Causal Discovery Combining K2 with Brain Storm Optimization Algorithm

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

Understanding causality and the mechanisms underlying psychological phenomena has been a cornerstone of psychological research, with significant implications for theory development and intervention design. While traditional methods such as experimental manipulations or structural equation modelling have been extensively used to explore causal relationships, recent advances in causal inference studies have introduced causal discovery methods as a powerful alternative. These methods can uncover complex causal structures from observational or interventional data, offering unique utility such as identifying causal directions and handling complex causal networks involving numerous variables. This paper provides an introduction to causal discovery methods tailored for psychological research. We review foundational concepts, introduce the classical algorithms, and present a practical tutorial in R, equipping researchers with tools to implement these methods on psychological data. We also discuss the potential of these methods to accelerate theory formation, refine interventions, and foster cross-disciplinary understanding of human cognition as well as the challenges of integrating causal discovery into psychological research.

An important goal across most scientific fields is the discovery of causal structures underling a set of observations. Unfortunately, causal discovery methods which are based on correlation or mutual information can often fail to identify causal links in systems which exhibit dynamic relationships. Such dynamic systems (including the famous coupled logistic map) exhibit ‘mirage’ correlations which appear and disappear depending on the observation window. This means not only that correlation is not causation but, perhaps counter-intuitively, that causation may occur without correlation. In this paper we describe Neural Shadow-Mapping, a neural network based method which embeds high-dimensional video data into a low-dimensional shadow representation, for subsequent estimation of causal links. We demonstrate its performance at discovering causal links from video-representations of dynamic systems.

Causal discovery in financial time series presents significant challenges due to the complex temporal dependencies and multi-sector interactions that characterize modern financial markets. Traditional statistical methods and conventional deep learning approaches often fail to capture the hierarchical nature of causal relationships across different market sectors and temporal scales. This paper proposes a novel Hierarchical Transformer Framework for Causal Discovery (HT-CD) that leverages multi-level attention mechanisms to identify causal relationships across multi-sector financial time series. Our framework introduces a sector-aware hierarchical encoder that processes financial data at multiple granularities, from individual asset-level patterns to sector-wide dynamics, while maintaining temporal consistency through specialized positional encoding schemes. The architecture incorporates a novel multi-head causal attention mechanism that explicitly models both contemporaneous and lagged causal effects across different sectors. Experimental evaluation on comprehensive financial datasets spanning multiple sectors demonstrates that HT-CD significantly outperforms existing causal discovery methods, achieving 23% improvement in causal structure accuracy while maintaining computational efficiency. The framework successfully identifies cross-sector causal relationships that align with established economic theories and provides interpretable insights into market contagion effects during financial stress periods.

Causal discovery from sequential data in ALS disease based on entropy criteria.

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.

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.

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>.

Discovering Causal Models with Optimization: Confounders, Cycles, and Feature Selection

We address two important issues in causal discovery from nonstationary or heterogeneous data, where parameters associated with a causal structure may change over time or across data sets. First, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, given a causal mechanism that varies over time or across data sets and whose qualitative structure is known, we aim to extract from data a low-dimensional and interpretable representation of the main components of the changes. For this purpose we develop a novel kernel embedding of nonstationary conditional distributions that does not rely on sliding windows. Second, the embedding also leads to a measure of dependence between the changes of causal modules that can be used to determine the directions of many causal arrows. We demonstrate the power of our methods with experiments on both synthetic and real data.

Memory degradation trends have been observed in many continuously running software systems. Applications running on cloud computing can also suffer from such memory degradation that may cause severe performance degradation or even experience a system failure. Therefore, it is essential to monitor such degradation trends and find the potential causes to provide reliable application services on cloud computing. In this paper, we consider both private and public cloud environments for deploying an image classification system and experimentally investigate the memory degradation that appeared in these environments. The degradation trends in the available memory statistics are confirmed by the Mann-Kendall test in both cloud environments. We apply causal structure discovery methods to process-level memory statistics to identify the causality of the observed memory degradations. Our analytical results identify the suspicious processes potentially leading to memory degradations in public and private cloud environments.

In “Flagpoles anyone? Causal and explanatory asymmetries”, James Woodward supplements his celebrated interventionist account of causation and explanation with a set of new ideas about causal and explanatory asymmetries, which he extracts from some cutting-edge methods for causal discovery from observational data. Among other things, Woodward draws interesting connections between observational causal discovery and interventionist themes that are inspired in the first place by experimental causal discovery, alluding to a sort of unity between observational and experimental causal discovery. In this paper, I make explicit what I take to be the implicated unity. Like experimental causal discovery, observational causal discovery also relies on interventions (or exogenous variations, to be more accurate), albeit interventions that are not carried out by investigators and hence need to be detected as part of the inference. The observational patterns appealed to in observational causal discovery are not only surrogates for would-be interventions, as Woodward sometimes puts it; they also serve to mark relevant interventions that actually happen in the data generating process.

Synthetic data generation has been widely adopted in software testing, data privacy, imbalanced learning, artificial intelligence explanation, etc. In all such contexts, it is important to generate plausible data samples. A common assumption of approaches widely used for data generation is the independence of the features. However, typically, the variables of a dataset de-pend on one another, and these dependencies are not considered in data generation leading to the creation of implausible records. The main problem is that dependencies among variables are typically unknown. In this paper, we design a synthetic dataset generator for tabular data that is able to discover nonlinear causalities among the variables and use them at generation time. State-of-the-art methods for nonlinear causal discovery are typically inefficient. We boost them by restricting the causal discovery among the features appearing in the frequent patterns efficiently retrieved by a pattern mining algorithm. To validate our proposal, we design a framework for generating synthetic datasets with known causalities. Wide experimentation on many synthetic datasets and real datasets with known causalities shows the effectiveness of the proposed method.