Reply on RC2

Based on benchmarking various methods and analyzing multiple real scRNA-seq datasets, a computational platform/workflow and a set of tips for best practices are developed for analyzing causal interactions or relationships in single cells.

Discovering and understanding the causal relationships underlying natural phenomena is important for many scientific disciplines, such as economics, computer science, education, medicine and biology. Meanwhile, new knowledge is revealed by discovering causal relationships from data. The causal discovery approach can be characterized as causal structure learning, where variables and their conditional dependencies are represented by a directed acyclic graph. Hence, causal structure discovery methods are necessary for discovering causal relationships from data. In this survey, we review the background knowledge and the causal discovery methods comprehensively. These methods are isolated into four categories, including constraint-based methods, score-based methods, functional causal models based methods and continuous optimization based methods. We mainly focus on the advanced methods which leverage continuous optimization. In addition, we introduce commonly utilized benchmark datasets and open source codes for researchers to evaluate and apply causal discovery methods.KeywordsCausal discoveryCausal structure learningDirected acyclic graphsContinuous optimization

Recovering the structure of causal graphical models from observational data is an essential yet challenging task for causal discovery in scientific scenarios. Domain-specific causal discovery usually relies on expert validation or prior analysis to improve the reliability of recovered causality, which is yet limited by the scarcity of expert resources. Recently, Large Language Models (LLM) have been used for causal analysis across various domain-specific scenarios, suggesting its potential as autonomous expert roles in guiding data-based structure learning. However, integrating LLMs into causal discovery faces challenges due to inaccuracies in LLM-based reasoning on revealing the actual causal structure. To address this challenge, we propose an error-tolerant LLM-driven causal discovery framework. The error-tolerant mechanism is designed three-fold with sufficient consideration on potential inaccuracies. In the LLM-based reasoning process, an accuracy-oriented prompting strategy restricts causal analysis to a reliable range. Next, a knowledge-to-structure transition aligns LLM-derived causal statements with structural causal interactions. In the structure learning process, the goodness-of-fit to data and adherence to LLM-derived priors are balanced to further address prior inaccuracies. Evaluation of eight real-world causal structures demonstrates the efficacy of our LLM-driven approach in improving data-based causal discovery, along with its robustness to inaccurate LLM-derived priors. Codes are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/tyMadara/LLM-CD</uri>.

The problem of Causal Structure Discovery is defined by given inputs, outputs, auxiliary knowledge of components and possible internal connections. Constraints Programming is employed to discover admissible system models. Existence of internal connections and predefined functionality of components is handled through reification.

The common interpretation of Bayesian networks is that they are vehicles for representing probability distributions, in a graphical form supportive of human understanding and with computational mechanisms supportive of probabilistic reasoning (updating). But the interpretation of Bayesian networks assumed by causal discovery algorithms is causal: the links in the graphs specifically represent direct causal connections between variables. However, there is some tension between these two interpretations. The philosophy of probabilistic causation posits a particular connection between the two, namely that causal relations of certain kinds give rise to probabilistic relations of certain kinds. Causal discovery algorithms take advantage of this kind of connection by ruling out some Bayesian networks given observational data not supported by the posited probability-causality relation. But the discovered (remaining) Bayesian networks are then specifically causal, and not simply arbitrary representations of probability.There are multiple contentious issues underlying any causal interpretation of Bayesian networks. We will address the following questions: Since Bayesian net construction rules allow the construction of multiple distinct networks to represent the very same probability distribution, how can we come to prefer any specific one as “the” causal network? Since Bayesian nets within a Verma-Pearl pattern are strongly indistinguishable, how can causal discovery ever come to select exactly one network as “the” causal network? Causal discovery assumes faithfulness (that d-connections in the model are accompanied by probabilistic dependency in the system modeled). However, some physical systems cannot be modeled faithfully under a causal interpretation. How can causal discovery cope with that? Here we introduce a causal interpretation of Bayesian networks by way of answering these questions and then apply this interpretation to answering further questions about causal power, explanation and responsibility.Keywordscausal discoveryfaithfulnessBayesian networksprobabilistic causalityinterventioncausal powercausal responsibility

Causal discovery and causal effect estimation are two fundamental tasks in causal inference. While many methods have been developed for each task individually, statistical challenges arise when applying these methods jointly: estimating causal effects after running causal discovery algorithms on the same data leads to “double dipping,” invalidating the coverage guarantees of classical confidence intervals. To this end, we develop tools for valid post-causal-discovery inference. Across empirical studies, we show that a naive combination of causal discovery and subsequent inference algorithms leads to highly inflated miscoverage rates; on the other hand, applying our method provides reliable coverage while allowing for a trade-off between causal discovery accuracy and confidence interval width. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Abstract. Accurately projecting future precipitation patterns over land is crucial for understanding climate change and developing effective mitigation and adaptation strategies. However, projections of precipitation changes in state-of-the-art climate models still exhibit considerable uncertainty, in particular over vulnerable and populated land areas. This study aims to address this challenge by introducing a novel methodology for constraining climate model precipitation projections with causal discovery. Our approach involves a multistep procedure that integrates dimension reduction, causal network estimation, causal network evaluation, and a causal weighting scheme which is based on the historical performance (the distance of the causal network of a model to the causal network of a reanalysis dataset) and the interdependence of Coupled Model Intercomparison Project Phase 6 (CMIP6) models (the distance of the causal network of a model to the causal network of other climate models). To uncover the significant causal pathways crucial for understanding dynamical interactions in the climate models and reanalysis datasets, we estimate the time-lagged causal relationships using the Peter–Clark momentary conditional independence (PCMCI) causal discovery algorithm. In the last step, a novel causal weighting scheme is introduced, assigning weights based on the performance and interdependence of the CMIP6 models' causal networks. For the end-of-century period, 2081–2100, our method reduces the very likely ranges (5th–95th percentile) of projected precipitation changes over land between 10 % and 16 % relative to the unweighted ranges across three global warming scenarios (SSP2-4.5, SSP3-7.0, and SSP5-8.5). The sizes of the likely ranges (17th–83rd percentile) are further reduced between 16 % and 41 %. This methodology is not limited to precipitation over land and can be applied to other climate variables, supporting better mitigation and adaptation strategies to tackle climate change.

