Intepretable and higher-order statistics for late-time cosmology

Jun 27, 2022, 9:00 AM → Jul 1, 2022, 5:30 PM Europe/Rome

Institute for Fundamental Physics of the Universe

Matteo Biagetti (SISSA), Alex Cole (University of Amsterdam), Jorge Noreña (Pontificia Universidad Catolica Valparaiso), Gary Shiu (University of Wisconsin-Madison), Juan Calles (Pontificia Universidad Católica de Valparaíso)

In the last decade, the study of the large-scale structures of the universe has undergone exponential progress thanks to increasingly powerful experiments. Galaxy surveys mapping the entire sky, observing millions of bright galaxies up to high redshifts, are transforming cosmology into a data-driven, precision science.

The goal of the focus week will be to discuss higher-order summary statistics as a promising method to extract cosmological information from galaxy surveys, providing complementary information to conventional methods based on low-order correlation functions.

Mon, June 27

9:00 AM → 10:00 AM Welcome Coffee + Registration

10:00 AM → 10:30 AM Introduction to the Workshop

Speakers: Alex Cole (University of Amsterdam), Matteo Biagetti (SISSA)

Introduction to the Workshop

10:30 AM → 12:00 PM Large Scale Structures in an hour or so

The goal of this lecture is to provide a pedagogical introduction to the standard cosmological model, with a particular focus on large-scale structure formation at late times.

Speaker: Emiliano Sefusatti (OATs)

2022 LSS Interpretable workshop.pdf

12:00 PM → 12:30 PM Introduction to the Data Challenge

Speakers: Juan Manuel Calles Hansen (Pontificia Universidad Católica de Valparaíso), Matteo Biagetti (SISSA)

Introduction to Data Challenge

12:30 PM → 2:00 PM Lunch Break

2:00 PM → 3:30 PM Practical, Informative, Spatial Statistics with Applications to Cosmological Large Scale Structure

Speaker: Tom Abel

StatisticsForLSS.key.pdf

3:30 PM → 4:30 PM Towards optimal likelihood-free inference for cosmology with deep learning

In this talk I will first show with toy examples how deep learning can find optimal summary statistics to extract the maximum information from cosmological data. I will then show how it can also perform really complex tasks like extracting information from very small, highly non-linear, scales while marginalizing over baryonic effects at the field level. I will also present the major challenges this method needs to overcome to achieve its goals.

Speaker: Dr Francisco Villaescusa-Navarro (CCA, Flatiron)

Towards optimal likelihood-free inference for cosmology with deep learning

4:30 PM → 5:00 PM Q & A for Data Challenge

Tue, June 28

9:30 AM → 10:30 AM An introduction to persistent homology

In this talk, I will first give a gentle introduction to persistent homology with an emphasis on certain theorems that will be referenced in Mathieu’s talk later in the day. After this, I will discuss some recent advances in multiparameter persistent homology.

Speaker: Magnus Botnan

SISSA.pdf

10:30 AM → 11:00 AM Coffee Break

11:00 AM → 12:00 PM Constraining Cosmology with Persistent Homology

Persistent homology naturally addresses the multi-scale characteristics of the large scale structure. I will discuss the specifics of its application to mock galaxy catalogues to construct a simple and interpretable summary statistic. With the Fisher matrix formalism, I will show that our approach outperforms the momentum-space statistics in constraining cosmological parameters and offers robustness against marginalization over nuisance parameters.

Speaker: Jacky Yip (University of Wisconsin-Madison)

Constraining Cosmology with Persistent Homology_Jacky Yip.pdf

12:00 PM → 2:00 PM Lunch Break

2:00 PM → 3:00 PM Higher-order statistics in cosmic shear

The weak gravitational lensing effect is a powerful tool to study the structure and evolution of our Universe and, according to the Dark Energy Task Force, one of the most promising methods to constrain the equation of state of dark energy. In this talk, I will present two higher-order shear statistics: the third-order aperture masses and persistent homology. I will discuss their potential uses, their advantages and disadvantages, and preliminary results from their application.

