Geir Olve Storvik

• Tandon, Kushagri; Thorarinsdottir, Thordis Linda & Storvik, Geir Olve (2026). Distributional properties of non-Gaussian spatial fields. I Bin, Riccardo De; Salucci, Clara Bertinelli & Hubin, Aliaksandr (Red.), Proceedings of the 40th International Workshop on Statistical Modelling 28.06 – 03.07.2026, Oslo, Norway. International Workshop on Statistical Modelling. ISSN 9788255325000. s. 526–529. Fulltekst i vitenarkiv
• Frommlet, Florian; Lachmann, Jon; Storvik, Geir Olve & Hubin, Aliaksandr (2026). FBMS: An R package for flexible Bayesian model selection and averaging with nonlinear models. Journal of Computational Science. ISSN 1877-7503. 100, s. 102947–102947. doi: 10.1016/j.jocs.2026.102947. Fulltekst i vitenarkiv Vis sammendrag

  The FBMS R package provides a unified interface for Bayesian model selection and model averaging across a broad class of regression models, including Gaussian regression, generalized linear models, and models with nonlinear functional relationships, with possible extensions to mixed-effects and survival models. Users specify candidate predictors together with transformation and interaction rules, and FBMS automatically explores the corresponding model spaces, estimates marginal likelihoods, and returns posterior model and inclusion probabilities, best and median probability models, posterior modes of parameters, and predictions with associated uncertainty. The core machinery combines mode-jumping Markov chain Monte Carlo with a genetically modified extension that iteratively generates and evaluates nonlinear features in the framework of Bayesian generalized nonlinear regression, while supporting flexible prior specification (including g-priors, Jeffreys priors, and empirical Bayes constructions), subsampling for large datasets, parallel computation, and the option to supply custom likelihoods for specialized applications. As special cases, the framework covers models based on fractional polynomials, logic regression, neural networks, symbolic regression, and classical linear regression.

• Skaaret-Lund, Lars; Storvik, Geir Olve & Hubin, Aliaksandr (2024). Sparsifying Bayesian neural networks with latent binary variables and normalizing flows. Transactions on Machine Learning Research (TMLR). 2024. doi: 10.48550/arXiv.2305.03395. Fulltekst i vitenarkiv Vis sammendrag

  Artificial neural networks are powerful machine learning methods used in many modern applications. A common issue is that they have millions or billions of parameters and tend to overfit. Bayesian neural networks (BNN) can improve on this since they incorporate parameter uncertainty. Latent binary Bayesian neural networks (LBBNN) further take into account structural uncertainty by allowing the weights to be turned on or off, enabling inference in the joint space of weights and structures. Mean-field variational inference is typically used for computation within such models. In this paper, we will consider two extensions of variational inference for the LBBNN: Firstly, by using the local reparametrization trick (LCRT), we improve computational efficiency. Secondly, and more importantly, by using normalizing flows on the variational posterior distribution of the LBBNN parameters, we learn a more flexible variational posterior than the mean field Gaussian. Experimental results on real data show that this improves predictive power compared to using mean field variational inference on the LBBNN method, while also obtaining sparser networks. We also perform a simulation study, where we consider variable selection in a logistic regression setting with highly correlated data, where the more flexible variational distribution improves results.

• Hubin, Aliaksandr & Storvik, Geir Olve (2024). Sparse Bayesian Neural Networks: Bridging Model and Parameter Uncertainty through Scalable Variational Inference. Mathematics. 12(6). doi: 10.3390/math12060788. Fulltekst i vitenarkiv Vis sammendrag

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, facilitating more rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, the construction of scalable techniques that combine both structural and parameter uncertainty remains a challenge. In this paper, we apply the concept of model uncertainty as a framework for structural learning in BNNs and, hence, make inferences in the joint space of structures/models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark datasets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs.

