All Years Seminars
[INMA] 2019-05-07 (14:00) : Spectral methods for certain inverse problems on graphs
At Euler building (room A.002)
Speaker :
Mihai Cucuringu (University of Oxford)
Abstract :
We study problems that share an important common feature: they can all be solved by exploiting the spectrum of their corresponding graph Laplacian. We first consider the classic problem of establishing a statistical ranking of a set of items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine learning. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO(2) of planar rotations, whose least squares solution can be approximated by either a spectral or a semidefinite programming relaxation. We also present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The proposed algorithm works in nearly-linear time, and consistently outperforms existing spectral approaches both in speed and quality. Furthermore, we propose an algorithm for clustering signed networks, where the edge weights between the nodes of the graph may take either positive or negative edges, and analyze it under a signed stochastic block model. Time permitting, we discuss recent work on clustering directed graphs, and applications of ranking to extracting leaders and laggers in multivariate time series data.
[INMA] 2019-04-30 (14:00) : Data-driven compressed sensing with inexact projected gradient iterations: application to magnetic resonance fingerprinting
At Euler building (room A.002)
Speaker :
Mohammad Golbabaee (The University of Bath)
Abstract :
We study the convergence of the iterative projected gradient algorithm where the projection oracles are computed approximately. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large data sets by fast approximate nearest neighbour search strategies based on the cover tree data structure.
This talk will also discuss recent advances in rapid quantitative MRI based on the emerging protocol of Magnetic Resonance Fingerprinting (MRF). MRF can be considered as an inverse problem which exploits a particular data driven signal model derived from the MR physics. We discuss the applications of the inexact iterations in addressing the computational challenge of solving such problems.
[INMA] 2019-04-23 (14:00) : Restoring natural tactile feedback in bionic hands through a peripheral nerve interface
At Euler building (room A.002)
Speaker :
Delhaye, Benoit
Abstract :
Tactile feedback is essential to achieve a dexterous bionic hand. Without touch, interactions with objects are slow and clumsy, and require constant attention. In this talk, I will describe recent advances toward restoring useful somatosensory feedback in bionic hands through electrical stimulation of the peripheral nerves using chronically implanted electrode arrays. First, I will show that the perceived intensity of a tactile stimulus can be systematically manipulated by modulating the aggregate response of tactile nerve fibers and discuss how this response can be systematically manipulated by controlling stimulation parameters. Second, I will discuss the advantages of the biomimetic approach to tactile restoration. In brief, the closer we can mimic the activity that would be produced in the nerve during natural tactile interactions with objects, the more natural and useful the evoked sensations will be. I describe an approach we have developed to convey such naturalistic tactile feedback.
[INMA] 2019-04-02 (14:00) : A primal-dual interior-point algorithm for nonsymmetric conic optimization
At Euler building (room A.002)
Speaker :
Erling Andersen (CEO of MOSEK)
Abstract :
It is well known that primal-dual interior-point algorithms for linear optimization can easily be extended to the case of symmetric conic optimization, as shown by Nesterov and Todd (NT) in their 1997 paper about self-scaled barriers.
Although many convex optimization problems can be expressed using symmetric cones then models involving for instance exponential functions do not belong to the class of symmetric conic optimization problems.
Therefore, several authors have suggested generalizations of the NT primal-dual interior-point algorithm to handle nonsymmetric cones such as the exponential cone. Based on this work we will present a generalization of the NT algorithm to the case of nonsymmetric conic optimization. Although we have no polynomial complexity proof for the suggested algorithm then it performs extremely well in practice as will be documented with computational results.
To summarize, this presentation should be interesting for users of convex optimization.
[INMA] 2019-03-26 (14:00) : Performance Estimation for Fixed Point Iterations
At Euler building (room A.002)
Speaker :
Felix Lieder (Universität Düsseldorf)
Abstract :
In recent years exact worst-case performance estimation of first-order methods has gained great attention: It is now well established (especially, but not solely, due to the work of de Klerk, Drori, Glineur, Hendrickx, Taylor and Teboulle) that we can find tight convergence rates for smooth (strongly) convex functions via semidefinite programming. Here the existing approach is transferred to the broader setting of fixed point iterations of non-expansive operators, again ensuring tight rates. Specifically we focus on two fixed point iterations, first the Halpern-Iteration and second the Krasnoselski-Mann-Iteration with constant step-size. In both cases we consider the convergence of the norm of the residuals as our performance criterion of interest. We are able to improve the existing bounds on the convergence rate and, more importantly, show tightness of both bounds. In particular, while the Krasnoselski-Mann-Iteration often performs better in practice, its (tight) rate is an order of magnitude worse than of the Halpern-Iteration, which possesses the fastest proven convergence rate among all fixed step methods.
Finally we discuss applications and possible future extensions, such as different performance criteria and automated algorithm modeling.
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