José Manuel Azcona

Jose González-Abad, Jorge Baño-Medina, José Manuel Gutiérrez

Deep learning (DL) has emerged as a promising tool to downscale climate projections at regional-to-local scales from large-scale atmospheric fields following the perfect-prognosis (PP) approach. Given their complexity, it is crucial to properly evaluate these methods, especially when applied to changing climatic conditions where the ability to extrapolate/generalise is key. In this work, we intercompare several DL models extracted from the literature for the same challenging use-case (downscaling temperature in the CORDEX North America domain) and expand standard evaluation methods building on eXplainable artifical intelligence (XAI) techniques. We show how these techniques can be used to unravel the internal behaviour of these models, providing new evaluation dimensions and aiding in their diagnostic and design. These results show the usefulness of incorporating XAI techniques into statistical downscaling evaluation frameworks, especially when working with large regions and/or under climate change conditions.

Antonio Pérez, Mario Santa Cruz, Daniel San Martín et al.

Super-resolution (SR) is a promising cost-effective downscaling methodology for producing high-resolution climate information from coarser counterparts. A particular application is downscaling regional reanalysis outputs (predictand) from the driving global counterparts (predictor). This study conducts an intercomparison of various SR downscaling methods focusing on temperature and using the CERRA reanalysis (5.5 km resolution, produced with a regional atmospheric model driven by ERA5) as example. The method proposed in this work is the Swin transformer and two alternative methods are used as benchmark (fully convolutional U-Net and convolutional and dense DeepESD) as well as the simple bicubic interpolation. We compare two approaches, the standard one using the full domain as input and a more scalable tiling approach, dividing the full domain into tiles that are used as input. The methods are trained to downscale CERRA surface temperature, based on temperature information from the driving ERA5; in addition, the tiling approach includes static orographic information. We show that the tiling approach, which requires spatial transferability, comes at the cost of a lower performance (although it outperforms some full-domain benchmarks), but provides an efficient scalable solution that allows SR reduction on a pan-European scale and is valuable for real-time applications.

Catharina Elisabeth Graafland, José Manuel Gutiérrez

Gene expression datasets consist of thousand of genes with relatively small samplesizes (i.e. are large-$p$-small-$n$). Moreover, dependencies of various orders co-exist in the datasets. In the Undirected probabilistic Graphical Model (UGM) framework the Glasso algorithm has been proposed to deal with high dimensional micro-array datasets forcing sparsity. Also, modifications of the default Glasso algorithm are developed to overcome the problem of complex interaction structure. In this work we advocate the use of a simple score-based Hill Climbing algorithm (HC) that learns Gaussian Bayesian Networks (BNs) leaning on Directed Acyclic Graphs (DAGs). We compare HC with Glasso and its modifications in the UGM framework on their capability to reconstruct GRNs from micro-array data belonging to the Escherichia Coli genome. We benefit from the analytical properties of the Joint Probability Density (JPD) function on which both directed and undirected PGMs build to convert DAGs to UGMs. We conclude that dependencies in complex data are learned best by the HC algorithm, presenting them most accurately and efficiently, simultaneously modelling strong local and weaker but significant global connections coexisting in the gene expression dataset. The HC algorithm adapts intrinsically to the complex dependency structure of the dataset, without forcing a specific structure in advance. On the contrary, Glasso and modifications model unnecessary dependencies at the expense of the probabilistic information in the network and of a structural bias in the JPD function that can only be relieved including many parameters.

Marco Scutari, Catharina Elisabeth Graafland, José Manuel Gutiérrez

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known (Cowell, 2001). In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and real-world complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.