Positive Definite Completions and Continuous Graphical Models

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In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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 ...

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 ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and ...

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

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 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 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 ...

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 ...

In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observatio ...

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright–Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation techniques that are of s ...

Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the presence of outliers, ...

Point clouds are effective data structures for the rep- resentation of three-dimensional media and hence adopted in a wide range of practical applications. In many cases, the portrayed data is expected to be visualized by humans. After acquisition, point c ...

Positive Definite Completions and Continuous Graphical Models

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Random matrix methods for high-dimensional machine learning models

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

Transportation-based functional ANOVA and PCA for covariance operators

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Anthony C Davison and Igor Rodionov's contribution to the Discussion of 'Estimating means of bounded random variables by betting' by Waudby-Smith and Ramdas

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Detecting whether a stochastic process is finitely expressed in a basis

The two-point correlation function covariance with fewer mocks

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

Probing the nature of Dark Energy through the study of large scale structures using spectroscopic surveys and their simulations

Stochastic adaptive resampling for the estimation of discrete choice models

Estimation of Self-Exciting Point Processes from Time-Censored Data

A Shape Derivative Approach to Domain Simplification

Functional data analysis with rough sample paths?

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

Robust discrete choice models with t-distributed kernel errors

Towards a multiscale point cloud structural similarity metric