Common Information Components Analysis

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The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Inferring protein-protein interactions from sequences is an important task in computational biology. Recent methods based on Direct Coupling Analysis (DCA) or Mutual Information (MI) allow to find interaction partners among paralogs of two protein families ...

In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback- Leibler Divergences/Mutu ...

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, ou ...

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

The dynamics of open quantum systems is often modeled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the outcome of ideal si ...

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-C-l estimates of tomographic cosmic shear power spectra. Using two existing publicly av ...

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle l ...

Neural networks are ubiquitous in applied machine learning for education. Their pervasive success in predictive performance comes alongside a severe weakness, the lack of explainability of their decisions, especially relevant in human-centric fields. We im ...

Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit nontrivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching envi ...

Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results i ...

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The pr ...

Common Information Components Analysis

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Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Correlations from structure and phylogeny combine constructively in the inference of protein partners from sequences

From Generalisation Error to Transportation-cost Inequalities and Back

The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Revealing higher-order light and matter energy exchanges using quantum trajectories in ultrastrong coupling

Euclid: Covariance of weak lensing pseudo-C-l estimates Calculation, comparison to simulations, and dependence on survey geometry

The Debiased Spatial Whittle likelihood

Evaluating the Explainers: Black-Box Explainable Machine Learning for Student Success Prediction in MOOCs

Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities

Feedback and Common Information: Bounds and Capacity for Gaussian Networks

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Optimal denoising of rotationally invariant rectangular matrices

Secrecy by Design With Applications to Privacy and Compression