How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...
Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. ...
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approxi ...
Measurements of large-scale structure (LSS), as performed on the largest 3D map of over two million extragalactic sources from the Sloan Digital Sky Survey, together with measurements of the cosmic microwave background (CMB) anisotropies, are in complete a ...
We test general relativity (GR) at the effective redshift (z) over tilde similar to 1.5 by estimating the statistic E-G, a probe of gravity, on cosmological scales 19 - 190 h(-1)Mpc. This is the highest redshift and largest scale estimation of E-G so far. ...
Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees hav ...
We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large-scale feature selection problems. Identifying the knockoff distribution requires solving a large-scale semidefinite progra ...
Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...
Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuatio ...
We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...
