Identifying causal mechanisms is a fundamental goal of social science. Researchers seek to study not only whether one variable affects another but also how such a causal relationship arises. Yet, commonly used statistical methods for identifying causal mechanisms rely upon untestable assumptions and are often inappropriate even under those assumptions. Randomizing treatment and intermediate variables is also insufficient. Despite these difficulties, study of causal mechanisms is too important to abandon. We make three contributions to improve research on causal mechanisms. First, we present a minimum set of assumptions required under standard designs of experimental and observational studies and develop a general algorithm for estimating causal mediation effects. Second, we provide a method to assess sensitivity of conclusions to potential violations of a key assumption. Third, we offer alternative research designs for identifying causal mechanisms under weaker assumptions. The proposed approach is illustrated using media framing experiments and incumbency advantage studies

Would the third-wave democracies have been democratized without prior modernization? What proportion of the past militarized disputes between non-democracies would have been prevented had those dyads been democratic? Although political scientists often ask these questions of causal attribution, existing quantitative methods fail to address them. This paper proposes an alternative statistical methodology based on the widely accepted counterfactual framework of causal inference. The contribution of this paper is threefold. First, the paper clarifies differences between causal attribution and causal effects by specifying the type of research questions to which each quantity is relevant. Second, it provides a clear resolution of the long-standing methodological debate on "selection on the dependent variable." Third, the paper derives new nonparametric identification results, showing that the complier probability of causal attribution can be identified using an instrumental variable. The proposed framework is illustrated via empirical examples from three subfields of political science.

Identifying causal relations from time series is the first step to understanding the behavior of complex systems. Although many methods have been proposed, few papers have applied multiple methods together to detect causal relations based on time series generated from coupled nonlinear systems with some unobserved parts. Here we propose the combined use of three methods and a majority vote to infer causality under such circumstances. Two of these methods are proposed here for the first time, and all of the three methods can be applied even if the underlying dynamics is nonlinear and there are hidden common causes. We test our methods with coupled logistic maps, coupled Rössler models, and coupled Lorenz models. In addition, we show from ice core data how the causal relations among the temperature, the CH4 level, and the CO2 level in the atmosphere changed in the last 800,000 years, a conclusion also supported by irregularly sampled data analysis. Moreover, these methods show how three regions of the brain interact with each other during the visually cued, two-choice arm reaching task. Especially, we demonstrate that this is due to bottom up influences at the beginning of the task, while there exist mutual influences between the posterior medial prefrontal cortex and the presupplementary motor area. Based on our results, we conclude that identifying causality with an appropriate ensemble of multiple methods ensures the validity of the obtained results more firmly.

Datasets as well as R and Python code of the empirical examples in the book "Causal Analysis" by Martin Huber (2023), published by MIT Press.

Collection of source code implementing methods and for reproducing experiments included in each chapter of the Ph.D. dissertation "Safer Causal Inference: Theory & Algorithms for Falsification, Trial Augmentation and Policy Evaluation". The source code also includes methods for generating simulated datasets used in the evaluation of the methods. The goal of the of the research was to develop methods to improve treatment effect estimation, this includes: methods to detect unmeasured confounding from observational data, methods to integrate historical data into randomized experiments to improve data efficiency, methods to evaluate treatment policies under treatment interference.

Replication package related to the paper "Estimating Causal effects of Multi-valued Treatments accounting for Network Interference: Immigration policies and crime rates"

If an experimental treatment is experienced by both treated and control group units, tests of hypotheses about causal effects may be difficult to conceptualize let alone execute. In this paper, we show how counterfactual causal models may be written and tested when theories suggest spillover or other network-based interference among experimental units. We show that the ``no interference'' assumption need not constrain scholars who have interesting questions about interference. We offer researchers the ability to model theories about how treatment given to some units may come to influence outcomes for other units. We further show how to test hypotheses about these causal effects, and we provide tools to enable researchers to assess the operating characteristics of their tests given their own models, designs, test statistics, and data. The conceptual and methodological framework we develop here is particularly applicable to social networks, but may be usefully deployed whenever a researcher wonders about interference between units. Interference between units need not be an untestable assumption; instead, interference is an opportunity to ask meaningful questions about theoretically interesting phenomena.

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may underestimate the simultaneous and reciprocal nature of causal interactions observed in real-world phenomena. Here, we present a causal-decomposition approach that is not based on prediction, but based on the covariation of cause and effect: cause is that which put, the effect follows; and removed, the effect is removed. Using empirical mode decomposition, we show that causal interaction is encoded in instantaneous phase dependency at a specific time scale, and this phase dependency is diminished when the causal-related intrinsic component is removed from the effect. Furthermore, we demonstrate the generic applicability of our method to both stochastic and deterministic systems, and show the consistency of causal-decomposition method compared to existing methods, and finally uncover the key mode of causal interactions in both modelled and actual predator–prey systems.

Cause-effect is a two dimensional database with two-variable cause-effect pairs chosen from the different datasets created by Max-Planck-Institute for Biological Cybernetics in Tuebingen, Germany.

