All Years Seminars
[INMA] 2021-05-25 (14h) : Master Students' presentations (2/2)
At MS Teams
Section 1:Disciplined Convex Programming
Speaker :
Aurélie de Borman
Abstract : Disciplined convex programming is a methodology for constructing convex optimization models. While convex programming requires a certain level of expertise, disciplined convex programming aims at lowering the expertise barrier. The methodology proposes an extensible collection of functions and sets to be combined according to a set of conventions for constructing convex models. In turn, much of the work to solve the models is automated.
Section 2:Large deviations theory
Speaker :
Sylvie Van Schendel
Abstract : Large deviations theory deals with the probabilities of rare events that decay
exponentially. I will start my talk with a basic example, based on the sample mean of
normally distributed i.i.d. random variables. This will lead us to the definition of the Large
Deviations Principle (LDP). Then, I will talk about 3 methods that can be used to show
that a random variable satisfies an LDP. Some main theorems of LD theory will be
presented. And finally, we will have a look at an application of Large Deviations Theory.
Section 3:Neural Networks: they work but one does not know why.
Speaker :
Pierre Veldeman
Abstract : Neural Networks are powerful tools (for example in image or speech recognition) but it is still difficult to interpret them and to understand clearly how they work, or to be able to distinguish the good architectures from the bad ones. In this presentation, we will first briefly introduce the neural networks, then we will highlight some of their astonishing properties and show that common measures of performance do not take those strange features into account.
[INMA] 2021-05-18 (14h) : Master Students' presentations (1/2)
At MS Teams
Section 1:A quick overview on different opinion dynamics models and the revisited agreement algorithm for reaching consensus
Speaker :
Albert Van Zeebroeck
Abstract : Opinion dynamics utilizes mathematical and physical models and the agent-based computational modeling tools, to investigate the spreading of opinions in a collection of human beings. In this 20 minutes presentation we will walk through a number of discrete and continuous opinion dynamics models such as the classical French-Haary-DeGroot or Abelson's model. In a second time we will have a look at the revisited agreement algorithm for reeching consensus as described by proffessors Vincent Blondel and Julien Hendrickx in 2005. In such algorithm, a number of agents exchange their values (or opinions) asynchronously and form weighted averages with values possessed by their neighbors
Section 2:Robust optimization – methodology and applications
Speaker :
Bousselmi, Nizar
Abstract : Optimization problems with uncertain data often arise in practice. Classical resolution of such problem can lead to very erroneous results. Therefore, it is crucial to have a methodology to robustly solve them. In this presentation, we propose to look at the well developed theory of robust optimization in the framework of linear, conic quadratic and semidefinite programming. And, we attempt to illustrate the importance of the robust optimization in practical applications.
Section 3:The mathematics of infectious diseases
Speaker :
Guillaume Roisin
Abstract : In this talk we will estimate values of the basic reproduction number R0 for various diseases. We will start by presenting simple SIR epidemic and endemic models and then extending the theory to MSEIR model. We will need to introduce demographic models with different age structures to obtain new expressions for R0 for the MSEIR and SEIR models with continuous age or age groups.
[INMA] 2021-05-11 (14h) : Welcome Seminar for new PhD students (#3)
At MS Teams
Section 1:Convex interpolation, Performance estimation problems and Automatic design and analysis of first order-methods for convex optimization
Speaker :
Kamri, Ahmed Yassine
Abstract : For many large-scale convex optimization problems, with low accuracy requirement on the solution, first-order methods are relevant due to their cheap computational cost and convergence properties. It is for example the case in machine learning, signal processing, imaging and control where first-order methods proved to be very useful. However, designing first-order methods with optimal worst-case guarantees can be complex without standard assumptions like smoothness or exactness of the first-order information. One aspect of my research will be to develop a framework for automatic design and analysis of optimal first- order methods for more general large-scale settings involving for instance noise, constraints, or non-smoothness. I will rely and expend on the recent works done on Performance estimation problems (PEP) which is a framework that casts the worst-case analysis of first- order methods as an optimization problem itself. Convex interpolation is one of the main ideas behind the tractable formulation of PEPs. Therefore, I will also present some preliminary results on convex interpolation.
