Publications related to An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Gibbs sampling the posterior of neural networks

Lenka Zdeborová, Giovanni Piccioli, Emanuele Troiani

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

Bristol2024

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

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Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

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On the asymptotic behavior of the solutions to parabolic variational inequalities

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We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

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Log Barriers for Safe Non-convex Black-box Optimization

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We address the problem of minimizing a smooth function f0(x) over a compact set D defined by smooth functional constraints fi(x)≤0, i=1,…,m given noisy value measurements of fi(x). This problem arises in safety-critical applications, where certain paramete ...

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Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

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on a Riemannian manifold

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Efficient Greedy Coordinate Descent for Composite Problems

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Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

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Fast Automatic Smoothing for Generalized Additive Models

Anthony Christopher Davison, Yousra El Bachir

Generalized additive models (GAMs) are regression models wherein parameters of probability distributions depend on input variables through a sum of smooth functions, whose degrees of smoothness are selected by L-2 regularization. Such models have become th ...

MICROTOME PUBL2019

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

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Gibbs sampling the posterior of neural networks

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Forward-Backward Splitting for Optimal Transport Based Problems

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

On the asymptotic behavior of the solutions to parabolic variational inequalities

Log Barriers for Safe Non-convex Black-box Optimization

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Efficient Greedy Coordinate Descent for Composite Problems

Fast Automatic Smoothing for Generalized Additive Models

Gibbs sampling the posterior of neural networks

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Fast Automatic Smoothing for Generalized Additive Models

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Forward-Backward Splitting for Optimal Transport Based Problems

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

On the asymptotic behavior of the solutions to parabolic variational inequalities

Log Barriers for Safe Non-convex Black-box Optimization

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Efficient Greedy Coordinate Descent for Composite Problems