Stationary time-vertex signal processing

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We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operat ...

We present FITCOV an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting ...

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 ...

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...

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. ...

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressi ...

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a ...

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii ...

The extension of convolutional neural networks to irregular domains has pavedthe way to promising graph data analysis methods. It has however come at theexpense of a reduced representation power, as most of these new network archi-tectures can only learn i ...

Proper modeling of stochastic errors in inertial sensors plays a crucial role in the achievable quality of GNSS-INS integration especially with low-cost inertial sensors. Generalized Method of Wavelet Moments (GMWM) can model the underlying process for suc ...

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length , one has no statistical information on ...

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical ...

Stationary time-vertex signal processing

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Transportation-based functional ANOVA and PCA for covariance operators

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

Positive Definite Completions and Continuous Graphical Models

Detecting whether a stochastic process is finitely expressed in a basis

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

The two-point correlation function covariance with fewer mocks

The Debiased Spatial Whittle likelihood

Covariance Estimation for Random Surfaces beyond Separability

Sparsely Observed Functional Time Series: Theory and Applications

Euclid : Effects of sample covariance on the number counts of galaxy clusters

SPHARMA approximations for stationary functional time series on the sphere

Certified And Fast Computations With Shallow Covariance Kernels

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

The n-term Approximation of Periodic Generalized Levy Processes

Gaussian and sparse processes are limits of generalized Poisson processes

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Learning anisotropic filters on product graphs

Optimal Stochastic Sensor Error Modeling based on Actual Impact on Quality of GNSS-INS Integrated Navigation

Recovering covariance from functional fragments

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems