Laplace Approximation

Laplace approximation is a widely used technique in Bayesian inference that approximates complex posterior distributions with simpler Gaussian distributions, facilitating efficient uncertainty quantification and model selection. Current research focuses on improving the accuracy and scalability of Laplace approximations, particularly within deep learning models, by addressing issues like variance reduction, handling high-dimensional data, and incorporating informative priors, including those derived from generative models or Gaussian processes. These advancements are significant because they enable more robust and reliable Bayesian inference in various applications, ranging from meta-learning and Bayesian optimization to data assimilation and uncertainty estimation in deep neural networks.

Papers

November 14, 2024

Laplace Transform Interpretation of Differential Privacy
Rishav Chourasia, Uzair Javaid, Biplap Sikdar
Differential Privacy Laplace Approximation DP Algorithm Privacy Loss

October 2, 2024

Reducing Variance in Meta-Learning via Laplace Approximation for Regression Tasks
Alfredo Reichlin, Gustaf Tegnér, Miguel Vasco, Hang Yin, Mårten Björkman, Danica Kragic
Meta Learning Regression Task Variance Reduction Gradient Based Meta Learning Laplace Approximation

July 18, 2024

FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learning
Tristan Cinquin, Marvin Pförtner, Vincent Fortuin, Philipp Hennig, Robert Bamler
Inductive Bias Bayesian Deep Learning Laplace Approximation Gaussian Prior Functional Prior Laplace fPINNs

May 22, 2024

Generalized Laplace Approximation
Yinsong Chen, Samson S. Yu, Zhong Li, Chee Peng Lim
Bayesian Deep Learning Laplace Approximation

March 14, 2024

On the Laplace Approximation as Model Selection Criterion for Gaussian Processes
Andreas Besginow, Jan David Hüwel, Thomas Pawellek, Christian Beecks, Markus Lange-Hegermann
Gaussian Process Model Performance Model Selection Laplace Approximation

February 26, 2024

Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems
Rafael Anderka, Marc Peter Deisenroth, So Takao
Partial Differential Equation Nonlinear Dynamic State Estimation Internal State Data Assimilation Parameter Estimation Laplace Approximation

December 16, 2023

Identity Curvature Laplace Approximation for Improved Out-of-Distribution Detection
Maksim Zhdanov, Stanislav Dereka, Sergey Kolesnikov
Uncertainty Estimation Bayesian Approach Understanding Out of Distribution Accurate Uncertainty Laplace Approximation

November 5, 2023

Riemannian Laplace Approximation with the Fisher Metric
Hanlin Yu, Marcelo Hartmann, Bernardo Williams, Mark Girolami, Arto Klami
Bayesian Inference Gaussian Distribution Laplace Approximation Fisher Information Metric Gaussian Approximation

August 31, 2023

Pure Differential Privacy for Functional Summaries via a Laplace-like Process
Haotian Lin, Matthew Reimherr
Differential Privacy Simple Function Output Space Laplace Approximation Non Private Infinite Dimensional

July 12, 2023

Online Laplace Model Selection Revisited
Jihao Andreas Lin, Javier Antorán, José Miguel Hernández-Lobato
Neural Network Laplace Approximation Neural Laplace Laplace fPINNs

June 12, 2023

Riemannian Laplace approximations for Bayesian neural networks
Federico Bergamin, Pablo Moreno-Muñoz, Søren Hauberg, Georgios Arvanitidis
Bayesian Neural Network Laplace Approximation Log Gradient

April 17, 2023

Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization
Agustinus Kristiadi, Alexander Immer, Runa Eschenhagen, Vincent Fortuin
Gaussian Process Bayesian Optimization Bayesian Neural Network RSD Difference of Gaussian Common Pitfall Promise Laplace Approximation

February 24, 2023

Variational Linearized Laplace Approximation for Bayesian Deep Learning
Luis A. Ortega, Simón Rodríguez Santana, Daniel Hernández-Lobato
Training Dynamic Bayesian Deep Learning Laplace Approximation Sparse Variational Gaussian Process Nystr\"om Approximation

October 23, 2022

Accelerated Linearized Laplace Approximation for Bayesian Deep Learning
Zhijie Deng, Feng Zhou, Jun Zhu
Bayesian Neural Network Neural Tangent Kernel Bayesian Deep Learning Gauss Newton Laplace Approximation

March 15, 2022

Generative models and Bayesian inversion using Laplace approximation
Manuel Marschall, Gerd Wübbeler, Franko Schmähling, Clemens Elster
Generative Model Probabilistic Generative Model Bayesian Inverse Problem Bayesian Inversion Laplace Approximation Prior Density

February 22, 2022

Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximations
Alexander Immer, Tycho F. A. van der Ouderaa, Gunnar Rätsch, Vincent Fortuin, Mark van der Wilk
Deep Learning Deep Neural Network Data Augmentation Laplace Approximation Invariance Learning Kronecker Product Approximation

November 9, 2021

Gaussian Process Meta Few-shot Classifier Learning via Linear Discriminant Laplace Approximation
Minyoung Kim, Timothy Hospedales
Gaussian Process Posterior Inference Shot Classification Meta Training Laplace Approximation

November 5, 2021

Mixtures of Laplace Approximations for Improved Post-Hoc Uncertainty in Deep Learning
Runa Eschenhagen, Erik Daxberger, Philipp Hennig, Agustinus Kristiadi
Deep Learning Deep Neural Network Mixture Component Bayesian Neural Network Gaussian Mixture Model Deep Ensemble Overconfident Prediction Laplace Approximation