Publications related to Probability density function

Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in t ...

2024

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Daniel Kressner, Haoze He

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 ...

Siam Publications2024

On distributional autoregression and iterated transportation

Victor Panaretos, Laya Ghodrati

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...

Wiley2024

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Robot Learning using Tensor Networks

Suhan Narayana Shetty

In various robotics applications, the selection of function approximation methods greatly influences the feasibility and computational efficiency of algorithms. Tensor Networks (TNs), also referred to as tensor decomposition techniques, present a versatile ...

EPFL2024

Graph generative deep learning models with an application to circuit topologies

Igor Krawczuk

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

EPFL2024

Density estimation in RKHS with application to Korobov spaces in high dimensions

Fabio Nobile, Yoshihito Kazashi

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

2023

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Frédéric Courbin, Gianluca Castignani, Austin Chandler Peel, Jean-Luc Starck, Maurizio Martinelli, Yi Wang, Richard Massey, Fabio Finelli, Marcello Farina

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale ...

EDP SCIENCES S A2023

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Yanina Yurina Shkel

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

2023

Polynomial-time universality and limitations of deep learning

Emmanuel Abbé

The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...

WILEY2023

Incentive Mechanism in the Sponsored Content Market With Network Effects

Olga Fink, Mina Montazeri

We propose an incentive mechanism for the sponsored content provider (CP) market in which the communication of users can be represented by a graph, and the private information of the users is assumed to have a continuous distribution function. The CP stipu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Stochastic particle transport by deep-water irregular breaking waves

Debbie Eeltink

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Cambridge University Press2023

Distributional Regression and Autoregression via Optimal Transport

Laya Ghodrati

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

EPFL2023

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning

Jean-Philippe Thiran, Roser Vinals Terres

Ultrafast ultrasound imaging, characterized by high frame rates, generates low-quality images. Convolutional neural networks (CNNs) have demonstrated great potential to enhance image quality without compromising the frame rate. However, CNNs have been most ...

2023

DESI mock challenge Halo and galaxy catalogues with the bias assignment method

Cheng Zhao, Ginevra Favole, Yu Yu

Context. We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. Aims. We aim to produce mock galaxy ...

EDP SCIENCES S A2023

Removing Algorithmic Discrimination (With Minimal Individual Error)

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Le Nguyen Hoang

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

2022

Assessment of the Lightning Performance of overhead distribution lines based on Lightning Location Systems data

Farhad Rachidi-Haeri

This article presents the Lightning Performance (LP) assessment of a realistic portion of the Italian distribution network with the use of probability distributions for lightning parameters inferred from local data recorded by a Lightning Location System ( ...

2022

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Daniel Kuhn, Zhi Chen, Wolfram Wiesemann

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...

2023

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

Nicolas Macris, Jean François Emmanuel Barbier

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 ...

AMER PHYSICAL SOC2022

Principles of checkpoint override

Ahmad Sadeghi

Why biological quality-control systems fail is often mysterious. Specifically, checkpoints such as the DNA damage checkpoint or the spindle assembly checkpoint are overriden after prolonged arrests allowing cells to continue dividing despite the continued ...

EPFL2022