Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that use augmented data to encode censoring information in the neural network input. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (${\rm PM}_{2.5}$) concentration over the whole of Saudi Arabia.

MOTIVATION: Leucine-aspartic acid (LD) motifs are short linear interaction motifs (SLiMs) that link paxillin family proteins to factors controlling cell adhesion, motility and survival. The existence and importance of LD motifs beyond the paxillin family is poorly understood. RESULTS: To enable a proteome-wide assessment of LD motifs, we developed an active learning based framework (LD motif finder; LDMF) that iteratively integrates computational predictions with experimental validation. Our analysis of the human proteome revealed a dozen new proteins containing LD motifs. We found that LD motif signalling evolved in unicellular eukaryotes more than 800 Myr ago, with paxillin and vinculin as core constituents, and nuclear export signal as a likely source of de novo LD motifs. We show that LD motif proteins form a functionally homogenous group, all being involved in cell morphogenesis and adhesion. This functional focus is recapitulated in cells by GFP-fused LD motifs, suggesting that it is intrinsic to the LD motif sequence, possibly through their effect on binding partners. Our approach elucidated the origin and dynamic adaptations of an ancestral SLiM, and can serve as a guide for the identification of other SLiMs for which only few representatives are known. AVAILABILITY AND IMPLEMENTATION: LDMF is freely available online at www.cbrc.kaust.edu.sa/ldmf; Source code is available at https://github.com/tanviralambd/LD/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.