Causal discovery is essential across various scientific fields to uncover causal structures within data. Traditional methods relying on observational data have limitations due to confounding variables. This paper presents an optimization-based approach using integer programming (IP) to design minimal intervention sets that ensure causal structure identifiability. Our method provides exact and modular solutions, adaptable to different experimental settings and constraints. We demonstrate its effectiveness through comparative analysis across different settings demonstrating its applicability and robustness.

Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, causal discovery based on a constraint approach could recover the causal structures from passive observational data in general cases, and had shown extensive prospects in numerous real world applications. However, when the graph was sufficiently large, it did not work well. To alleviate this problem, an improved causal structure learning algorithm named brain storm optimization (BSO), is presented in this paper, combining K2 with brain storm optimization (K2-BSO). Here BSO is used to search optimal topological order of nodes instead of graph space. This paper assumes that dataset is generated by conforming to a causal diagram in which each variable is generated from its parent based on a causal mechanism. We designed an elaborate distance function for clustering step in BSO according to the mechanism of K2. The graph space therefore was reduced to a smaller topological order space and the order space can be further reduced by an efficient clustering method. The experimental results on various real-world datasets showed our methods outperformed the traditional search and score methods and the state-of-the-art genetic algorithm-based methods.

SLIVER: Unveiling large scale gene regulatory networks of single-cell transcriptomic data through causal structure learning and modules aggregation

Many investigations into the world, including philosophical ones, aim to discover causal knowledge, and many experimental methods have been developed to assist in causal discovery. More recently, algorithms have emerged that can also learn causal structure from purely or mostly observational data, as well as experimental data. These methods have started to be applied in various philosophical contexts, such as debates about our concepts of free will and determinism. This paper provides a “user's guide” to these methods, though not in the sense of specifying exact button presses in a software package. Instead, we explain the larger “pipeline” within which these methods are used and discuss key steps in moving from initial research idea to validated causal structure.

Abstract. Understanding the dependencies of the terrestrial carbon and water cycle with meteorological conditions is a prerequisite to anticipate their behaviour under climate change conditions. However, terrestrial ecosystems and the atmosphere interact via a multitude of variables across temporal and spatial scales. Additionally these interactions might differ among vegetation types or climatic regions. Today, novel algorithms aim to disentangle the causal structure behind such interactions from empirical data. The estimated causal structures can be interpreted as networks, where nodes represent relevant meteorological variables or land-surface fluxes and the links represent the dependencies among them (possibly including time lags and link strength). Here we derived causal networks for different seasons at 119 eddy covariance flux tower observations in the FLUXNET network. We show that the networks of biosphere–atmosphere interactions are strongly shaped by meteorological conditions. For example, we find that temperate and high-latitude ecosystems during peak productivity exhibit biosphere–atmosphere interaction networks very similar to tropical forests. In times of anomalous conditions like droughts though, both ecosystems behave more like typical Mediterranean ecosystems during their dry season. Our results demonstrate that ecosystems from different climate zones or vegetation types have similar biosphere–atmosphere interactions if their meteorological conditions are similar. We anticipate our analysis to foster the use of network approaches, as they allow for a more comprehensive understanding of the state of ecosystem functioning. Long-term or even irreversible changes in network structure are rare and thus can be indicators of fundamental functional ecosystem shifts.

Toward Explainable and Sustainable Manufacturing: Benchmarking Causal Discovery on Process Duration and Energy Use

Causal discovery by continuous optimization with weighted superstructure.

Missing data are an unavoidable complication frequently encountered in many causal discovery tasks. When a missing process depends on the missing values themselves (known as self-masking missingness), the recovery of the joint distribution becomes unattainable, and detecting the presence of such self-masking missingness remains a perplexing challenge. Consequently, due to the inability to reconstruct the original distribution and to discern the underlying missingness mechanism, simply applying existing causal discovery methods would lead to wrong conclusions. In this work, we found that the recent advances additive noise model has the potential for learning causal structure under the existence of the self-masking missingness. With this observation, we aim to investigate the identification problem of learning causal structure from missing data under an additive noise model with different missingness mechanisms, where the `no self-masking missingness' assumption can be eliminated appropriately. Specifically, we first elegantly extend the scope of identifiability of causal skeleton to the case with weak self-masking missingness (i.e., no other variable could be the cause of self-masking indicators except itself). We further provide the sufficient and necessary identification conditions of the causal direction under additive noise model and show that the causal structure can be identified up to an IN-equivalent pattern. We finally propose a practical algorithm based on the above theoretical results on learning the causal skeleton and causal direction. Extensive experiments on synthetic and real data demonstrate the efficiency and effectiveness of the proposed algorithms.