• Storvik, Geir Olve; Palomares, Alfonso Diz-Lois; Engebretsen, Solveig; Rø, Gunnar Øyvind Isaksson; Engø-Monsen, Kenth & Kristoffersen, Anja Bråthen [Vis alle 8 forfattere av denne artikkelen] (2023). A sequential Monte Carlo approach to estimate a time-varying reproduction number in infectious disease models: the Covid-19 case. Journal of the Royal Statistical Society, Series A (Statistics in Society). ISSN 0964-1998. 186(4), s. 616–632. doi: 10.1093/jrsssa/qnad043. Fulltekst i vitenarkiv Vis sammendrag

  Abstract The Covid-19 pandemic has required most countries to implement complex sequences of non-pharmaceutical interventions, with the aim of controlling the transmission of the virus in the population. To be able to take rapid decisions, a detailed understanding of the current situation is necessary. Estimates of time-varying, instantaneous reproduction numbers represent a way to quantify the viral transmission in real time. They are often defined through a mathematical compartmental model of the epidemic, like a stochastic SEIR model, whose parameters must be estimated from multiple time series of epidemiological data. Because of very high dimensional parameter spaces (partly due to the stochasticity in the spread models) and incomplete and delayed data, inference is very challenging. We propose a state-space formalization of the model and a sequential Monte Carlo approach which allow to estimate a daily-varying reproduction number for the Covid-19 epidemic in Norway with sufficient precision, on the basis of daily hospitalization and positive test incidences. The method was in regular use in Norway during the pandemics and appears to be a powerful instrument for epidemic monitoring and management.

• Lachmann, Jon; Storvik, Geir Olve; Frommlet, Florian & Hubin, Aliaksandr (2022). A subsampling approach for Bayesian model selection. International Journal of Approximate Reasoning. ISSN 0888-613X. 151, s. 33–63. doi: 10.1016/j.ijar.2022.08.018. Fulltekst i vitenarkiv Vis sammendrag

  It is common practice to use Laplace approximations to decrease the computational burden when computing the marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to compute the posterior marginal probabilities of models and individual covariates. This allows performing Bayesian model selection and model averaging. For large sample sizes, even the Laplace approximation becomes computationally challenging because the optimisation routine involved needs to evaluate the likelihood on the full dataset in multiple iterations. As a consequence, the algorithm is not scalable for large datasets. To address this problem, we suggest using stochastic optimisation approaches, which only use a subsample of the data for each iteration. We combine stochastic optimisation with Markov chain Monte Carlo (MCMC) based methods for Bayesian model selection and provide some theoretical results on the convergence of the estimates for the resulting time-inhomogeneous MCMC. Finally, we report results from experiments illustrating the performance of the proposed algorithm.

• Hubin, Aliaksandr; Storvik, Geir & Frommlet, Florian (2021). Flexible Bayesian Nonlinear Model Configuration. The journal of artificial intelligence research. ISSN 1076-9757. 72, s. 901–942. doi: 10.1613/JAIR.1.13047. Fulltekst i vitenarkiv Vis sammendrag

  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 input variables and a response. Such relationships can be better described through flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introduce a flexible approach for the construction and selection of highly flexible nonlinear parametric regression models. Nonlinear features are generated hierarchically, similarly to deep learning, but have additional flexibility on the possible types of features to be considered. This flexibility, combined with variable selection, allows us to find a small set of important features and thereby more interpretable models. Within the space of possible functions, a Bayesian approach, introducing priors for functions based on their complexity, is considered. A genetically modified mode jumping Markov chain Monte Carlo algorithm is adopted to perform Bayesian inference and estimate posterior probabilities for model averaging. In various applications, we illustrate how our approach is used to obtain meaningful nonlinear models. Additionally, we compare its predictive performance with several machine learning algorithms.

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• Palomares, Alfonso Diz-Lois & Storvik, Geir Olve (2026). Parameter estimation in Conditional Sequential Monte Carlo algorithms through Particle Learning. Fulltekst i vitenarkiv Vis sammendrag

  In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We include an application to the estimation of weights in a branching process model against synthetic data and show that, in this setting, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs implementations.

