All Years Seminars
[INMA] 2023-03-07 (14h) : Structure-Aware Methods for Expensive Derivative-Free Nonsmooth Composite Optimization
At Euler building (room A.002)
Speaker :
Jeffrey Larson (Argone National Laboratory, USA)
Abstract :
We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive function. We provide accompanying implementations of these methods: in particular, a novel manifold sampling algorithm with subproblems that are in a sense primal versions of the dual problems solved by previous manifold sampling methods and a method that employs more difficult optimization subproblems. For these two methods, we provide rigorous convergence analysis and guarantees. We demonstrate extensive testing of these methods.
[INMA] 2023-02-28 (14h) : Towards Compressive Recovery of Sparse Precision Matrices
At Euler building (room A.002)
Speaker :
Titouan Vayer (OCKHAM, LIP, ENS Lyon, France)
Abstract :
We consider the problem of learning a graph modeling the statistical relations of the "d" variables of a dataset with "n" samples. Standard approaches amount to searching for a precision matrix Θ representative of a Gaussian graphical model that adequately explains the data. However, most maximum likelihood based estimators usually require to store the "d^2" values of the empirical covariance matrix, which is often too costly in a high-dimensional setting. In this work we adopt a “compressive” viewpoint and look for estimating a sparse Θ from a sketch of the data, i.e. a lowdimensional vector of size "n ≪ d^2" carefully designed from the data using nonlinear random features. Under certain assumptions on the spectrum of Θ, we show that it is theoretically possible to estimate it robustly from a sketch of size "m = O((d + 2k) ln(d))" where "k" is the maximal number of edges of the underlying graph and with an error that decreases in "O(n^{-1/2})". These guarantees are inspired from the compressed sensing theory and involve restricted isometric properties and instance optimal decoders. Our estimator requires solving a non-convex inverse problem and we investigate the possibility of achieving practical recovery by a variant of the Davis-Yin three operator splitting algorithm. We compare our approach with “Graphical LASSO” type estimators on synthetic datasets. Finally, we discuss in a last part the limitations and perspectives of this work, which partially answers some questions but also opens many others.
[INMA] 2023-02-21 (14h) : Interferometric Lensless Imaging: Rank-one Projections of Image Frequencies with Speckle Illuminations
At Euler building(room a.002)
Speaker :
Leblanc, Olivier
Abstract : Lensless endoscopy with multicore fibers (MCF) is a technology that enables fluorescent imaging of biological samples at cellular scale.
In this talk, I will show that under a common far-field approximation, the corresponding speckle imaging process is tantamount to collecting multiple symmetric rank-one projections (SROP) of an Hermitian interferometric matrix---a matrix encoding a subsampling of the Fourier transform of the sample image. Specifically, each SROP of this matrix is achieved with the complex vector shaping the incident wavefront using a spatial light modulator (SLM), and, for specific MCF core arrangements, the interferometric matrix collects as many image frequencies as the square of the core number. Configuring the SLM randomly allows us to characterize the sample complexity of the system through a two-component sensing perspective.
In particular, by inspecting the separate dimensional conditions ensuring the specific restricted isometry properties of the two composing sensing models in the observation of sparse images, we show that a basis pursuit denoising (BPDN) program associated with an L1-fidelity cost provably provides a stable and robust image estimate. In parallel, numerical and experimental reconstruction results demonstrate the effectiveness of this imaging procedure for a TV-penalized formulation of the inverse problem.
[INMA] 2023-02-14 (14h) : Tight Lyapunov function existence analysis for first-order methods
At Euler building(room a.002)
Speaker :
Gisselson Pontus (Lund University)
,
and
Updhyaya Manu (Lund University)
Abstract : We present a unifying framework for establishing linear convergence rates for common first-order methods used to solve convex optimization problems. In particular, we consider i) classes of convex optimization problems of finite sum form with (possibly strongly) convex and (possibly) smooth functional components, and ii) first-order methods that can be written in so-called state-space form, i.e., as a linear system in feedback interconnection with the subdifferentials of the functional components of the objective function. The validity of a given target linear convergence rate is established by deriving a necessary and sufficient condition for verifying the existence of a quadratic Lyapunov function for the algorithm and problem class under consideration for the chosen rate, which amounts to the feasibility of a small-sized semidefinite program. This allows us to find the smallest linear convergence rate for which such a quadratic Lyapunov function exists, by bisection search, yielding a tight procedure. The approach is numerically exemplified on several algorithmic schemes.
[INMA] 2023-02-07 (14h) : Feedback system analysis: back to the future
At Euler building(room a.002)
Speaker :
Sepulchre, Rodolphe
Abstract : Back in 1960, George Zames proposed to ground the theory of feedback systems in incremental input-output analysis. Sixty years later, the theory of nonlinear control is primarily grounded in non-incremental state-space analysis. The talk will examine some consequences of that evolution and describe ongoing efforts to revive Zames proposal in the algorithmic age of control. Joint work with Tom Chaffey, Fulvio Forni, and Henk Van Waarde.
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Mon – Fri 9:00A.M. – 5:00P.M.
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