Publications related to Is there an analog of Nesterov acceleration for gradient-based MCMC?

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

Fast Mean Estimation with Sub-Gaussian Rates

Nicolas Henri Bernard Flammarion

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we make an additional ...

2019

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Wolfram Wiesemann

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood ...

2019

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Mirrored Langevin Dynamics

Volkan Cevher, Paul Thierry Yves Rolland, Ya-Ping Hsieh, Ali Kavis

We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror descent, to derive ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Mirrored Langevin Dynamics

Volkan Cevher, Paul Thierry Yves Rolland, Ya-Ping Hsieh, Ali Kavis

We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror descent, to derive ...

2018

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

Safe Adaptive Importance Sampling

Martin Jaggi, Sebastian Urban Stich, Anant Raj

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants - using importance values defined by the complete gradient information which changes during optimization - ...

2017

Sampling at unknown locations, with an application in surface retrieval

Martin Vetterli, Benjamin Bejar Haro, Adam James Scholefield, Michalina Wanda Pacholska

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

2017

Is there an analog of Nesterov acceleration for gradient-based MCMC?

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On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fast Mean Estimation with Sub-Gaussian Rates

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Mirrored Langevin Dynamics

Mirrored Langevin Dynamics

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Safe Adaptive Importance Sampling

Sampling at unknown locations, with an application in surface retrieval

Safe Adaptive Importance Sampling

Fast Mean Estimation with Sub-Gaussian Rates

Mirrored Langevin Dynamics

Mirrored Langevin Dynamics

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Sampling at unknown locations, with an application in surface retrieval

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Approximation of Non-decaying Signals from Shift-Invariant Subspaces