Causal Structure Learning and Inference: A Selective Review

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.

Causality-informed machine learning has been proposed as an avenue for achieving many of the goals of modern machine learning, from ensuring generalization under domain shifts to attaining fairness, robustness, and interpretability. A key component of causal machine learning is the inference of causal structures from observational data; in practice, this data may be incompletely observed. Prior work has demonstrated that adversarial perturbations of completely observed training data may be used to force the learning of inaccurate structural causal models (SCMs). However, when the data can be audited for correctness (e.g., it is cryptographically signed by its source), this adversarial mechanism is invalidated. This work introduces a novel attack methodology wherein the adversary deceptively omits a portion of the true training data to bias the learned causal structures in a desired manner (under strong signed sample input validation, this behavior seems to be the only strategy available to the adversary). Under this model, theoretically sound attack mechanisms are derived for the case of arbitrary SCMs, and a sample-efficient learning-based heuristic is given. Experimental validation of these approaches on real and synthetic datasets, across a range of SCMs from the family of additive noise models (linear Gaussian, linear non-Gaussian, and non-linear Gaussian), demonstrates the effectiveness of adversarial missingness attacks at deceiving popular causal structure learning algorithms.

Causal inference aims to estimate the causal relationships and effect sizes among treatments and outcomes. Electronic health record (EHR) data is a valuable healthcare data source that can support causal inference. However, a large percentage of the data is missing in EHRs and they are missing not at random (MNAR). Ignoring MNAR can lead to severe biases, to the extent where the causal structure underlying the data gets distorted. We proposed a new causal inference methodology that addresses the MNAR problem and thus helps preserve the causal structure. We compared the performance of our proposed method with the traditional causal inference method, structural equation modeling (SEM). We evaluated these methods for their accuracy in estimating the causal effect sizes and their ability to converge at all. We employed both simulation studies and real-world EHR data sets. We demonstrated that imputation under the improper missingness mechanism distorted the causal structure to a degree where SEM found it incompatible with the data and failed to. converge. Even when 20 to 30 % of the values were missing, SEM failed to converge in as many as 50% of the runs. The proposed causal inference method achieved a higher convergence rate and more accurate estimation of latent treatment effects both on the synthetic data and on a real EHR data set. We proposed a new methodology that incorporates the knowledge of missing data mechanisms. It significantly mitigated the biases associated with MNAR in the EHR dataset and substantially outperformed SEM that uses the improper missing data mechanism.

A good deal of humility: Cochran on observational studies

Ecology has yet to embrace causal inference, yet most questions in ecology are causal. Despite the common use of terms that imply causation, such as "shapes", "drives", or "impacts", many studies shy away from directly acknowledging their causal ambitions. This avoidance not only obscures the true intent of research but also underpins a broader challenge within the field's approach to science. Ecology relies heavily on observational data, and so the necessity for robust causal inference becomes paramount. However, causal methods are also needed for non-randomised experiments. We critique the predominance in ecology of scientifically empty statistical procedures that lack scientific clarity and value. We advocate for a shift towards explicit causal inference, arguing that understanding causality is not confined to randomised controlled trials but can also be enriched through observational data when paired with rigorous causal inference methodologies. This paper elucidates the common pitfalls in ecological studies, such as throwing all variables into an analysis, use of the Akaike information criterion (AIC) for model selection, the "Table 2 fallacy" and the misuse of controls: all of which can lead to misleading scientific understanding. The good news is that causal inference is not primarily a statistical problem, but rather a scientific one that is accessible to all ecologists. We can achieve reasonable progress by continuing to use the standard statistical toolbox based around regression models, familiar to many ecologists, paired with causal diagrams. For regression, causal inference is about understanding what we should condition on (good controls) and what we should not condition on (bad controls). We provide not only a critique but a constructive guide, aiming to demystify causal inference and encourage its adoption in ecological studies using familiar approaches. By doing so, we seek to elevate the quality and impact of ecological research, moving beyond routine convenient statistical procedures and towards a more scientifically sound and insightful understanding of ecology.

