Related papers: Laplace Approximations for Mixed-Effects and Gauss…
The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the…
Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification,…
We propose a new family of error distributions for model-based quantile regression, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while,…
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…
To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…
Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension…
Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…
Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…
Predictive coding (PC) accounts of perception now form one of the dominant computational theories of the brain, where they prescribe a general algorithm for inference and learning over hierarchical latent probabilistic models. Despite this,…
We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model…
The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to…
The hierarchical prior used in Latent Gaussian models (LGMs) induces a posterior geometry prone to frustrate inference algorithms. Marginalizing out the latent Gaussian variable using an integrated Laplace approximation removes the…
Bayesian inference is a popular method to build learning algorithms but it is hampered by the fact that its key object, the posterior probability distribution, is often uncomputable. Expectation Propagation (EP) (Minka (2001)) is a popular…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
Laplace approximations are among the simplest and most practical methods for approximate Bayesian inference in neural networks, yet their Euclidean formulation struggles with the highly anisotropic, curved loss surfaces and large symmetry…