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06/13/2023
The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions
Inference and simulation in the context of high-dimensional dynamical sy...
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06/12/2023
Benchmarking Neural Network Training Algorithms
Training algorithms, broadly construed, are an essential part of every d...
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05/24/2023
Probabilistic Exponential Integrators
Probabilistic solvers provide a flexible and efficient framework for sim...
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05/22/2023
Uncertainty and Structure in Neural Ordinary Differential Equations
Neural ordinary differential equations (ODEs) are an emerging class of d...
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05/22/2023
Bayesian Numerical Integration with Neural Networks
Bayesian probabilistic numerical methods for numerical integration offer...
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02/14/2023
The Geometry of Neural Nets' Parameter Spaces Under Reparametrization
Model reparametrization – transforming the parameter space via a bijecti...
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12/23/2022
Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers
Linear partial differential equations (PDEs) are an important, widely ap...
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08/02/2022
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs
Neural operators are a type of deep architecture that learns to solve (i...
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05/30/2022
Posterior and Computational Uncertainty in Gaussian Processes
Gaussian processes scale prohibitively with the size of the dataset. In ...
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05/20/2022
Posterior Refinement Improves Sample Efficiency in Bayesian Neural Networks
Monte Carlo (MC) integration is the de facto method for approximating th...
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05/16/2022
Wasserstein t-SNE
Scientific datasets often have hierarchical structure: for example, in s...
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03/07/2022
Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference
Full Bayesian posteriors are rarely analytically tractable, which is why...
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02/02/2022
Fenrir: Physics-Enhanced Regression for Initial Value Problems
We show how probabilistic numerics can be used to convert an initial val...
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12/03/2021
ProbNum: Probabilistic Numerics in Python
Probabilistic numerical methods (PNMs) solve numerical problems via prob...
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11/05/2021
Mixtures of Laplace Approximations for Improved Post-Hoc Uncertainty in Deep Learning
Deep neural networks are prone to overconfident predictions on outliers....
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10/22/2021
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations
This work develops a class of probabilistic algorithms for the numerical...
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10/22/2021
Probabilistic ODE Solutions in Millions of Dimensions
Probabilistic solvers for ordinary differential equations (ODEs) have em...
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10/20/2021
Pick-and-Mix Information Operators for Probabilistic ODE Solvers
Probabilistic numerical solvers for ordinary differential equations comp...
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07/01/2021
Reducing the Variance of Gaussian Process Hyperparameter Optimization with Preconditioning
Gaussian processes remain popular as a flexible and expressive model cla...
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06/28/2021
Laplace Redux – Effortless Bayesian Deep Learning
Bayesian formulations of deep learning have been shown to have compellin...
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06/18/2021
Being a Bit Frequentist Improves Bayesian Neural Networks
Despite their compelling theoretical properties, Bayesian neural network...
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06/14/2021
Linear-Time Probabilistic Solutions of Boundary Value Problems
We propose a fast algorithm for the probabilistic solution of boundary v...
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06/04/2021
ViViT: Curvature access through the generalized Gauss-Newton's low-rank structure
Curvature in form of the Hessian or its generalized Gauss-Newton (GGN) a...
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05/13/2021
Informed Equation Learning
Distilling data into compact and interpretable analytic equations is one...
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05/07/2021
Laplace Matching for fast Approximate Inference in Generalized Linear Models
Bayesian inference in generalized linear models (GLMs), i.e. Gaussian re...
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03/18/2021
A Probabilistic State Space Model for Joint Inference from Differential Equations and Data
Mechanistic models with differential equations are a key component of sc...
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02/22/2021
A Probabilistically Motivated Learning Rate Adaptation for Stochastic Optimization
Machine learning practitioners invest significant manual and computation...
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02/15/2021
High-Dimensional Gaussian Process Inference with Derivatives
Although it is widely known that Gaussian processes can be conditioned o...
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02/12/2021
Bayesian Quadrature on Riemannian Data Manifolds
Riemannian manifolds provide a principled way to model nonlinear geometr...
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02/12/2021
Cockpit: A Practical Debugging Tool for Training Deep Neural Networks
When engineers train deep learning models, they are very much "flying bl...
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12/18/2020
Stable Implementation of Probabilistic ODE Solvers
Probabilistic solvers for ordinary differential equations (ODEs) provide...
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12/15/2020
Calibrated Adaptive Probabilistic ODE Solvers
Probabilistic solvers for ordinary differential equations (ODEs) assign ...
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11/09/2020
Self-Tuning Stochastic Optimization with Curvature-Aware Gradient Filtering
Standard first-order stochastic optimization algorithms base their updat...
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10/19/2020
Probabilistic Linear Solvers for Machine Learning
Linear systems are the bedrock of virtually all numerical computation. M...
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10/16/2020
Robot Learning with Crash Constraints
In the past decade, numerous machine learning algorithms have been shown...
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10/06/2020
Learnable Uncertainty under Laplace Approximations
Laplace approximations are classic, computationally lightweight means fo...
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10/06/2020
Fixing Asymptotic Uncertainty of Bayesian Neural Networks with Infinite ReLU Features
Approximate Bayesian methods can mitigate overconfidence in ReLU network...
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07/30/2020
When are Neural ODE Solutions Proper ODEs?
A key appeal of the recently proposed Neural Ordinary Differential Equat...
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07/03/2020
Descending through a Crowded Valley – Benchmarking Deep Learning Optimizers
Choosing the optimizer is among the most crucial decisions of deep learn...
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04/01/2020
Bayesian ODE Solvers: The Maximum A Posteriori Estimate
It has recently been established that the numerical solution of ordinary...
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03/02/2020
Fast Predictive Uncertainty for Classification with Bayesian Deep Networks
In Bayesian Deep Learning, distributions over the output of classificati...
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02/24/2020
Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks
The point estimates of ReLU classification networks—arguably the most wi...
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02/21/2020
Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
Likelihood-free (a.k.a. simulation-based) inference problems are inverse...
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12/23/2019
BackPACK: Packing more into backprop
Automatic differentiation frameworks are optimized for exactly one thing...
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11/14/2019
Conjugate Gradients for Kernel Machines
Regularized least-squares (kernel-ridge / Gaussian process) regression i...
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10/21/2019
Integrals over Gaussians under Linear Domain Constraints
Integrals of linearly constrained multivariate Gaussian densities are a ...
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07/24/2019
Classified Regression for Bayesian Optimization: Robot Learning with Unknown Penalties
Learning robot controllers by minimizing a black-box objective cost usin...
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06/27/2019
Uncertainty Estimates for Ordinal Embeddings
To investigate objects without a describable notion of distance, one can...
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05/29/2019
Limitations of the Empirical Fisher Approximation
Natural gradient descent, which preconditions a gradient descent update ...
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05/24/2019