Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used approximations like the Laplace method struggle with scalability and posterior accuracy in modern deep networks. In this work, we revisit sampling techniques for posterior exploration, proposing a simple variation tailored to efficiently sample from the posterior in over-parameterized networks by leveraging the low-dimensional structure of loss minima. Building on this, we introduce a model that learns a deformation of the parameter space, enabling rapid posterior sampling without requiring iterative methods. Empirical results demonstrate that our approach achieves competitive posterior approximations with improved scalability compared to recent refinement techniques. These contributions provide a practical alternative for Bayesian inference in deep learning.

Despite their successes, modern neural networks (NNs) still suffer from several shortcomings that limit their applicability in some settings.

Despite their successes, modern neural networks (NNs) still suffer from several shortcomings that limit their applicability in some settings.

Uncertainty quantification is an important prerequisite for the deployment of deep learning models in safety-critical areas. Yet, this hinges on the uncertainty estimates being useful to the extent the prediction intervals are well-calibrated and sharp. In the absence of inherent uncertainty estimates (e.g. pretrained models predicting only point estimates), popular approaches that operate post-hoc include Laplace's method and split conformal prediction (split-CP). However, Laplace's method can be miscalibrated when the model is misspecified and split-CP requires sample splitting, and thus comes at the expense of statistical efficiency. In this work, we construct prediction intervals for neural network regressors post-hoc without held-out data. This is achieved by approximating the full conformal prediction method (full-CP). Whilst full-CP nominally requires retraining the model for every test point and candidate label, we propose to train just once and locally perturb model parameters using Gauss-Newton influence to approximate the effect of retraining. Coupled with linearization of the network, we express the absolute residual nonconformity score as a piecewise linear function of the candidate label allowing for an efficient procedure that avoids the exhaustive search over the output space. On standard regression benchmarks and bounding box localization, we show the resulting prediction intervals are locally-adaptive and often tighter than those of split-CP.

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of architecture, hyperparameters and optimization procedure. However, deploying deep learning models out-of-distribution, in sequential decision-making tasks, or in safety-critical domains, necessitates reliable uncertainty quantification, not just a point estimate. The machinery of modern approximate inference -- Bayesian deep learning -- should answer the need for uncertainty quantification, but its effectiveness has been challenged by our inability to define useful explicit inductive biases through priors, as well as the associated computational burden. Instead, in this work we demonstrate, both theoretically and empirically, how to regularize a variational deep network implicitly via the optimization procedure, just as for standard deep learning. We fully characterize the inductive bias of (stochastic) gradient descent in the case of an overparametrized linear model as generalized variational inference and demonstrate the importance of the choice of parametrization. Finally, we show empirically that our approach achieves strong in- and out-of-distribution performance without tuning of additional hyperparameters and with minimal time and memory overhead over standard deep learning.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Objectives: This paper develops two algorithms to achieve federated generalized linear mixed effect models (GLMM), and compares the developed model's outcomes with each other, as well as that from the standard R package (`lme4'). Methods: The log-likelihood function of GLMM is approximated by two numerical methods (Laplace approximation and Gaussian Hermite approximation), which supports federated decomposition of GLMM to bring computation to data. Results: Our developed method can handle GLMM to accommodate hierarchical data with multiple non-independent levels of observations in a federated setting. The experiment results demonstrate comparable (Laplace) and superior (Gaussian-Hermite) performances with simulated and real-world data. Conclusion: We developed and compared federated GLMMs with different approximations, which can support researchers in analyzing biomedical data to accommodate mixed effects and address non-independence due to hierarchical structures (i.e., institutes, region, country, etc.).

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 Bayesian leave-one-out (LOO) cross-validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data. Our main objective is to assess the accuracy of the approximative LOO cross-validation estimators. That is, for each method (Laplace and EP) we compare the approximate fast computation with the exact brute force LOO computation. Secondarily, we evaluate the accuracy of the Laplace and EP approximations themselves against a ground truth established through extensive Markov chain Monte Carlo simulation. Our empirical results show that the approach based upon a Gaussian approximation to the LOO marginal distribution (the so-called cavity distribution) gives the most accurate and reliable results among the fast methods.

In this study, we propose an automatic learning method for variables selection based on Lasso in epidemiology context. One of the aim of this approach is to overcome the pretreatment of experts in medicine and epidemiology on collected data. These pretreatment consist in recoding some variables and to choose some interactions based on expertise. The approach proposed uses all available explanatory variables without treatment and generate automatically all interactions between them. This lead to high dimension. We use Lasso, one of the robust methods of variable selection in high dimension. To avoid over fitting a two levels cross-validation is used. Because the target variable is account variable and the lasso estimators are biased, variables selected by lasso are debiased by a GLM and used to predict the distribution of the main vector of malaria which is Anopheles. Results show that only few climatic and environmental variables are the mains factors associated to the malaria risk exposure.