26 citations · 58 across the 10 of their papers we have counts for
12 papers
SDEs for Minimax Optimization
Enea Monzio Compagnoni, Antonio Orvieto, Hans Kersting +2
Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization m…
An SDE for Modeling SAM: Theory and Insights
Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto +3
We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic…
On the Theoretical Properties of Noise Correlation in Stochastic Optimization
Aurelien Lucchi, Frank Proske, Antonio Orvieto +2
Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that…
Mean first exit times of Ornstein-Uhlenbeck processes in high-dimensional spaces
Hans Kersting, Antonio Orvieto, Frank Proske +1
The -dimensional Ornstein--Uhlenbeck process (OUP) describes the trajectory of a particle in a -dimensional, spherically symmetric, quadratic potential. The OUP is composed o…
Explicit Regularization in Overparametrized Models via Noise Injection
Antonio Orvieto, Anant Raj, Hans Kersting +1
Injecting noise within gradient descent has several desirable features, such as smoothing and regularizing properties. In this paper, we investigate the effects of injecting noise…
Anticorrelated Noise Injection for Improved Generalization
Antonio Orvieto, Hans Kersting, Frank Proske +2
Injecting artificial noise into gradient descent (GD) is commonly employed to improve the performance of machine learning models. Usually, uncorrelated noise is used in such pertur…
A Fourier State Space Model for Bayesian ODE Filters
Hans Kersting, Maren Mahsereci
Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of t…
Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
Hans Kersting, Nicholas Krämer, Martin Schiegg +3
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likel…
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Filip Tronarp, Hans Kersting, Simo Särkkä +1
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measureme…
Convergence Rates of Gaussian ODE Filters
Hans Kersting, T. J. Sullivan, Philipp Hennig
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. T…
Bayesian Filtering for ODEs with Bounded Derivatives
Emilia Magnani, Hans Kersting, Michael Schober +1
Recently there has been increasing interest in probabilistic solvers for ordinary differential equations (ODEs) that return full probability measures, instead of point estimates, o…
Active Uncertainty Calibration in Bayesian ODE Solvers
Hans Kersting, Philipp Hennig
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates.…