CosmosClub: Tobias Liaudat (11/02/2019)

Date: February 11th 2019, 11am

Speaker: Tobias Liaudat (ENSAE ParisTech)

Title: Optimal Transport for Signed Measures

Room: Cassini


Abstract

Optimal transport has become a mathematical gem at the interface of probability, analysis and optimization. It is a theory longly developed by the mathematician community, started by Monge and followed by Kantorovich which found applications in several fields like differential geometry, PDEs or gradient flows just to name a few.

Lately, it began to make its way into the machine learning and data treatment community. The optimal transport can be used to define a distance that is very useful when comparing histograms or point clouds, a typical scenario in nowadays applications. Some breakthrough contributions, like the entropic regularization, allowed to convexify and efficiently solve the transport problem opening the doors for many applications like Wasserstein barycenters or dictionary learning for example.

Nevertheless, Optimal Transport has not entered fully into the signal treatment community. One of the obstacles is the fact that the theory is well developed in the space of nonnegative measures but very little work has been done to extend it to signed measures. Considering a machine learning point of view, this presentation will deal with some theoretic aspects of an Optimal Transport based "distance" for signed measures that can be useful for future applications like Blind Source Separation. An algorithm for its efficient calculation will be presented as well.

Journal Club#2: DES cosmological constraints, Stochastic PALM and email signature

Date: February 7th 2019, 11am

Presenters: Fadi, Kostas & Martin

Room: Cassini


Journal Club#1: Genetic Algorithms, Adaptive Moments and Latex drawings

CosmosClub: Pol del Aguila Pla (14/01/2019)

Date: January 14th 2018, 10am

Speaker: Pol del Aguila Pla (KTH Royal Institute of Technology)

Title: Cell detection by functional inverse diffusion and non-negative group sparsity - Biology, physics, math and engineering [slides]

Room: Kepler


Abstract

Image-based immunoassays are used every day across the world to develop new drugs, diagnose diseases, and research the workings of the human body. Since August, some of these are analyzed by technology that, at its core, has an algorithm included in my Ph.D. work. In this talk, I will outline the research project that lead to this algorithm and go through the modeling and optimization results we present in [1] and [2]. This will include, among others, the modeling of complex biochemical assays as systems of partial differential equations, a linear-systems view on diffusion models, investigations in group-sparsity regularization in function spaces, and first-order methods for optimization problems with more than 25 million variables. To conclude the presentation, I will go through the new paths we have started to explore in connecting all this work to deep learning frameworks [3].

[1]: Pol del Aguila Pla and Joakim Jaldén, “Cell detection by functional inverse diffusion and non-negative group sparsity—Part I: Modeling and Inverse Problems”, IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5407–5421, 2018
[2]: Pol del Aguila Pla and Joakim Jaldén, “Cell detection by functional inverse diffusion and non-negative group sparsity—Part II: Proximal optimization and Performance Evaluation”, IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5422–5437, 2018
[3]: Pol del Aguila Pla, Vidit Saxena, and Joakim Jaldén, “SpotNet – Learned iterations for cell detection in image-based immunoassays”, Submitted to the 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), arXiv: 1810.06132 [eess.SP]

 

 

 

CosmosClub: Sylvain Vanneste (16/11/2018)

Date: October 16th 2018, 2pm

Speaker: Sylvain Vanneste (LAL)

Title: Detecting CMB B-modes

Room: Kepler


Abstract

The discovery of the Cosmic Microwave Background (CMB) by Penzias and Wilson in 1964 was an important confirmation of the Big Bang theory. The CMB constitutes a background of photons emitted during the first instants of our Universe history, and still permeates it today. Since its discovery, numerous telescopes, balloon-born, or satellite experiments such as Planck, have made it possible to produce measurements and precise temperature maps of the CMB, of which we have been able to deduce important information about our Universe.
However, a piece of the cosmological puzzle is still missing: the inflation, corresponding to a short period during which the Universe would have seen its size growing exponentially. Inflation is a theory introduced to solve several major cosmological questions, and which, to date, has only been verified indirectly.
The inflation phase, however, should produce a stochastic background of primordial gravitational waves that may have left an imprint on the CMB. More particularly, these gravitational waves would induce the so-called B-modes patterns on the polarisation maps of CMB photons. The precise measurement of the B-modes, still undetected to this day, represents the most powerful probe of inflationary physics.
The B-modes expected signal is however of low intensity, and many additional experimental difficulties arise when aiming at measuring it. Dust from our own galaxy partially masks the CMB, and many models are developed to clean up galactic contaminations. The extraction and analysis of the measured data signal thus requires the development of precise statistical algorithms. These must take into account the complexity of the data produced, such as residual galactic contaminations, incomplete sky map coverage, as well as statistical and instrumental errors.
 

 

CosmosClub: Jia Liu (07/11/2018)

Date: November 7th 2018, 2pm

Speaker: Jia Liu (Princeton University)

Title: Cosmology in the nonlinear regime with massive neutrinos [slides]

Room: Kepler


Abstract

The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. I will discuss recent progress and future prospects to constrain the neutrino mass sum with cosmology, with a focus on observables in the nonlinear regime.

CosmosClub: Chieh-An Lin (09/10/2018)

Date: October 9th 2018

Speaker: Chieh-An Lin (IfA, University of Edinburgh)

Title: Predicting weak-lensing covariance with a fast simulator


Weak lensing has been shown as an outstanding tool to constrain cosmology. The state-of-the-art studies have used the power spectrum and peak counts as estimators, and the combination of the two can break down parameter degeneracies and maximize the information extraction.

To constrain cosmology with both estimators, understanding the joint covariance is crucial. However, calculating it analytically seems to be intractable for peaks, and the empirical approach with N-body simulations will be expensive as the size of lensing surveys increase.

I will present a fast solution to solve this problem. The proposed approach simulates lognormal fields and halo models to predict lensing signals. We compared the resulting joint covariance with the one from a large number of N-body simulations and found an excellent agreement. In addition, our approach is orders of magnitude faster than N-body runs.

CosmosClub: Benjamin l’Huillier (13/09/2018)

Date: September 13th 2018

Speaker: Benjamin l'Huillier (Korea Astronomy and Space Science Institute)

Title: Cosmological structure formation in LCDM and beyond: Testing LCDM with N-body simulations and advanced statistical methods [slides]


The current concordance cosmological paradigm relies on a few assumptions: gravity is described by General Relativity, the Universe is Homogeneous and Isotropic on large scales, and a phase of inflation in the early Universe. Under these assumptions, the solution to the Einstein Equations is the Friedmann—Lemaître—Robertson—Walker (FLRW) metric, a general metric describing an expanding Universe. Observationally, the Universe seems flat, dominated by dark energy, thought to be responsible for the late-time acceleration of the Universe, and by a smooth dark matter component. Albeit reasonable, these are all assumptions. Therefore, it is important to test these assumptions in order to falsify the concordance model. 
In the first part of my talk, I will show how to probe extension to the LCDM paradigm via cosmological simulations (Modified Gravity and dark energy, primordial power spectrum): how do haloes form in modified gravity? can we use the large-scale structure to probe features in the primordial power spectrum?
I will then move on to the falsification of the concordance model via model-independent tests of the concordance model from the data at the background (FLRW metric, flatness, Lambda dark energy) and the perturbation (growth rate gamma), and obtain model-independent constraints on some key cosmological parameters.