Size: 83 datasets of various sizes

Number of features: 2 in every datasets

Ground truth: avalaible for every dataset

Type of Graph: directed

Extension of the datasets used in CauseEffectPairs task. Each dataset consists of samples of a pair of statistically dependent random variables, where one variable is known to cause the other one. The task is to identify for each pair which of the two variables is the cause and which one the effect, using the observed samples only

More information about the dataset is contained in causal_description.html file.

Reference

J. M. Mooij, J. Peters, D. Janzing, J. Zscheischler, B. Schoelkopf: “Distinguishing cause from effect using observational data: methods and benchmarks”, Journal of Machine Learning Research 17(32):1-102, 2016

Causal AI Market size was valued at USD 11.77 Million in 2024 and is projected to reach USD 256.73 Million by 2031, growing at a CAGR of 47.1% during the forecast period 2024-2031.

Causal AI also known as causal artificial intelligence is a significant innovation in the fields of artificial intelligence and machine learning that focuses on identifying and harnessing cause-and-effect linkages in data. Traditional AI models generally use correlation-based methods to detect patterns and generate predictions. While these methods can be quite useful in specific applications, they frequently fall short in situations where understanding the underlying causal mechanisms is critical. Causal AI overcomes this issue by incorporating principles from causal inference, a branch of statistics and philosophy that investigates how to infer causal correlations from data.

Causal AI is a huge leap in the field of artificial intelligence allowing us to go beyond correlation to discover the true drivers of observed occurrences. Its applications are broad and diverse including healthcare, finance, marketing, policymaking, operations, education, the environment, and social sciences. Causal AI improves decision-making and allows for the development of focused solutions to meet difficult situations by offering a richer grasp of causality.

Causal AI (Artificial Intelligence) has the potential to change a wide range of domains by providing more precise and actionable insights than typical machine learning models. Causal AI differs from traditional AI in that it focuses on understanding the cause-and-effect relationships underlying data rather than correlations and patterns. This change from correlation to causation is a huge step forward with the potential to improve decision-making processes make better forecasts, and maximize outcomes in a variety of industries including healthcare, finance, marketing, and others.

Social scientists are interested in the effects of low-dimensional latent treatments within texts, such as the effect of an attack on a candidate in a political advertisement. We provide a framework for causal inference with latent treatments in high-dimensional interventions. Using this framework, we show that the randomization of texts alone is insufficient to identify the causal effects of latent treatments, because other unmeasured treatments in the text could confound the measured treatment's effect. We provide a set of assumptions that is sufficient to identify the effect of latent treatments and a set of strategies to make these assumptions more plausible, including explicitly adjusting for potentially confounding text features and non-traditional experimental designs involving many versions of the text. We apply our framework to a survey experiment and an observational study, demonstrating how our framework makes text-based causal inferences more credible.

Electronic health records store a lot of data about a patient. These data often include age, health problems, current medicines, and lab results. Looking at these data may help doctors treating patients after a trauma predict how likely it is that they will respond well to a treatment and survive. This information can help doctors make better treatment decisions. But first, researchers need to figure out how to combine and analyze data to make accurate predictions. In this study, the research team created new statistical methods to combine data from patient records. They used these methods to predict patient health outcomes. Then the team used health record data collected from patients in hospital trauma centers to test their predictions. To access the methods and software, please visit the following GitHubs: origami varimpact opttx

This collection consists of 5 structure learning datasets from the Bayesian Network Repository (Scutari, 2010).

Task: The dataset collection can be used to study causal discovery algorithms.

Summary:

• Size of collection: 5 datasets with 3 - 56 columns of various sizes
• Task: Causal Discovery
• Data Type: Discrete
• Dataset Scope: Collection
• Ground Truth: Known / Estimated
• Temporal Structure: No
• License: TBD
• Missing Values: No

Missingness Statement: There are no missing values.

Collection:

The alarm dataset contains the following 37 variables:

• CVP (central venous pressure): a three-level factor with levels LOW, NORMAL and HIGH.
• PCWP (pulmonary capillary wedge pressure): a three-level factor with levels LOW, NORMAL and HIGH.
• HIST (history): a two-level factor with levels TRUE and FALSE.
• TPR (total peripheral resistance): a three-level factor with levels LOW, NORMAL and HIGH.
• ... (33 more variables, see the corresponding .html file)

The binary synthetic asia dataset:

• D (dyspnoea), a two-level factor with levels yes and no.
• T (tuberculosis), a two-level factor with levels yes and no.
• L (lung cancer), a two-level factor with levels yes and no.
• B (bronchitis), a two-level factor with levels yes and no.
• A(visit to Asia), a two-level factor with levels yes and no.
• S (smoking), a two-level factor with levels yes and no.
• X (chest X-ray), a two-level factor with levels yes and no.
• E (tuberculosis versus lung cancer/bronchitis), a two-level factor with levels yes and no.

The binary coronary dataset:

• