Behind Distribution Shift: Mining Driving Forces of Changes and Causal Arrows.

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

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.

Infrared (IR) images are essential to improve the visibility of dark or camouflaged objects. Object recognition and segmentation based on a neural network using IR images provide more accuracy and insight than color visible images. But the bottleneck is the amount of relevant IR images for training. It is difficult to collect real-world IR images for special purposes, including space exploration, military and fire-fighting applications. To solve this problem, we created color visible and IR images using a Unity-based 3D game editor. These synthetically generated color visible and IR images were used to train cycle consistent adversarial networks (CycleGAN) to convert visible images to IR images. CycleGAN has the advantage that it does not require precisely matching visible and IR pairs for transformation training. In this study, we discovered that additional synthetic data can help improve CycleGAN performance. Neural network training using real data (N = 20) performed more accurate transformations than training using real (N = 10) and synthetic (N = 10) data combinations. The result indicates that the synthetic data cannot exceed the quality of the real data. Neural network training using real (N = 10) and synthetic (N = 100) data combinations showed almost the same performance as training using real data (N = 20). At least 10 times more synthetic data than real data is required to achieve the same performance. In summary, CycleGAN is used with synthetic data to improve the IR image conversion performance of visible images.

This is a comment on "Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach" by Krich et al., Biogeosciences, 17, 1033–1061, 2020, which gives a good introduction to causal discovery, but confines the scope by investigating the outcome of a single algorithm. In this comment, we argue that the outputs of causal discovery algorithms should not usually be considered as end results but starting points and hypothesis for further study. We illustrate how not only different algorithms, but also different initial states and prior information of possible causal model structures, affect the outcome. We demonstrate how to incorporate expert domain knowledge with causal structure discovery and how to detect and take into account overfitting and concept drift.

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>.

Mining combined causes in large data sets

Conventional temporal causal discovery (CD) methods suffer from high dimensionality, fail to identify lagged causal relationships, and often ignore dynamics in relations. In this study, we present a novel constraint-based CD approach for autocorrelated and non-stationary time series data (eCDANs) capable of detecting lagged and contemporaneous causal relationships along with temporal changes. eCDANs addresses high dimensionality by optimizing the conditioning sets while conducting conditional independence (CI) tests and identifies the changes in causal relations by introducing a surrogate variable to represent time dependency. Experiments on synthetic and real-world data show that eCDANs can identify time influence and outperform the baselines.

We present an algorithmic framework for learning local causal structure around target variables of interest in the form of direct causes/effects and Markov blankets applicable to very large data sets with relatively small samples. The selected feature sets can be used for causal discovery and classification. The framework (Generalized Local Learning, or GLL) can be instantiated in numerous ways, giving rise to both existing state-of-the-art as well as novel algorithms. The resulting algorithms are sound under well-defined sufficient conditions. In a first set of experiments we evaluate several algorithms derived from this framework in terms of predictivity and feature set parsimony and compare to other local causal discovery methods and to state-of-the-art non-causal feature selection methods using real data. A second set of experimental evaluations compares the algorithms in terms of ability to induce local causal neighborhoods using simulated and resimulated data and examines the relation of predictivity with causal induction performance. Our experiments demonstrate, consistently with causal feature selection theory, that local causal feature selection methods (under broad assumptions encompassing appropriate family of distributions, types of classifiers, and loss functions) exhibit strong feature set parsimony, high predictivity and local causal interpretability. Although non-causal feature selection methods are often used in practice to shed light on causal relationships, we find that they cannot be interpreted causally even when they achieve excellent predictivity. Therefore we conclude that only local causal techniques should be used when insight into causal structure is sought. In a companion paper we examine in depth the behavior of GLL algorithms, provide extensions, and show how local techniques can be used for scalable and accurate global causal graph learning.

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.

Causal relationships play an irreplaceable role in revealing the mechanisms of phenomena and guiding intervention actions. However, due to limitations in existing frameworks regarding model representations and learning algorithms, only a few studies have explored causal discovery on non-Euclidean data. In this paper, we address the issue by proposing a causal mapping process based on coordinate representations for heterogeneous non-Euclidean data. We propose a data generation mechanism between the parent nodes and the child nodes and create a causal mechanism based on multi-dimensional tensor regression. Furthermore, within the aforementioned theoretical framework, we propose a two-stage causal discovery approach based on regularized generalized canonical correlation analysis. Using the discrete representation in the shared projection direction, causal relationships between heterogeneous non-Euclidean variables can be discovered more accurately. Finally, empirical research is conducted on real-world industrial sensor data, which demonstrates the effectiveness of the proposed method for discovering causal relationships in heterogeneous non-Euclidean data.

This study discusses the scaling properties of the spatial distribution of the December 26, 2004, Sumatra aftershocks. We estimate the spatial correlation dimension D2 of the epicentral distribution of aftershocks recorded by a local network operated by Geological Survey of India. We estimate the value of D2 for five blocks in the source area by using generalized correlation integral approach. We assess its bias due to finite data points, scaling range, effects of location errors, and boundary effects theoretically and apply it to real data sets. The correlation dimension was computed both for real as well as synthetic data sets that include randomly generated point sets obtained using uniform distributions and mimicking the number of events and outlines of the effective areas filled with epicenters. On comparing the results from the real data and random point sets from simulations, we found the lower limit of bias in D2 estimates from limited data sets to be 0.26. Thus, the spatial variation in correlation dimensions among different blocks using local data sets cannot be directly compared unless the influence of bias in the real aftershock data set is taken into account. They cannot also be used to infer the geometry of the faults. We also discuss the results in order to add constraints on the use of synthetic data and of different approaches for uncertainty analysis on spatial variation of D2. A difference in D2 values, rather than their absolute values, among small blocks is of interest to local data sets, which are correlated with their seismic b values. Taking into account the possible errors and biases, the average D2 values vary from 1.05 to 1.57 in the Andaman–Nicobar region. The relative change in D2 values can be interpreted in terms of clustering and diffuse seismic activity associated with the low and high D2 values, respectively. Overall, a relatively high D2 and low b value is consistent with high-magnitude, diffuse activity in space in the source region of the 2004 Sumatra earthquake.

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independence tests only determine causal structure up to Markov equivalence, the number of consistent joint structures returned by these approaches can be quite large. The last decade has seen the development of elegant algorithms for discovering causal relations beyond conditional independence, which can distinguish among Markov equivalent structures. In this work we adapt and extend these so-called bivariate causal discovery algorithms to the problem of learning consistent causal structures from multiple datasets with overlapping variables belonging to the same generating process, providing a sound and complete algorithm that outperforms previous approaches on synthetic and real data.

Accurately modelled computer-generated data can be used in place of real-world signals for the design, test and validation of signal processing techniques in situations where real data is difficult to obtain. Bio-signal processing researchers interested in working with fNIRS data are restricted due to the lack of freely available fNIRS data and by the prohibitively expensive cost of fNIRS systems. We present a simplified mathematical description and associated MATLAB implementation of model-based synthetic fNIRS data which could be used by researchers to develop fNIRS signal processing techniques. The software, which is freely available, allows users to generate fNIRS data with control over a wide range of parameters and allows for fine-tuning of the synthetic data. We demonstrate how the model can be used to generate raw fNIRS data similar to recorded fNIRS signals. Signal processing steps were then applied to both the real and synthetic data. Visual comparisons between the temporal and spectral properties of the real and synthetic data show similarity. This paper demonstrates that our model for generating synthetic fNIRS data can replicate real fNIRS recordings.

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.