperforms OMP. Furthermore, we implement an image reconstruction from noisy and undersampled data in MATLAB. Here, LASSO using a regularization parameter chosen by our proposed approach, reconstructs with a smaller error than OMP.
Room: 03.10.011

Thursday, 14.06.2018 12:30-14:00
Speaker: Marcello Carioni (Karl-Franzens-Universität Graz)
Title:
This talk is concerned with the study of minimizers of general inverse problems of the forms F(u) + G(Au), where F is a seminorm, G is convex, and A is a linear operator mapping to a finite dimensional vector space. We prove, under suitable hypothesis, existence of a "sparse" solution. In our setting, by "sparse" minimizer we mean a minimizer that is represented by a finite linear combination of extremal points of the ball associated to F. Moreover we relate the number of elements in the linear combination with the dimension of the image of A.
Then we apply our result to relevant inverse problems. In particular, we consider the case where F is the TV norm of the distributional gradient of a function of bounded variation. In this case we are able to characterize the extremal points of the ball associated with F, applying our result directly.
This is a joint work with Kristian Bredies.
Room: 02.08.011

Monday, 11.06.2018 14:00-15:30
Speaker: Dominik Nagel (University Osnabrück)
Title:
The multivariate Prony method is quite well understood for well-separated nodes on the d-dimensional torus. Here we study the case of nearly colliding nodes and the condition number of associated Vandermonde matrices.
The situation with nodes that are lying on a grid have been studied by several authors.
Though, in order to apply this to Prony’s method it is necessary to have estimates for condition numbers of Vandermonde matrices with “off-grid” nodes. Starting from the well-separated, one dimensional setting, I present our results for different cases when nodes are nearly colliding.
Room: 03.10.011

Monday, 28.05.2018 14:00-15:30
Speaker: Frank Filbir (Helmholtz Zentrum München and Technische Universität München)
Title:
TBA
Room: 03.10.011

Monday, 14.05.2018 14:00-15:30
Speaker: Hans Georg Feichtinger (NuHAG, Vienna and TUM)
Title:
See here
Room: 03.10.011

Monday, 07.05.2018 14:00-15:30
Speaker: Marie-Therese Wolfram (University of Warwick)
Title:
We introduce and analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. Lucas and Moll assumed that agents either increase their knowledge level by exchanging ideas in learning events or produce goods with the knowledge they already have. Their dynamics can be described by a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analysis of the fully coupled system and in particular the existence of so-called balanced growth path. These solutions relate to exponential growth of the overall productivity in time. Finally we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations.

Joint work with M. Burger and A. Lorz.
Room: 03.10.011

Thursday, 26.04.2018 10:15-11:45
Speaker: Bosu Choi ((Michigan State University)
Title:
The development of sublinear-time compressive sensing methods for signals which are sparse in Tensorized Bases of Bounded Orthonormal Functions (TBBOFs) will be discussed. These new methods are obtained from CoSaMP by replacing its usual support identification procedure with a new faster one inspired by fast Sparse Fourier Transform (SFT) techniques. The resulting sublinearized CoSaMP method allows for the rapid approximation of TBBOF-sparse functions of many variables.
Both numerics and theoretical recovery guarantees will be presented.
Room: 02.08.011

Monday, 23.04.2018 14:00-15:30
Speaker: Bernd Sturmfels (MPI Leipzig)
Title:
This lecture discusses the role of algebraic geometry in data science. We report on recent work with Paul Breiding, Sara Kalisnik and Madeline Weinstein. We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on topological and algebraic features, such as dimension and defining polynomials. All algorithms are tested on a range of datasets and made available in a Julia package.
Room: 03.10.011

Monday, 16.04.2018 14:00-15:30
Speaker: Ayush Bhandari (MIT)
Title:
The ability to resolve over-lapping echoes or pulses is an indefensible art that finds applications across several areas of science and engineering. This problem boils down to recovery of a sparse signal given its low-pass projections. In the recent years, a number of solutions have been proposed to solve this problem and variations on the theme include convex programing approaches, atomic norm minimization and high resolution frequency estimation.

That said, in many practical cases of interest, the pulse may be distorted due to physical properties of propagation and transmission. Such cases can not be handled well by existing signal models. Inspired by problems in spectroscopy, radar, photoacoustic imaging and ultra-wide band arrays, on which we base our case studies, in this work we take a step towards recovering continuous-time spikes from time-varying pulses. To this end, we re-purpose existing super-resolution approach and extend its utility to the case of distorted pulses by developing the idea of steerable pulses. Application of our algorithm on the above-mentioned case studies results in substantial improvement in peak-signal-to-noise ratio, thus promising interesting future directions. Finally, we show how this approach can be used to infer geometry of red blood cells from photoacoustic tomography which was previously not possible in literature.
Room: 03.10.011

