Related papers: Cosmological tests of General Relativity: a princi…
Weak lensing peak counts are a powerful statistical tool for constraining cosmological parameters. So far, this method has been applied only to surveys with relatively small areas, up to several hundred square degrees. As future surveys…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
Weak lensing provides a direct measure of the distribution of mass in the universe, and is therefore a uniquely powerful probe of dark matter. Weak lensing can also be used to measure the twin phenomenon of dark energy, via its effect upon…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
Cosmological constraints using weak gravitational lensing measurements from the Roman Space Telescope will require a powerful method for modelling uncertainties in the galaxy redshift distribution. In this work, we use an optimized version…
The nature of the dark matter remains a mystery. The possibility of an unstable dark matter particle decaying to invisible daughter particles has been explored many times in the past few decades. Meanwhile, weak gravitational lensing shear…
Gravitational lenses can provide crucial information on the geometry of the Universe, on the cosmological scenario of formation of its structures as well as on the history of its components with look-back time. In this review, I focus on…
We perform an empirical consistency test of General Relativity/dark energy by disentangling expansion history and growth of structure constraints. We replace each late-universe parameter that describes the behavior of dark energy with two…
Combining measurements on the expansion history of the Universe and on the growth rate of cosmic structures is key to discriminate between alternative cosmological frameworks and to test gravity. Recently, Linder (2017) proposed a new…
We modified the CLASS code in order to include relativistic galaxy number counts in spatially curved geometries; we present the formalism and study the effect of relativistic corrections on spatial curvature. The new version of the code is…
Maximising the information that can be extracted from weak lensing measurements is a key goal for upcoming surveys such as LSST and Euclid. This is typically achieved through statistics that are complementary to the cosmic shear two-point…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
The next generation of weak lensing surveys will measure the matter distribution of the local Universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of…
We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards…
This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…
In this Thesis I discuss several recent results obtained using the CMB spectra measured by Planck and several other cosmological probes. Extensions of the $\Lambda$CDM model are studied, including the presence of an additional sterile…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
The study of the Cosmic Microwave Background (CMB) lensing potential has established itself by now as a robust way of probing the physics of large-scale structure growth. The most common estimators of the lensing potential are derived under…