QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.
problem Overconfident out-of-distribution predictions from DNNs.
method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.
result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.
New methods improve Laplace approximations for deep neural networks by selecting key parameters.
problem Improving uncertainty quantification in deep neural networks using computationally feasible approximations.
method Gradient-Laplace and Greedy-Laplace methods for selecting parameters in sub-network Laplace approximations.
result Gradient-Laplace method outperforms existing heuristic approaches and provides formal optimality guarantees.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Improves Laplace approximation for Bayesian inference on Riemannian manifolds.
problem Inaccurate Gaussian approximations for complex targets and finite-data posteriors.
method Develops alternative variants of the Laplace approximation using a Riemannian metric.
result Exact approximations at the limit of infinite data, improving practical performance.
Revisits online Laplace methods for neural networks, showing they are sound under certain conditions.
problem Online Laplace methods violate the Laplace approximation's critical assumption.
method Re-derives online Laplace methods, showing they target a variational bound on a mode-corrected variant of the Laplace evidence.
result Online Laplace and its mode-corrected counterpart share stationary points that satisfy the Laplace method's assumption.
Bayesian neural networks approximate Gaussian, this method adapts to non-Gaussian posteriors.
problem Bayesian neural networks struggle with non-Gaussian posteriors, leading to poor performance.
method Proposes a Riemannian Laplace approximation to adapt to the shape of the true posterior.
result Consistently improves over conventional Laplace approximation across tasks.
New iterative methods improve Vecchia-Laplace approximations for large data sets.
problem Inaccurate and slow Vecchia-Laplace approximations for large data sets.
method Iterative methods to improve Vecchia-Laplace approximations, including preconditioners and novel methods for predictive variances.
result Order of magnitude speed-up and threefold increase in prediction accuracy compared to state-of-the-art methods.
Enhances predictive performance in Bayesian deep learning via generalized Laplace approximation.
problem Inconsistency in Bayesian deep learning.
method Interprets posterior tempering as a correction for model misspecification and recalibration of priors. Introduces generalized Laplace approximation.
result Generalized Laplace approximation enhances predictive performance.
Bayesian deep learning method using subnetwork inference.
problem Improving deep neural networks' calibration and efficiency.
method Perform inference over a subset of model weights, keeping others as point estimates.
result Subnetwork inference enables accurate predictive posteriors without full network approximations.
New metrics using Laplace approximation improve Gaussian process model selection.
problem Finding a balance between model accuracy, interpretability, and simplicity.
method Introducing multiple metrics based on the Laplace approximation to evaluate Gaussian process models.
result Our metrics provide comparable performance to dynamic nested sampling but are significantly faster.
Fast approximate inference for non-Gaussian data.
problem Efficient inference for non-Gaussian data.
method Laplace Matching for fast approximate inference in latent Gaussian models.
result Achieves high approximation quality with low computational cost.
Geometrically reformulates the Laplace method for optimal transport.
problem Approximating integrals using the Laplace method without geometric interpretation.
method Introduces the Kim-McCann Riemannian metric to give a geometric formulation of the Laplace method.
result Expresses the first-order term of the Laplace method using geometric objects.
This thesis disentangles Gauss-Newton and variational approximations in Bayesian deep learning.
problem Understanding the interplay between the Gauss-Newton method and variational approximations in Bayesian deep learning.
method Analysis of the Gauss-Newton method and Laplace/Gaussian variational approximations for neural networks.
result The combination of the Gauss-Newton method with approximate inference can be cast as inference in a linear or Gaussian process model.
New algorithms improve likelihood of finding global optima in Bayesian inference.
problem Finding global optima in Bayesian inference is difficult due to nonconvexity.
method Developed two algorithms: consistent Laplace approximation (CLA) and consistent stochastic variational inference (CSVI).
result Both CSVI and CLA improve likelihood of obtaining global optima compared to standard methods.
We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the we…
The paper addresses the invariance issue in Bayesian neural networks using linearized Laplace approximation.
problem Bayesian neural networks fail to maintain invariance under reparameterization, leading to different posterior densities for identical functions.
method Developed a geometric view of reparameterizations and a Riemannian diffusion process to extend reparameterization invariance to neural network predictive.
result Empirically improved posterior fit through approximate posterior sampling.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.
Variational Laplace improves Bayesian neural networks performance.
problem Improving Bayesian neural networks performance.
method Develops variational Laplace for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms other inference methods.
Combines Laplace approximations of deep networks for better uncertainty quantification.
problem Overconfident predictions on outliers in deep learning models.
method Gaussian mixture model posterior using weighted sum of Laplace approximations of pre-trained deep networks.
result Mitigates overconfidence 'far away' from training data.