Section 2:Essential tremor, a cerebellar disorder?
Speaker :
Blondiaux, Florence
Abstract : Essential tremor is a common disorder affecting up to 4% of the population above 40 years old. It usually affects patients with hand shaking, mainly during movement. To date, little is known about the origin of this disorder, although a role of cerebellum is suspected. The current treatments used for this tremor and the diagnostic methods are based on indirect countermeasures and would benefit to be improved.
Combining systems theory and an experimental approach, we aim to better understand the role of cerebellum in the generation of the tremor by testing patients in a series of tasks known to depend on this brain structure. We suspect that the oscillations observed in the biological system could be due to an erroneous estimation of the feedback delays, inherent to the conduction of the neural sensory signals through the nerves. This step is hypothesized to be performed by the cerebellum, which is why we studied the abilities of essential tremor patients in these tasks to better characterize the functional impact of ET on cerebellar-dependent control mechanisms.
Section 3:Optical random features and asymmetric random features in kernel methods
Speaker :
Delogne, Rémi
Abstract : Within machine learning, kernel methods provide a clever way to “kernelise” or distort the feature space to allow linear algorithms to successfully classify instances that would normally require non-linear algorithms. The standard way to apply this kernelisation is to use the “kernel trick” that use a similarity function (kernel function) on pairs of instances in the original feature space to exactly replicate the inner product of the instances in the kernelised feature space. However this trick does not scale well with large datasets due to its algorithmic complexity. A way to work around this limitation is to approximate the kernel function with random projections. They map the features to a randomised lower dimensional feature space allowing for computational complexity independent of the number of instances in the dataset.
Performing the random mapping can be achieved with physical projections of an instance, transformed into a light beam, through a piece of scattering material. Our first purpose is to study what kernel such an optical projection is capable of approximating and with what statistical guarantees.
This approach assumes we perform the inner product between two instances transformed using the same mapping. However that is not always going to be the case in practice. Some instances could indeed be quantised while the others are not. Our second objective is to work on such asymmetric random features, exploring the framework and give statistical guarantees on their use.
Section 4:Interferometric Lensless Endoscopy: Rank-one Projections of Image Frequencies with Speckle Illuminations
Speaker :
Leblanc, Olivier
Abstract : Lensless endoscopy (LE) with multicore fibers (MCF) enables fluorescent imaging of biological samples at cellular scale. The first approaches to image a 2-D biological sample consisted in raster scanning (RS) it with a focused beam illuminated from the MCF distal end; the light re-emitted by the fluorescent sample being collected and recorded pixel by pixel for each focused spot location. In a recent scheme called speckle imaging and inspired by the compressive sensing theory, the sample is illuminated with random speckles—achieved by randomly configuring the SLM—which mimics a compressive imaging system with random waveforms and allows for faster reconstruction.
In this talk, I will show that by exploiting the physics of light propagation under a common far-field approximation, the corresponding imaging process is tantamount to collecting multiple rank-one projections (ROP) of an Hermitian interferometric matrix— a matrix encoding a subsampling of the Fourier transform of the sample image. Specifically, each ROP 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.
[INMA] 2021-05-04 (14h) : Data-driven decision making and the scenario approach
At MS Teams
Speaker :
Marco Claudio Campi (University of Brescia, Italy)
Abstract :
Abstract: Decisions are based on past experience but they are applied to future cases. In this talk, we shall present the "scenario approach", a broad methodology to make data-driven decisions, and present a theory to rigorously judge the probability that a decision based on experience will under-perform in new situations. The generality of this approach makes it useful across a variety of fields, including control, finance and medical applications.
Biography: Marco Claudio Campi is Professor of Inductive Methods and Systems Theory at the University of Brescia, Italy. He was in various capacities on the editorial board of leading journals including Automatica, Systems and Control Letters and the European Journal of Control. Since 2016, he has been a Distinguished Lecturer of the IEEE Control Systems Society. He has delivered plenary and semi-plenary addresses at major conferences including CDC, SYSID, ECC and MTNS.. In year 2008, he received the IEEE Control Systems Society George S. Axelby Outstanding Paper Award. Marco Campi is a Fellow of IEEE and a Fellow of IFAC.