Speaker: Sven Heydenreich

22_06_HOS_cosmic_shear_pdf.pdf

3:00 PM → 5:00 PM Collaboration Time

Wed, June 29

9:30 AM → 10:30 AM Introduction to Topological Machine Learning

In this talk, I will show through several examples and applications how persistence theory can be used to build relevant topological descriptors/signatures from data sets, that encode useful topological information that is often complementary to other usual descriptors. Then, we will show how these signatures can be converted into features for further data analysis and machine learning tasks, by using either finite or infinite-dimensional vectorizations into reproducing kernel Hilbert spaces, i.e., kernel methods. We will finally present several recent applications of topological data analysis in deep learning, involving differentiating persistence (in order to, eg, being able to incorporate topological penalties in the loss functions of classifiers) and mimicking persistence computations with deep neural networks.

Speaker: Mathieu Carriere

ictp2022.pdf

10:30 AM → 11:00 AM Coffee Break

11:00 AM → 12:00 PM Antifragile Persistent Homology using Fisher Information

Antifragility is a property of systems in which they increase their capability to thrive in the presence of volatility and noise. I will present how persistent homology can be made adaptive by learning the optimal filtration that is resilient to noise in data. This is done by maximizing the Fisher Information among a variational family of filtration parameters using gradient descent. By doing so, we construct an informative persistence diagram and consequently, a compressed summary of the input data that is sensitive to the input parameters. I will illustrate this with a few examples and compare the performance with the other standard filtrations.

Speaker: Karthik Viswanathan

Antifragile Persistent Homology using Fisher Information (1).pdf

12:00 PM → 2:00 PM Lunch Break

2:00 PM → 3:00 PM Scattering transforms, recent applications in astrophysics and cosmology

New statistical descriptions related to the so-called Scattering Transform recently obtained attractive results for several astrophysical applications. These statistics share ideas with convolutional neural networks, but do not require to be learned, allowing for a direct characterization of interactions between scales in non-linear processes. In this talk, I will present these statistical descriptions, and give an overview of their recent successful applications to astrophysics. After highlighting in particular the results that have been obtained on LSS studies, I will also discuss the ongoing promising work on components separation.

Speaker: Erwan Allys

EA_IFPU_29_06.pdf

3:00 PM → 5:30 PM Collaboration Time

Thu, June 30

9:30 AM → 10:30 AM Cosmology beyond the average with one-point statistics

One-point statistics such as counts-in-cells capture essential non-Gaussian properties of the cosmic web, including peculiar regions of high and low density. I will show that those statistics not only provide information complementary to common two-point statistics, but also allow for accurate theoretical predictions. I will explain how matter counts-in-cells statistics and their dependence on cosmological parameters can be predicted from first principles. I demonstrate the power of the matter PDF and its complementarity to the matter power spectrum at mildly nonlinear scales for constraining wCDM parameters, the total neutrino mass, the primordial skewness and modified gravity parameters. Finally, I will give an outlook on how predictions for the matter PDF can be adapted to predict survey observables related to galaxy clustering and weak lensing.

Speaker: Cora Uhlemann

TalkCosmologyOnePointStatistics_IFPUTrieste.pdf

10:30 AM → 11:00 AM Coffee Break

11:00 AM → 12:00 PM Joint power spectrum-bispectrum covariance and the squeezed configurations

Predictions from single-field inflation are consistent with CMB observations. Large-scale structure observations will improve our knowledge of the early universe. In particular, we can learn much about the inflationary era by testing for primordial non-Gaussianity (PNG). The upcoming galaxy surveys promise to improve such constraints by mapping the 3-dimensional distribution of matter and galaxies in the universe to scales of the order of the Hubble horizon. Then, to extract infor- mation about the early universe, we need to compute observables with the same precision as the observations, for example, the galaxy Power Spectrum and Bispectrum. A precise estimation for the covariance is a relevant ingredient in determining the information content of a given observable. The main goal of the talk is to study how the modelling of the joint power spectrum-bispectrum covariance is improved by including non-Gaussian terms that agree with N-body simulations at a 20% level. We will see that the non-Gaussian terms in the covariance are significant for observables evaluated at the squeezed limit, as in the case of the local PNG factor. Then, by doing a Fisher analysis on the constraining power of PNG, it is confirmed that non-Gaussian terms have to be taken into account, as they degrade the constraint by more than a factor of 2. Finally, I will talk about a work in progress where we want to include shot noise contribution and use the theoreti- cal covariance to estimate the uncertainty in measuring PNG from the power spectrum response function.