In 2002, the Agency for Healthcare Research and Quality (AHRQ) defined health services research as ''research [that] examines how people get access to health care, how much care costs, and what happens to patients as a result of this care. The main goals of health services research are to identify the most effective ways to organize, manage, finance, and deliver high quality care; reduce medical errors; and improve patient safety'' (http://www.academy health.org). AcademyHealth's (AH) definition is parallel but focuses more explicitly on the factors studied. Thus AH defines health services research as ''the multidisciplinary field of scientific investigation that studies how social factors, financing systems, organizational structures and processes, health technologies, and personal behaviors affect access to health care, the quality and cost of health care, and ultimately our health and well-being. Its research domains are individuals, families, organizations, institutions, communities, and populations'' (http://www.academyhealth.org). Explicit in both definitions is the notion that health services researchers should strive to identify and estimate the causal effects on outcomes of interest of alternative organizational structures, management approaches, financing systems, provider practices, and personal choices regarding lifestyle and behavior. Without a focus on causal effects, it would be impossible to identify the most effective ways to achieve the outcomes we seek through clinical, management, or policy interventions.

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

BackgroundCausal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model.MethodsIt remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability – the causal false-positive risk – is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied.ResultsResults show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias.ConclusionWhile the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

BackgroundTo estimate the causal relationship between two variables it is important to first establish the potential causal pathways and to consider causes of bias. Omission of key confounders from the...

Learning causal effects from observational data greatly benefits a variety of domains such as health care, education, and sociology. For instance, one could estimate the impact of a new drug on specific individuals to assist clinical planning and improve the survival rate. In this paper, we focus on studying the problem of estimating the Conditional Average Treatment Effect (CATE) from observational data. The challenges for this problem are two-fold: on the one hand, we have to derive a causal estimator to estimate the causal quantity from observational data, in the presence of confounding bias; on the other hand, we have to deal with the identification of the CATE when the distributions of covariates over the treatment group units and the control units are imbalanced. To overcome these challenges, we propose a neural network framework called Adversarial Balancing-based representation learning for Causal Effect Inference (ABCEI), based on recent advances in representation learning. To ensure the identification of the CATE, ABCEI uses adversarial learning to balance the distributions of covariates in the treatment and the control group in the latent representation space, without any assumptions on the form of the treatment selection/assignment function. In addition, during the representation learning and balancing process, highly predictive information from the original covariate space might be lost. ABCEI can tackle this information loss problem by preserving useful information for predicting causal effects under the regularization of a mutual information estimator. The experimental results show that ABCEI is robust against treatment selection bias, and matches/outperforms the state-of-the-art approaches. Our experiments show promising results on several datasets, encompassing several health care (and other) domains.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect the manipulated variable and the outcome. Such an "experiment on data" to estimate the causal effect of the manipulated variable is useful for validating an experiment design using historical data or for exploring confounders when studying a new relationship. However, existing data-driven methods for causal effect estimation face some major challenges, including poor scalability with high dimensional data, low estimation accuracy due to heuristics used by the global causal structure learning algorithms, and the assumption of causal sufficiency when hidden variables are inevitable in data. In this paper, we develop a theorem for using local search to find a superset of the adjustment (or confounding) variables for causal effect estimation from observational data under a realistic pretreatment assumption. The theorem ensures that the unbiased estimate of causal effect is included in the set of causal effects estimated by the superset of adjustment variables. Based on the developed theorem, we propose a data-driven algorithm for causal query. Experiments show that the proposed algorithm is faster and produces better causal effect estimation than an existing data-driven causal effect estimation method with hidden variables. The causal effects estimated by the proposed algorithm are as accurate as those by the state-of-the-art methods using domain knowledge.

