arXiv subjects

Fabio Sigrist

Publications and source records attributed to Fabio Sigrist.

26 records · Page 2Linked to original sources

arXiv2021

Joint Variable Selection of both Fixed and Random Effects for Gaussian Process-based Spatially Varying Coefficient Models

Spatially varying coefficient (SVC) models are a type of regression model for spatial data where covariate effects vary over space. If there are several covariates, a natural question is which covariates have a spatially varying effect and which not. We present a new variable selection approach for Gaussian process-based SVC models. It relies on a penalized maximum likelihood estimation (PMLE) and allows variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach both in a simulation study as well as a real world data set. Our novel approach shows good selection performance in the simulation study. In the real data application, our proposed PMLE yields sparser SVC models and achieves a smaller information criterion than classical MLE. In a cross-validation applied on the real data, we show that sparser PML estimated SVC models are on par with ML estimated SVC models with respect to predictive performance.

stat.ME↗

arXiv2021

KTBoost: Combined Kernel and Tree Boosting

We introduce a novel boosting algorithm called `KTBoost' which combines kernel boosting and tree boosting. In each boosting iteration, the algorithm adds either a regression tree or reproducing kernel Hilbert space (RKHS) regression function to the ensemble of base learners. Intuitively, the idea is that discontinuous trees and continuous RKHS regression functions complement each other, and that this combination allows for better learning of functions that have parts with varying degrees of regularity such as discontinuities and smooth parts. We empirically show that KTBoost significantly outperforms both tree and kernel boosting in terms of predictive accuracy in a comparison on a wide array of data sets.

cs.LG↗

arXiv2020

Maximum Likelihood Estimation of Spatially Varying Coefficient Models for Large Data with an Application to Real Estate Price Prediction

In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian process-based spatially varying coefficient (SVC) model can be estimated using maximum likelihood estimation (MLE). In addition, we present an approach that scales to large data by applying covariance tapering. We compare our methodology to existing methods such as a Bayesian approach using the stochastic partial differential equation (SPDE) link, geographically weighted regression (GWR), and eigenvector spatial filtering (ESF) in both a simulation study and an application where the goal is to predict prices of real estate apartments in Switzerland. The results from both the simulation study and application show that the MLE approach results in increased predictive accuracy and more precise estimates. Since we use a model-based approach, we can also provide predictive variances. In contrast to existing model-based approaches, our method scales better to data where both the number of spatial points is large and the number of spatially varying covariates is moderately-sized, e.g., above ten.

stat.ME↗

arXiv2020

Gradient and Newton Boosting for Classification and Regression

Boosting algorithms are frequently used in applied data science and in research. To date, the distinction between boosting with either gradient descent or second-order Newton updates is often not made in both applied and methodological research, and it is thus implicitly assumed that the difference is irrelevant. The goal of this article is to clarify this situation. In particular, we present gradient and Newton boosting, as well as a hybrid variant of the two, in a unified framework. We compare these boosting algorithms with trees as base learners using various datasets and loss functions. Our experiments show that Newton boosting outperforms gradient and hybrid gradient-Newton boosting in terms of predictive accuracy on the majority of datasets. We also present evidence that the reason for this is not faster convergence of Newton boosting. In addition, we introduce a novel tuning parameter for tree-based Newton boosting which is interpretable and important for predictive accuracy.

stat.ML↗

arXiv2019

Grabit: Gradient Tree-Boosted Tobit Models for Default Prediction

A frequent problem in binary classification is class imbalance between a minority and a majority class such as defaults and non-defaults in default prediction. In this article, we introduce a novel binary classification model, the Grabit model, which is obtained by applying gradient tree boosting to the Tobit model. We show how this model can leverage auxiliary data to obtain increased predictive accuracy for imbalanced data. We apply the Grabit model to predicting defaults on loans made to Swiss small and medium-sized enterprises (SME) and obtain a large and significant improvement in predictive performance compared to other state-of-the-art approaches.

stat.ME↗

arXiv2016

Stochastic partial differential equation based modelling of large space-time data sets

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a flexible model class for spatio-temporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has in general a nonseparable covariance structure. Furthermore, its parameters can be physically interpreted as explicitly modeling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. In order to obtain computationally efficient statistical algorithms we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational costs of Bayesian or frequentist inference being dominated by the fast Fourier transform. The proposed model is applied to postprocessing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast to the raw forecasts from the numerical model, the postprocessed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.

stat.ME↗

arXiv2013

A dynamic nonstationary spatio-temporal model for short term prediction of precipitation

Precipitation is a complex physical process that varies in space and time. Predictions and interpolations at unobserved times and/or locations help to solve important problems in many areas. In this paper, we present a hierarchical Bayesian model for spatio-temporal data and apply it to obtain short term predictions of rainfall. The model incorporates physical knowledge about the underlying processes that determine rainfall, such as advection, diffusion and convection. It is based on a temporal autoregressive convolution with spatially colored and temporally white innovations. By linking the advection parameter of the convolution kernel to an external wind vector, the model is temporally nonstationary. Further, it allows for nonseparable and anisotropic covariance structures. With the help of the Voronoi tessellation, we construct a natural parametrization, that is, space as well as time resolution consistent, for data lying on irregular grid points. In the application, the statistical model combines forecasts of three other meteorological variables obtained from a numerical weather prediction model with past precipitation observations. The model is then used to predict three-hourly precipitation over 24 hours. It performs better than a separable, stationary and isotropic version, and it performs comparably to a deterministic numerical weather prediction model for precipitation and has the advantage that it quantifies prediction uncertainty.

stat.AP↗

arXiv2012

Using The Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default

Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables that are a fraction or a proportion. It is shown how to fit these models and they are applied to a Loss Given Default dataset from insurance to which they provide a good fit.

stat.AP↗