[INMA] 2021-04-27 (14h) : Welcome Seminar for new PhD students (#2)
At MS Teams
Section 1:Matrix Completion Methods for Exoplanet Detection
Speaker :
Daglayan Sevim, Hazan
Abstract : Exoplanet detection by direct imaging is a difficult process because the planet is faint in the light of the star. The presence of quasi-static speckles in the images, which obscure the astrophysical signatures, also makes detecting the planet difficult. Angular Differential Imaging, which takes advantage of the earth's rotation to take several images in a night to differentiate between rotating planets and quasi-static speckles, is one of the most commonly recommended methods for removing these speckles. A low-rank matrix approximation of the images can capture the speckle noise while ignoring moving planets. As a result, the difference between the original image and the low-rank matrix approximation can help to detect the planets. But in this method, the signal of the planet can also be absorbed into the model. We aim to propose a new technique that uses matrix completion. We start by assuming the presence of a planet at a specific location and calculating its path through the data cube. Then we take this path out of the cube and use matrix completion to fill in the blanks and obtain a low-rank approximation. We also propose a maximum-likelihood estimator to compute the intensity of the planet while comparing the model to the original data along the path.
Section 2:Discrete Exterior Calculus framework and proximal alternating minimization for solving discrete Mumford-Shah and Amborsio-Tortorelli models
Speaker :
Le Hoang Trieu Vy (UCLouvain and ENS Lyon)
Abstract : This work is dedicated to joint image restoration and contour detection. We consider both the discrete Mumford-Shah and the Ambrosio-Tortorelli models, which can be formulated as a minimization involving the sum of a data fidelity term, a term enforcing smoothness everywhere in the image except at the location of the contours, and a third term that penalizes the length of the contours, being the discrete counterpart of the 1D Hausdorff measure. A particular attention is paid for the derivation of the coupling and the penalization terms relying on the derivative operator and expressed by means of the Discrete Exterior Calculus framework.
In this work, we derive proximal alternating minimization schemes with convergence guarantees (PALM-AT and SL-PAM) to estimate a critical point of our energy. We compare their behaviors when the discrete counterpart of the 1D Hausdorff measure is modeled either by an l1-norm or Ambrosio-Tortorelli penalization. The closed-form expressions of the involved proximity operators are provided. A thorough numerical study is conducted to evaluate the performance of both numerical schemes as well as comparisons between l1-norm and Ambrosio-Tortorelli penalization.
Section 3:Alternating Simulation on Hierarchical Abstractions
Speaker :
Calbert, Julien
Abstract : Abstraction techniques provide formal guarantees for generic optimal control problems on nonlinear and hybrid systems.
Computing an abstraction solving the problem over the whole state-space is computationally demanding in high-dimensional spaces.
We circumvent this curse of dimensionality by introducing a hierarchical abstraction approach for solving an optimal control
problem for nonlinear systems with three nested partitions.
These nested partitions allow the construction of auxiliary systems that characterize simulation relations, which are suitably exploited
to provide upper and lower bounds for a branch and bound algorithm to yield an optimal solution for the control problem.
Section 4:Categorification of path complete lyapunov function
Speaker :
Sébastien Mattenet
Abstract : In this talk I will consider the proof of stability of a variety of different system with the same general algorithm.
In mathematic, one of the several types of proof at your disposal, is the proof by monovariant, where you introduce some value on the state of a system (like energy in the case of physical system) and show that it only goes one way, concluding something for the evolution of the system, without having to solve it exactly.
One important property we may ask of a given system is the so called Global Asymptotic Stability, roughly saying that there is one point of equilibrium and every starting point eventually tends toward it. Luckily such a property is equivalent to the existence of a Lyapunov function, which is a particular example of a monovariant.
Given a particular system, several algorithm have been proposed to find some Lyapunov function, each with their limitation and narrow scope of application, moreover those algorithm are often only valid in one class of system. The goal of my research is to use the tool of category theory to extend the scope of application of existing tactics, in particular, to extend them to greater class of system.
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