Related papers: Laplace approximation for fast Bayesian inference …
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
This is a hands-on introduction to Generalised Additive Mixed Models (GAMMs) in the context of linguistics with a particular focus on dynamic speech analysis (e.g. formant contours, pitch tracks, diachronic change, etc.). The main goal is…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
In this thesis, we disentangle the generalized Gauss-Newton and approximate inference for Bayesian deep learning. The generalized Gauss-Newton method is an optimization method that is used in several popular Bayesian deep learning…
As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based…
We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying…
Although the Laplace approximation offers a simple route to uncertainty quantification in deep neural networks, its reliance on inverting large Hessian matrices has motivated a range of computationally feasible low-dimensional or sparse…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…
Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive…
Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…
Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…
We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed,…
Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through…
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…
While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of 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…
Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free…