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
problem Scalability limitations of Gaussian process regression.
method Bayesian tensor train kernel machine with Laplace approximation and variational inference.
result VI replaces cross-validation and offers up to 65x faster training.
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
LaLoRA prevents forgetting in LoRA fine-tuning.
problem Catastrophic forgetting in fine-tuned models.
method LaLoRA applies Laplace approximation to LoRA weights for regularization.
result Improved learning-forgetting trade-off with controllable regularization strength.
A new method for uncertainty estimation in neural networks using existing optimization steps.
problem Uncertainty quantification in deep neural networks.
method L2M: Practical posterior Laplace approximation with optimization-driven second moment estimation.
result L2M method yields reasonable results without requiring changes in models or extra computational steps.
A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.
problem How to provide principled uncertainty estimates for tensor network kernel machines.
method Employing a linearized Laplace approximation for Bayesian inference.
result Consistently matches or surpasses Gaussian Processes and BNNs across diverse UCI regression benchmarks.
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…
The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient …
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
Laplace approximation improves deep learning efficiency without sacrificing performance.
problem Bayesian deep learning's practical implementation and efficiency.
method Review and implementation of Laplace approximation (LA) in PyTorch.
result Laplace approximation is competitive with popular alternatives in performance but significantly more efficient.
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies. Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler…
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
Bayesian meta-reinforcement learning improves over point estimates with Laplace approximation.
problem Improving meta-reinforcement learning by providing full posterior distributions.
method Augmenting point estimates with Laplace approximation for full posterior distributions.
result Our method performs similarly to variational baselines with fewer parameters.
Paper develops federated GLMM algorithms for analyzing hierarchical data.
problem Analyzing hierarchical data with non-independent observations in a federated setting.
method Developed two federated GLMM algorithms using Laplace and Gaussian Hermite approximations.
result Federated GLMM can handle hierarchical data and achieve comparable or superior performance.
We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We …
A new method combines ANN and Laplace for fast Bayesian inference in ODE models.
problem Bayesian inference for ODE systems with non-analytical solutions is computationally expensive.
method Hybrid approach using ANN for tractable likelihood and Laplace approximation.
result Effective posterior inference with improved computational cost compared to traditional methods.
Algorithm computes eigenvalues and eigenforms on Calabi-Yau threefolds.
problem Computing spectra of Laplace-de Rham operator on Calabi-Yau manifolds.
method Numerical algorithm using approximate Calabi-Yau metric.
result Computed eigenvalues and eigenforms for the Fermat quintic threefold.
Meta-learning variance reduced via Laplace approximation for regression tasks.
problem High variance in meta-learning due to limited support data for each task.
method Laplace approximation to estimate posterior variance and reduce gradient estimate variance.
result Effective variance reduction in meta-learning, improving generalization performance.
Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of variational sampling (i.e., combining quadrature with variational approximation). Exper…
Solves geodesics and Laplace-Beltrami spectrum on flag manifolds.
problem Geodesics and Laplace-Beltrami spectrum on flag manifolds.
method Invariant metrics and finite-dimensional approximations.
result Explicit solutions for geodesics and spectrum.
This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.
problem Approximating the Laplace-Beltrami operator using optimal transport with quadratic regularization.
method Deriving first-order optimal potentials and analyzing the convergence of discrete Laplace operators.
result The discrete Laplace operators converge to the Laplace-Beltrami operator on smooth manifolds.
Proposes a new method to approximate Bayesian predictive uncertainty.
problem Bayesian uncertainty quantification in model predictions.
method Self-supervised learning approach to approximate posterior predictive distribution.
result SSLA and ASSLA outperform classical Laplace approximations in predictive calibration.
New method corrects Laplace/BIC errors in singular models, revealing effective dimension.
problem Laplace/BIC errors in singular models due to incorrect effective dimension assumption.
method RLCT (real log canonical threshold) to correct effective dimension in linear models.
result Correct evidence slope and effective dimension estimation in linear settings.
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of …
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
Corrects errors in ILA for Bayesian inference in LGMs.
problem Error in ILA for non-Gaussian likelihoods in LGMs.
method Importance sampling scheme to correct ILA errors.
result Corrected posterior converges to the true posterior with increased samples.
Adapts linearised Laplace method for deep learning models.
problem Incompatibility of linearised Laplace method with modern deep learning tools.
method Examines and adapts linearised Laplace method for model selection in deep learning.
result Recommendations for better adapting linearised Laplace method to modern deep learning.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.