Publications related to Multivariate random variable

Global eigenvalue distribution of matrices defined by the skew-shift

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

2019

Unsupervised Scalable Representation Learning for Multivariate Time Series

Martin Jaggi, Aymeric Daphnis Kévin Dieuleveut

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn universal embeddings ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Recovering covariance from functional fragments

Victor Panaretos, Marie-Hélène Descary

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 ...

2019

Averaging Stochastic Gradient Descent on Riemannian Manifolds

Nicolas Henri Bernard Flammarion

We propose an estimator for the mean of a random vector in Rd that can be computed in time O(n3.5 + n2d) for n i.i.d. samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has ...

2018

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear esti ...

IEEE2018

High Dimensional Bayesian Optimization via Additive Models with Overlapping Groups

Volkan Cevher, Paul Thierry Yves Rolland, Jonathan Mark Scarlett, Ilija Bogunovic

Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the development of a ...

2018

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

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 ...

2018

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

Asynchronous adaptive networks

Ali H. Sayed

In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to streamin ...

Elsevier2018

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

Multivariate random variable

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Global eigenvalue distribution of matrices defined by the skew-shift

Unsupervised Scalable Representation Learning for Multivariate Time Series

Recovering covariance from functional fragments

Averaging Stochastic Gradient Descent on Riemannian Manifolds

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

High Dimensional Bayesian Optimization via Additive Models with Overlapping Groups

Chebyshev Inequalities for Products of Random Variables

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Asynchronous adaptive networks

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Global eigenvalue distribution of matrices defined by the skew-shift

Unsupervised Scalable Representation Learning for Multivariate Time Series

Averaging Stochastic Gradient Descent on Riemannian Manifolds

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Recovering covariance from functional fragments

Chebyshev Inequalities for Products of Random Variables

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

High Dimensional Bayesian Optimization via Additive Models with Overlapping Groups

Asynchronous adaptive networks