• Storvik, Geir Olve (2025). Maskinlæring versus statistisk modellering. Fulltekst i vitenarkiv
• Storvik, Geir Olve (2025). Maskinlæring versus statistisk modellering. Fulltekst i vitenarkiv
• Storvik, Geir Olve; Engebretsen, Solveig; Blasio, Birgitte Freiesleben De & Frigessi, Arnoldo (2025). Flaws in the Article “Nearly Instantaneous Time-Varying Reproduction Number for Contagious Diseases—a Direct Approach Based on Nonlinear Regression". Journal of Computational Biology. ISSN 1066-5277. 32(8), s. 813–818. doi: https:/www.liebertpub.com/doi/full/10.1177/15578666251360613. Fulltekst i vitenarkiv
• Engebretsen, Solveig; Thorarinsdottir, Thordis Linda; Palomares, Alfonso Diz-Lois; Storvik, Geir Olve; Frigessi, Arnoldo & Blasio, Birgitte Freiesleben De (2025). Contribution to the Discussion of 'Some statistical aspects of the Covid-19 response' by Wood et al. Journal of the Royal Statistical Society, Series A (Statistics in Society). ISSN 0964-1998. 189(1), s. 71–72. doi: 10.1093/jrsssa/qnaf080. Fulltekst i vitenarkiv
• Hubin, Aliaksandr; Storvik, Geir Olve; Frommlet, Florian & Lachmann, Jon (2024). A subsampling MCMC approach for Bayesian model selection and model averaging. Fulltekst i vitenarkiv
• Storvik, Geir Olve & Palomares, Alfonso Diz-Lois (2023). Sequential Monte Carlo for infectious disease models - the Covid-19 case. Fulltekst i vitenarkiv
• Lachmann, Jon; Storvik, Geir Olve; Frommlet, Florian & Hubin, Aliaksandr (2022). A subsampling approach for Bayesian model selection. Fulltekst i vitenarkiv
• Hubin, Aliaksandr & Storvik, Geir Olve (2022). Variational Bayes for inference on model and parameter uncertainty in Bayesian neural networks. Fulltekst i vitenarkiv Vis sammendrag

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques [1]. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In the presented piece of research [2] we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark data sets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. This is particularly the case in model selection settings, but also within a Bayesian model averaging setting a considerable sparsification is achieved. As expected, model uncertainties give higher, but more reliable uncertainty measures. References: [1] Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. (2015). Weight uncertainty in neural networks. International Conference on Machine Learning, 1613 - 1622. [2] Hubin, A., Storvik, G. (2019). Combining model and parameter uncertainty in Bayesian neural networks, arXiv preprint arXiv:1903.07594.

• Hubin, Aliaksandr & Storvik, Geir Olve (2022). Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertainty. Fulltekst i vitenarkiv
• Hubin, Aliaksandr & Storvik, Geir Olve (2021). Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertainty. Fulltekst i vitenarkiv Vis sammendrag

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark data sets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. This is particularly the case in model selection settings, but also within a Bayesian model averaging setting a considerable sparsification is achieved. As expected, model uncertainties give higher, but more reliable uncertainty measures.

• Hubin, Aliaksandr; Frommlet, Florian & Storvik, Geir Olve (2021). Reversible Genetically Modified MCMCs. Fulltekst i vitenarkiv Vis sammendrag

  In this work, we introduce a reversible version of a genetically modified Markov chain Monte Carlo algorithm (GMJMCMC) for inference on posterior model probabilities in complex functional spaces, where the number of explanatory variables or functions of explanatory variables is prohibitively large for simple Markov Chain Monte Carlo methods. A genetically modified Markov chain Monte Carlo algorithm (GMJMCMC) was introduced in [5, 4, 2] for Bayesian model selection/averaging problems when the total number of function of covariates is prohibitively large. More specifically, these applications include GWAS studies with Bayesian generalized linear models [2] as well as Bayesian logic regressions [5] and Bayesian generalized nonlinear models [4]. If its regularity conditions are met, GMJMCMC algorithm can asymptotically explore all models in the defined model spaces. At the same time, GMJMCMC is not a proper MCMC in a sense that its limiting distribution does not correspond to marginal posterior model probabilities and thus only renormalized estimates of these probabilities [3, 1] can be obtained. Unlike the standard GMJMCMC algorithm, the introduced algorithm is a proper MCMC and its limiting distribution corresponds to posterior marginal model probabilities in the explored model spaces under reasonable regularity conditions.

• Sunde, Leif-Martin Sæther; Hubin, Aliaksandr & Storvik, Geir Olve (2023). Spherical Priors for Bayesian Deep Learning. Universitetet i Oslo. Fulltekst i vitenarkiv

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