Speaker: Lina Castiblanco

Covariance.pdf

12:00 PM → 2:00 PM Lunch Break

2:00 PM → 3:00 PM Analysing the PDF of density fluctuations - can it work in real data?

Key analyses of the cosmic large-scale structure only capture the "scale-dimension" of the cosmic web: they measure the variance of fluctuations as a function of scale. A powerful way to complement this vast compression of data is to add the "density-dimension": at a fix smoothing scale one can analyse the entire shape of the probability density function (PDF) of density fluctuations (cf. Cora Uhlemann's talk). I will give an overview on a number of efforts ( arxiv.org/abs/1710.05162 ; arxiv.org/abs/1912.06621 ; arxiv.org/abs/2107.02300 ; and more) that have helped PDF-analyses to catch up with 2-point functions, and I will discuss how to employ these techniques in real data.

Speaker: Oliver Friedrich

joint_PDF.pdf

3:00 PM → 4:00 PM Collaboration Time

4:00 PM → 5:00 PM Amplitudes meet the Swampland

This talk is hosted by ICTP

Speaker: Gary Shiu

ICTP_2022.pdf

Fri, July 1

9:00 AM → 10:00 AM The Quijote PNG simulations - A test bed for higher order statistics and primordial non-Gaussianity

Constraints on primordial non-Gaussianity (PNG) provide powerful insights into the early universe. To date, the CMB has been the leading source of information and I will briefly overview what more we expect to gain from upcoming experiments. Large scale structure measurements potentially have a wealth of information that could surpass the CMB. However, due to the non-linear nature of structure formation, fully accessing this is challenging. To help address this issue, my collaborators and I present the Quijote-PNG simulations. This is a suite of large scale structure simulations which contain three types of primordial non-Gaussianity. These simulations are designed to complement the existing Quijote simulations, which varied the $\Lambda$CDM cosmological parameters, and are a useful test bed for developing new PNG estimators. We present an example of their utility by exploring the information content in measurements of the bispectrum on non-linear scales. As a bonus I will also discuss a new method for improving the estimation of the Fisher information, when you only have access to simulations. This new method provides a test of the stability of numerical Fisher estimates and can also dramatically reduce the number of simulations required to have robust results.

Speaker: William Coulton

wcoulton.pdf

10:00 AM → 10:30 AM Final Updates on Data Challenge

10:30 AM → 11:00 AM Coffee Break

11:00 AM → 12:00 PM Dark Matter Dynamics

IFPU Colloquium

Speaker: Tom Abel

DarkMatterDynamics2022.key.pdf

12:00 PM → 2:00 PM Lunch Break

2:00 PM → 3:00 PM Cosmology with Cosmic Voids

Voids in the large-scale structure of the Universe are currently entering the realm of precision cosmology. Most ongoing and planned surveys are considering them as a cosmological probe in various ways. The aim is to extract information that is complementary to what is already accessible via the traditional probes. I will present some recent highlights from the analysis of cosmic voids in both simulated, as well as observational data. These include constraints on cosmological parameters from dynamic and geometric distortions of voids in SDSS with prospects for Euclid, measurements of gravitational lensing around voids in DES, and their expected signatures from primordial non-Gaussianity and massive neutrinos based on simulations.

Speaker: Nico Hamaus (LMU Munich)

IFPU_01_07_2022_Hamaus.pdf

3:00 PM → 4:00 PM The Initial Shape of the Universe

We want to explore the potential of topological data analysis in detecting primordial non-Gaussianity through observations of the large scale structures of the universe. As a proof of concept, we estimate the Fisher information content on primordial non-Gaussianity using halo catalogs generated from N-body simulations run with both Gaussian and non-Gaussian initial conditions. We perform several tests to verify the reliability of our Fisher matrix calculation. We find promising figures for the estimated uncertainties on primordial non-Gaussianity of the local and equilateral type, proving that TDA is indeed a promising tool for analysing galaxy surveys in search for primordial non-Gaussianity.

Speaker: Juan Manuel Calles Hansen (Pontificia Universidad Católica de Valparaíso)

Slides_PNG_PH.pdf

4:00 PM → 4:30 PM Final Updates on Data Challenge - Part II