Seminar Details
2021-05-11 (14h) : Welcome Seminar for new PhD students (#3)
At MS Teams
Organized by Mathematical Engineering
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.