Winter semester 2017/2018

Tuesday, 27.02.2018 11:30-13:00
Speaker: Maik Kahnt (DESY)
Title:
X-ray ptychography is the newest and most promising microscopy technique at synchrotron sources. The resolution is neither limited by fabrication errors of the optics, the size of the sample nor the beam size on the sample. This talk focuses on the ptychographic phase retrieval algorithm and the challenges when it is applied to real experimental data.
Room: 02.08.020

Monday, 05.02.2018 14:00-15:30
Speaker: Emanuele Dolera Pfeil (University of Pavia)
Title: Existence and optimal rate of convergence to equilibrium for the homogeneous Boltzmann equation
Room: 02.08.020

Monday, 29.01.2018 14:00-15:30
Speaker: Friedrich Philipp Pfeil (Universität Eichstätt)
Title: Dynamical Sampling on Finite Index Sets
Room: 02.08.020

Monday, 22.01.2018 14:00-15:30
Speaker: Manuel Stein Pfeil (Vrije Universiteit Brussel)
Title:
The talk focuses on signal processing with measurements obtained by an array of sensors which feature a low-resolution digitization process. Employing a large number of antennas in conjunction with low-complexity analog-to-digital conversion is motivated via the technical requirements of exemplary future wireless systems. We outline the challenges associated with statistical processing and analysis under such a system architecture. Reducing the intractable probabilistic models arising under hard-limiting within the exponential family, we then conservatively approximate established information measures connected to signal processing performance. Finally, the presented methods are exploited to study the favorable design of high-performance wireless sensor systems with low hardware complexity.
Room: 02.08.020

Monday, 15.01.2018 14:00-15:30
Speaker: Johannes Maly, Sara Krause-Solberg (TUM)
Title: TBA
Room: 02.08.020

Thursday, 11.01.2018 11:00-12:00
Speaker: Young-Pil Choi Pfeil (Inha University, South Korea)
Title:
In this talk, we discuss an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. We study the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions.
Room: 00.10.011

Thursday, 11.01.2018 10:00-11:00
Speaker: Philippe Sünnen
Title:
In this talk I will sketch the proof of a uniqueness theorem on a class of neural nets. The important requirements of the proof are that the neural nets satisfy the so- called generic conditions and that the activation function of the output function is given by the hyperbolic tangent. Under these requirements it can be shown that two neural nets with the same output function are isomorphic, which means that the depths of the nets are equal and that the weights and the thresholds are equal up to permutations and changes in sign. The basic idea is to continue the output function to an open subset of the complex plane and read off the information to reconstruct the net from the set of singularities.
Room: 00.10.011

Monday, 08.01.2018 14:00-15:30
Speaker: Florian Boßmann Pfeil (Universität Passau)
Title: Structural reconstruction using quadratic sparsity penalisation
Room: 02.08.020

Monday, 18.12.2017 14:00-15:30
Speaker: Andreas Langer Pfeil (Universität Stuttgart)
Title:
In image reconstruction one often minimizes a non-smooth functional consisting of one or two data- fidelity terms, a regularization term, and parameters, which balance the aforementioned terms. The proper choice of the parameters is delicate. In fact, badly chosen weights either may not only remove noise but also details in images, or retain noise in homogeneous regions. Hence a good reconstruction may be obtained by choosing the parameters such that a good compromise of the aforementioned effects are made. We revisit the disrcepancy principle and demonstrate how it can be used for finding parameters in functionals consisting of one and two data terms. However, since images consist of multiple objects of different scales, it is expected that spatially varying weights would give better reconstructions than a scalar parameter. In this vein we adapte our proposed algorithm for computing distributed weights. We study the convergence behaviour of the proposed algorithms and present several numerical experiments for image reconstruction.
Room: 02.08.020

Monday, 11.12.2017 14:00-15:30
Speaker: Jeff Hogan Pfeil (The University of Newcastle, Australia)
Title:
A family of real-valued, regular, compactly supported, orthonormal, multiresolution wavelets on the line was produced by Ingrid Daubechies in 1988. Several of the techniques used by Daubechies, including spectral factorization, are unavailable in higher dimensions. In work with David Franklin (Newcastle) and Matthew Tam (Goettingen) the application of techniques such as iterated projections, the Douglas-Rachford algorithm, and PALM (Proximal Alternating Linearized Minimization) to the construction of (non-tensorial) multidimensional wavelets has been investigated. I'll report on the progress of this project and discuss several extensions we hope to address in future work.
Room: 02.08.020

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

Summer semester 2017

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 Pfeil (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 Pfeil (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 Pfeil ( 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 Pfeil (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 Pfeil (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 Pfeil (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

Contact

Sorted ascending Person E-Mail Office
Contact Person Carlos Améndola Cerón carlos.amendolaemattum.de MI 02.10.020
Contact Person Sandro Belz sandro.belzematma.tum.de MI 02.10.052
Organizer Massimo Fornasier massimo.fornasierematma.tum.de MI 02.10.058
Organizer Felix Krahmer felix.krahmeremattum.de MI 02.10.039

-- MarcoMorandotti - 12 April 2018.