Tim Gyger, in collaboration with HSLU

The Gaussian Process regression model, provides a flexible method of interpolation by identifying the underlying spatial structure in the data, commonly referred to as Kriging. A recent proposal in advocates the incorporation of tree-boosting algorithms to model the fixed effects in the regression model. This approach has the advantage that complex functions in the predictor variables can be learned. The model parameters are typically estimated through the repetitive calculation of the negative log marginal likelihood and its derivative with respect to the hyperparameters. However, this calculation becomes computationally unfeasible for large datasets.

To address this issue, we propose a novel approach that enables scaling to larger datasets through the utilization of a full-scale covariance approximation (FSA) combined with conjugate gradient algorithms for the linear solves and stochastic trace estimations for the log-determinant and its derivative.

Through first simulations, we evaluated that a simple preconditioner given by the structure of FSA has a highly positive impact on the convergence of the conjugate gradient method and the variance reduction in trace estimations. This leads to improvements in runtime and accuracy of the log-likelihood estimates. Moreover, we investigate a novel approach for a low-rank covariance approximation based on variants of the Lanczos Algorithm. Furthermore, we will apply our model to a real-world dataset describing specific structural characteristics of the Laegeren mountain. We will evaluate the predictive accuracy of our approach and compare it with state-of-the-art methods.

Publication: 

• https://doi.org/10.1016/j.compbiomed.2022.105740
• https://CRAN.R-project.org/package=abn
• https://github.com/matteodelucchi/bnaiaR

Marc Lischka, in collaboration with Anna Graff and other NCCR EvolvingLanguage members

With increasing availability of linguistic data in large-scale databases, the perspective of appropriately merging data from such databases via language identifiers (such as glottocodes) and performing large-scale analyses on such aggregated datasets becomes attractive, especially for analyses that aim at testing hypotheses at global scales, for which data collection may not be feasible for large numbers of variables.
Some of these databases have near-complete variable coding density for all languages present (e.g. PHOIBLE, Grambank), others’ variables are coded for very different sets of languages (e.g. AUTOTYP, Lexibank, WALS), resulting in sparse variable-language matrices. Additionally, combining data from various databases results in further sparsity. Our initial dataset including original variables, modified variables and merged variables has an overall coding density of ~15%. It is clear that many languages and variables in such an initial dataset have such low coding densities that including them in analysis is not sufficiently beneficial, e. g. due to their contribution to extra computational time. 

We develop an iterative procedure to prune the aggregated matrix, following criteria set with the aim to optimise the language-variable matrix in terms of coding density and taxonomic diversity, primarily. The criteria we employ relate to a) the taxonomic importance of each language given the current language sample (we could call this a “vertical” criterion) and b) weighted density of data for both languages and variables (criterion both “vertical” and “horizontal”). Point (a) means we want to make the removal of a language representative of a family that is present with few languages in the current sample more expensive than the removal of a language from a family that is present in the matrix with many languages.
In addition to the raw coding densities of languages and variables, we want to base our decision as to which of them to prune in a given step on weighted densities. It makes sense to keep languages that are coded for variables of high density and, vice versa, to keep variables coded for languages of high density. Hence, weighted language densities are computed using the variable densities as weights and vice versa. This approach can be iterated.

Jakob Dambon, in collaboration with Fabio Sigrist (HSLU)

Spatial modelling usually assumes the marginal effects of covariates to be constant and only incorporates a spatial structure on the residuals. However, there exist cases where such an assumption is too strong and we assume non-stationarity for the effects, i.e., coefficients. Spatially varying coefficient (SVC) models account for non-stationarity of the coefficients where their effect sizes are depending on the observation location. We present a new methodology where the coefficients are defined by Gaussian processes (GPs), so called GP-based SVC models. These models are highly flexible yet simple to interpret. We use maximum likelihood estimation (MLE) that has been optimized for large data sets where the number of observations exceeds 10⁵ and the number of SVCs is moderate. Further, a variable selection methodology for GP-based SVC models is presented. A software implementation of the described methods is given in the R package varycoef.