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Discovering causal relationships from purely observational data is often not possible. In this case, combining observational and experimental data can allow for the identifiability of the underlying causal structure. In Earth Systems sciences, carrying out interventional experiments is often impossible for ethical and practical reasons. However, “natural interventions”, are often present in the data, and these represent regime changes caused by changes to exogenous drivers. In [3,4], the Invariant Causal Prediction (ICP) methodology was presented to identify the causes of a target variable of interest from a set of candidate causes. This methodology takes advantage of natural interventions, resulting in different cause variables distributions across different environments. In [2] this methodology is implemented in a geoscience problem, namely identifying the causes of Pyrocumulunimbus (pyroCb), and storm clouds resulting from extreme wildfires. Although a set of plausible causes is produced, certain heuristic adaptations to the original ICP methodology were implemented to overcome some of the practical. limitations of ICP: a large number of hypothesis tests required and a failure to identify causes when these have a high degree of interdependence. In this work, we try to circumvent these difficulties by taking a different approach. We use a learning paradigm similar to that presented in [3] to learn causal representations invariant across different environments. Since we often don’t know exactly how to define the different environments best, we also propose to learn functions that describe their spatiotemporal extent. We apply the resulting algorithm to the pyroCb database in [1] and other Earth System sciences datasets to verify the plausibility of the causal representations found and the environments that describe the so-called natural interventions.. [1] Tazi et al. 2022. https://arxiv.org/abs/2211.13052[2] Díaz et al. 2022 .https://arxiv.org/abs/2211.08883[3] Arjovsky et al. 2019. https://arxiv.org/abs/1907.02893[4] Peters et al.2016. https://www.jstor.org/stable/4482904[5] Heinze-Deml et al. 2018. https://doi.org/10.1515/jci-2017

Hybrid modeling describes the synergy between parametric models and machine learning [1]. Parts of a parametric equation are substituted by non-parametric machine learning models, which can then represent complex functions. These are inferred together with the parameters of the equation from the data. Hybrid modeling promises to describe complex relationships and to be scientifically interpretable. These promises, however, need to be taken with a grain of salt. With too flexible models, such as deep neural networks, the problem of equifinality arises: There is no identifiable optimal solution. Instead, many outcomes describe the data equally well, and we will obtain one of them by chance. Interpreting the result may lead to erroneous conclusions. Moreover, studies have shown that regularization techniques can introduce a bias on jointly estimated physical parameters [1].We propose double machine learning (DML) to solve these problems [2]. DML is a theoretically well-founded technique for fitting semi-parametric models, i.e., models consisting of a parametric and a non-parametric component. DML is widely used for debiased treatment effect estimation in economics. We showcase its use for geosciences on two problems related to carbon dioxide fluxes: Flux partitioning, which aims at separating the net carbon flux (NEE) into its main contributing gross fluxes, namely, RECO and GPP. Estimation of the temperature sensitivity parameter of ecosystem respiration Q10. First, we show that in the case of synthetic data for Q10 estimation, we can consistently retrieve the true value of Q10 where the naive neural network approach fails. We further apply DML to the carbon flux partitioning problem and find that it is 1) able to retrieve the true fluxes of synthetic data, even in the presence of strong (and more realistic) heteroscedastic noise, 2) retrieves main gross carbon fluxes on real data consistent with established methods, and 3) allows us to causally interpret the retrieved GPP as the direct effect of the photosynthetically active radiation on NEE. This way, the DML approach can be seen as a causally interpretable, semi-parametric version of the established daytime methods. We also investigate the functional relationships inferred with DML and the drivers modulating the obtained light-use efficiency function. In conclusion, DML offers a solid framework to develop hybrid and semiparametric modeling and can be of widespread use in geosciences. [1] Reichstein, Markus, et al. “Combining system modeling and machine learning into hybrid ecosystem modeling.” Knowledge-Guided Machine Learning (2022). https://doi.org/10.1201/9781003143376-14[2] Chernozhukov, Victor, et al. “Double/debiased machine learning for treatment and structural parameters.” The Econometrics Journal, Volume 21, Issue 1, 1 (2018): C1–C68. https://doi.org/10.1111/ectj.12097

