# Adaptive LASSO estimation for functional hidden dynamic geostatistical model

arXiv: https://arxiv.org/abs/2208.05528 · HTML: https://mlsanity.com/paper/2208.05528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 119 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 12 of 12)

- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference](https://mlsanity.com/paper/2112.14591/) (2021)
- [Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models](https://mlsanity.com/paper/1704.06988/) (2017)
- [Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering](https://mlsanity.com/paper/2006.16901/) (2020)
- [Multi-resolution filters for massive spatio-temporal data](https://mlsanity.com/paper/1810.04200/) (2018)
- [Smooth Lasso Estimator for the Function-on-Function Linear Regression Model](https://mlsanity.com/paper/2007.00529/) (2020)
- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)
- [Adaptive Lasso and group-Lasso for functional Poisson regression](https://mlsanity.com/paper/1412.6966/) (2014)
- [Bootstrap based uncertainty bands for prediction in functional kriging](https://mlsanity.com/paper/1505.06966/) (2015)
- [D-STEM v2: A Software for Modelling Functional Spatio-Temporal Data](https://mlsanity.com/paper/2101.11370/) (2021)
- [Scalable Spatio-Temporal Smoothing via Hierarchical Sparse Cholesky Decomposition](https://mlsanity.com/paper/2207.09384/) (2022)

## Built on by (most cited first, 1 of 1)

- [Enhancing Credit Risk Prediction: A Multi-stage Ensemble Pipeline](https://mlsanity.com/paper/2509.22381/) (2025)

## Abstract (arXiv)

We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the parameters of interest are functions across this domain. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed-effects relationship between the response variable and the covariates. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire effect of irrelevant regressors. The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (LASSO) penalty function, wherein the weights are obtained by the unpenalised f-HDGM maximum-likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the likelihood. Through a Monte Carlo simulation study, we analysed the performance of the algorithm under different scenarios, including strong correlations among the regressors. We showed that the penalised estimator outperformed the unpenalised estimator in all the cases we considered. We applied the algorithm to a real case study in which the recording of the hourly nitrogen dioxide concentrations in the Lombardy region in Italy was modelled as a functional process with several weather and land cover covariates.