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We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

Optimization and Control · Mathematics 2021-12-22 Adrien Taylor , Francis Bach

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

Machine Learning · Statistics 2025-03-25 Zehao Li , Yijie Peng

We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…

Data Analysis, Statistics and Probability · Physics 2016-12-06 Juan M. Restrepo , Shankar C. Venkataramani

Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…

Machine Learning · Computer Science 2010-03-04 Joshua V Dillon , Guy Lebanon

We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…

Data Structures and Algorithms · Computer Science 2020-06-17 Michael Mitzenmacher , Sergei Vassilvitskii

The Boltzmann Machine (BM) is a neural network composed of stochastically firing neurons that can learn complex probability distributions by adapting the synaptic interactions between the neurons. BMs represent a very generic class of…

Mesoscale and Nanoscale Physics · Physics 2021-09-16 Brian Kiraly , Elze J. Knol , Hilbert J. Kappen , Alexander A. Khajetoorians

To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic…

Artificial Intelligence · Computer Science 2009-03-09 S. Armagan Tarim , Suresh Manandhar , Toby Walsh

Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…

Probability · Mathematics 2018-04-12 Soumyadip Ghosh , Henry Lam

Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate…

Image and Video Processing · Electrical Eng. & Systems 2024-05-21 Guy Ohayon , Theo Adrai , Michael Elad , Tomer Michaeli

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…

Machine Learning · Computer Science 2020-10-30 Jerome Bolte , Edouard Pauwels

It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based…

Methodology · Statistics 2024-03-12 Mohamed Abdalmoaty , Efe C. Balta , John Lygeros , Roy S. Smith

Combining efficient and safe control for safety-critical systems is challenging. Robust methods may be overly conservative, whereas probabilistic controllers require a trade-off between efficiency and safety. In this work, we propose a…

Systems and Control · Electrical Eng. & Systems 2022-09-16 Tim Brüdigam , Robert Jacumet , Dirk Wollherr , Marion Leibold

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

Discrete Mathematics · Computer Science 2021-12-22 Nicolas Behr , Bello Shehu Bello , Sebastian Ehmes , Reiko Heckel

Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…

Statistical Mechanics · Physics 2018-05-24 Daan Frenkel , K. Julian Schrenk , Stefano Martiniani

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

Probability · Mathematics 2014-03-10 Christophe Andrieu , Matti Vihola

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Optimization and Control · Mathematics 2011-07-01 Qihang Lin , Xi Chen , Javier Pena

This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…

Discrete Mathematics · Computer Science 2013-05-20 Pablo Arrighi , Nicolas Schabanel , Guillaume Theyssier

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Machine Learning · Statistics 2013-09-11 Julien Mairal

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…

Dynamical Systems · Mathematics 2019-01-30 Omar Kebiri , Lara Neureither , Carsten Hartmann

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…

Machine Learning · Computer Science 2020-04-23 Joe Watson , Hany Abdulsamad , Jan Peters
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