The current situation regarding food insecurity in the continent of Africa, and the Horn of Africa in particular, is at an unprecedented risk level triggered by continuous drought events, complicated interactions between food prices, crop yield, energy inflation and lack of humanitarian aid, along with disrupting conflicts and migration flows. The study of a food-secure environment is a complex, multivariate, multiscale, and non-linear problem difficult to understand with canonical data science methodologies. We propose an alternative approach to the food insecurity problem from a causal inference standpoint to discover the causal relations and evaluate the likelihood and potential consequences of specific interventions. In particular, we demonstrate the use of causal inference for understanding the impact of humanitarian interventions on food insecurity in Somalia. In the first stage of the problem, we apply different data transformations to the main drivers to achieve the highest degree of correlation with the interested variable. In the second stage, we infer causation from the main drivers and interested variables by applying different causal methods such as PCMCI or Granger causality. We analyze and harmonize different time series, per district of Somalia, of the global acute malnutrition (GAM) index, food market prices, crop production, conflict levels, drought and flood internal displacements, as well as climate indicators such as the NDVI index, precipitation or land surface temperature. Then, assuming a causal graph between the main drivers causing the food insecurity problem, we estimate the effect of increasing humanitarian interventions on the GAM index, considering the effects of a changing climate, migration flows, and conflict events. We show that causal estimation with modern methodologies allows us to quantify the impact of humanitarian aid on food insecurity. References [1] Runge, J., Bathiany, S., Bollt, E. et al. Inferring causation from time series in Earth system sciences. Nat Commun 10, 2553 (2019). https://doi.org/10.1038/s41467-019-10105-3[2] Sazib Nazmus, Mladenova lliana E., Bolten John D., Assessing the Impact of ENSO on Agriculture Over Africa Using Earth Observation Data, Frontiers in Sustainable Food Systems, 2020, 10.3389/fsufs.2020.509914. https://www.frontiersin.org/article/10.3389/fsufs.2020.509914[3] Checchi, F., Frison, S., Warsame, A. et al. Can we predict the burden of acute malnutrition in crisis-affected countries? Findings from Somalia and South Sudan. BMC Nutr 8, 92 (2022). https://doi.org/10.1186/s40795-022-00563-2

Multi-label classification problems require each instance to be assigned a subset of a defined set of labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of binary classes. In this paper we study the decision boundaries of two widely used approaches for building multi-label classifiers, when Bayesian network-augmented naive Bayes classifiers are used as base models: Binary relevance method and chain classifiers. In particular extending previous single-label results to multi-label chain classifiers, we find polynomial expressions for the multi-valued decision functions associated with these methods. We prove upper boundings on the expressive power of both methods and we prove that chain classifiers provide a more expressive model than the binary relevance method. We study the expressive power of binary relevance and chain classifier with BN.We find polynomial expression for the decision functions of the two methods.We bound the expressive power of both methods.We prove that chain classifiers are indeed more expressive than binary relevance.

The development of 3D visualization and reconstruction methods to analyse microscopic structures at different levels of resolutions is of great importance to define brain microorganization and connectivity. MultiMap is a new tool that allows the visualization, 3D segmentation and quantification of fluorescent structures selectively in the neuropil from large stacks of confocal microscopy images. The major contribution of this tool is the posibility to easily navigate and create regions of interest of any shape and size within a large brain area that will be automatically 3D segmented and quantified to determine the density of puncta in the neuropil. As a proof of concept, we focused on the analysis of glutamatergic and GABAergic presynaptic axon terminals in the mouse hippocampal region to demonstrate its use as a tool to provide putative excitatory and inhibitory synaptic maps. The segmentation and quantification method has been validated over expert labeled images of the mouse hippocampus and over two benchmark datasets, obtaining comparable results to the expert detections.

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.

In recent years, a plethora of approaches have been proposed to deal with the increasingly challenging task of multi-output regression. This study provides a survey on state-of-the-art multi-output regression methods, that are categorized as problem transformation and algorithm adaptation methods. In addition, we present the mostly used performance evaluation measures, publicly available data sets for multi-output regression real-world problems, as well as open-source software frameworks. WIREs Data Mining Knowl Discov 2015, 5:216-233. doi: 10.1002/widm.1157

Mixtures of polynomials MoPs are a nonparametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multidimensional marginal MoPs from data have recently been proposed. In this paper, we introduce two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate and study the methods using data sampled from known parametric distributions, and demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions MoTBFs. The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

Bayesian network classifiers are widely used in machine learning because they intuitively represent causal relations. Multi-label classification problems require each instance to be assigned a subset of a defined set of h labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of h binary classes. In this paper we obtain the decision boundaries of two widely used Bayesian network approaches for building multi-label classifiers: Multi-label Bayesian network classifiers built using the binary relevance method and Bayesian network chain classifiers. We extend our previous single-label results to multi-label chain classifiers, and we prove that, as expected, chain classifiers provide a more expressive model than the binary relevance method.

In this article, we describe the algorithms for causal structure learning from time series data that won the Causality 4 Climate competition at the Conference on Neural Information Processing Systems 2019 (NeurIPS). We examine how our combination of established ideas achieves competitive performance on semi-realistic and realistic time series data exhibiting common challenges in real-world Earth sciences data. In particular, we discuss a) a rationale for leveraging linear methods to identify causal links in non-linear systems, b) a simulation-backed explanation as to why large regression coefficients may predict causal links better in practice than small p-values and thus why normalising the data may sometimes hinder causal structure learning. For benchmark usage, we detail the algorithms here and provide implementations at {https://github.com/sweichwald/tidybench}. We propose the presented competition-proven methods for baseline benchmark comparisons to guide the development of novel algorithms for structure learning from time series.