arXiv subjects

Kristoffer H. Hellton

Publications and source records attributed to Kristoffer H. Hellton.

5 recordsLinked to original sources

arXiv2023

Influence of single observations on the choice of the penalty parameter in ridge regression

Penalized regression methods such as ridge regression heavily rely on the choice of a tuning or penalty parameter, which is often computed via cross-validation. Discrepancies in the value of the penalty parameter may lead to substantial differences in regression coefficient estimates and predictions. In this paper, we investigate the effect of single observations on the optimal choice of the tuning parameter, showing how the presence of influential points can change it dramatically. We distinguish between points as ``expanders'' and ``shrinkers'', based on their effect on the model complexity. Our approach supplies a visual exploratory tool to identify influential points, naturally implementable for high-dimensional data where traditional approaches usually fail. Applications to simulated and real data examples, both low- and high-dimensional, are presented. The visual tool is implemented in the R package influridge.

stat.ME↗

arXiv2020

Penalized angular regression for personalized predictions

Personalization is becoming an important feature in many predictive applications. We introduce a penalized regression method implementing personalization inherently in the penalty. Personalized angle (PAN) regression constructs regression coefficients that are specific to the covariate vector for which one is producing a prediction, thus personalizing the regression model itself. This is achieved by penalizing the angles in a hyperspherical parametrization of the regression coefficients. For an orthogonal design matrix, it is shown that the PAN estimate is the solution to a low-dimensional eigenvector equation. Using a parametric bootstrap procedure to select the tuning parameter, simulations show that PAN regression can outperform ordinary least squares and ridge regression in terms of prediction error. We further prove that by combining the PAN penalty with an $L_{2}$ penalty the resulting method will have uniformly smaller mean squared prediction error than ridge regression, asymptotically. Finally, we demonstrate the method in a medical application.

stat.ME↗

arXiv2019

Multivariate postprocessing methods for high-dimensional seasonal weather forecasts

Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical postprocessing of the output to correct systematic biases and unrealistic uncertainty assessments. We propose a multivariate postprocessing approach utilizing covariance tapering, combined with a dimension reduction step based on principal component analysis for efficient computation. Our proposed technique can correctly and efficiently handle non-stationary, non-isotropic and negatively correlated spatial error patterns, and is applicable on a global scale. Further, a moving average approach to marginal postprocessing is shown to flexibly handle trends in biases caused by global warming, and short training periods. In an application to global sea surface temperature forecasts issued by the Norwegian Climate Prediction Model (NorCPM), our proposed methodology is shown to outperform known reference methods.

stat.ME↗

arXiv2019

Tuning parameter calibration for prediction in personalized medicine

Personalized medicine has become an important part of medicine, for instance predicting individual drug responses based on genomic information. However, many current statistical methods are not tailored to this task, because they overlook the individual heterogeneity of patients. In this paper, we look at personalized medicine from a linear regression standpoint. We introduce an alternative version of the ridge estimator and target individuals by establishing a tuning parameter calibration scheme that minimizes prediction errors of individual patients. In stark contrast, classical schemes such as cross-validation minimize prediction errors only on average. We show that our pipeline is optimal in terms of oracle inequalities, fast, and highly effective both in simulations and on real data.

stat.AP↗

arXiv2018

Bayesian regional flood frequency analysis for large catchments

Regional flood frequency analysis is commonly applied in situations where there exists insufficient data at a location for a reliable estimation of flood quantiles. We develop a Bayesian hierarchical modeling framework for a regional analysis of data from 203 large catchments in Norway with the generalized extreme value (GEV) distribution as the underlying model. Generalized linear models on the parameters of the GEV distribution are able to incorporate location-specific geographic and meteorological information and thereby accommodate these effects on the flood quantiles. A Bayesian model averaging component additionally assesses model uncertainty in the effect of the proposed covariates. The resulting regional model is seen to give substantially better predictive performance than the regional model currently used in Norway.

stat.AP↗