Bayesian networks have been widely used to generate causal hypotheses from multivariate data. Despite their popularity, the vast majority of existing causal discovery approaches make the strong assumption of a (partially) homogeneous sampling scheme. However, such assumption can be seriously violated, causing significant biases when the underlying population is inherently heterogeneous. To this end, we propose a novel causal Bayesian network model, termed BN-LTE, that embeds heterogeneous samples onto a low-dimensional manifold and builds Bayesian networks conditional on the embedding. This new framework allows for more precise network inference by improving the estimation resolution from the population level to the observation level. Moreover, while causal Bayesian networks are in general not identifiable with purely observational, cross-sectional data due to Markov equivalence, with the blessing of causal effect heterogeneity, we prove that the proposed BN-LTE is uniquely identifiable under relatively mild assumptions. Through extensive experiments, we demonstrate the superior performance of BN-LTE in causal structure learning as well as inferring observation-specific gene regulatory networks from observationaldata.

Optimizing operational decisions, routine actions within some business or operational process, is a key challenge across a variety of domains and application areas. The increasing availability of data, computational power, and advanced machine learning (ML) algorithms offers exciting opportunities for data-driven decision support. To advance the potential of ML for optimizing operational decision-making, we explore two research directions, aiming to develop ML models that are decision-focused and causal. This dissertation presents several developments in machine learning in these two areas. ML is effective at making predictions from historical data: for example, estimating a transaction's fraud probability by comparing it to past cases. However, decision-makers not only need to consider these predictions, but also the operational context. For example, the decision-maker uses predicted fraud probabilities to determine which transactions to investigate, while aiming to minimize monetary losses due to fraud and considering the available capacity of the fraud investigations team. Predictions can help reduce uncertainty (e.g., by predicting the fraud probability), but standard ML models are prediction-focused, instead of decision-focused. This distinction involves two challenges for data-driven decision-making. First, prediction-focused models prioritize predictive accuracy instead of the resulting decision quality (e.g., fraud losses recovered by the bank). Second, these models fail to account for operational constraints, such as the available investigation capacity. Decision-focused learning aims to improve data-driven decision-making by addressing these issues and incorporating the operational context into the optimization of ML models. In this dissertation, we analyze cost-sensitive learning within this prediction-optimization framework and evaluate general strategies for making cost-optimal decisions with ML. Additionally, we propose a novel ML method for optimal decision-making under capacity constraints based on learning to rank. To make effective decisions, a decision-maker has to estimate the causal effect of possible interventions in order to choose actions that achieve the desired outcome. Unfortunately, standard ML models identify correlations in the data instead of causal relationships. Because of this, these models cannot guarantee the effectiveness of decisions made based on their predictions. Causal inference provides a formal framework for reasoning about causality and identifying causal effects from data. This dissertation explores the intersection of causality and ML. First, we illustrate the potential of causal ML for optimizing preventive maintenance. Next, we propose novel causal ML methods for predicting causal effect distributions and for addressing informative sampling when predicting treatment outcomes over time. We also argue for a practical, end-to-end perspective for building ML pipelines for causal inference and propose an automated framework doing so. Finally, we combine decision-focused learning with causal inference by introducing ranking metalearners to optimize treatment decisions under capacity constraints.

The world is changing so fast, and therefore education needs to adapt to the challenges of times. In order to update the content of school education in the Republic of Kazakhstan modern trends are going to be used. These trends contain pedagogical methods that can be used to preserve and even increase internal motivation, as active learning. Active learning method is an treatment where students participate or interact with the learning process, as opposed to passively taking in the information.The goal of this study is to identify the impact of active learning method on 10th grade students’ attitude towards mathematics of the students the second semester of the school year 2019-2020. More specifically, it attempted to determine and compare the attitude toward mathematics of students’ exposure to active learning and traditional teaching strategy. The Likert scale used to evaluate the attitude of students toward mathematics. Mean, Cronbach value, T-test were the statistical tools used in anatomizing and interpreting the research data. The discovering showed that the students in the active learning group had auspicious attitude than students in the conventional teaching group. According to the findings after research, we saw the direct relation between attitude and active learning. It is concluded that the students’ attitude toward mathematics was better by using active learning strategy. It is recommended that mathematics teacher should use active learning strategy in order to improve the attitude toward mathematics of the students.Keywords: attitude, mathematics, active learning