Related papers: On Bayesian Generalized Additive Models
Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. However, glass-box interpretability…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…
Generalized additive models (GAMs, Hastie & Tibshirani, 1990; Wood, 2017) are an extension of the generalized linear model that allows the effects of covariates to be modelled as smooth functions. GAMs are increasingly used in many areas of…
Over the last decades, the challenges in applied regression and in predictive modeling have been changing considerably: (1) More flexible model specifications are needed as big(ger) data become available, facilitated by more powerful…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. This study develops a general framework for fast and flexible non-Gaussian regression, especially for…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability.…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Symbolic regression has excelled in uncovering equations from physics, chemistry, biology, and related disciplines. However, its effectiveness becomes less certain when applied to experimental data lacking inherent closed-form expressions.…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…
Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…
We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the…
Generalized additive models (GAMs) are favored in many regression and binary classification problems because they are able to fit complex, nonlinear functions while still remaining interpretable. In the first part of this paper, we…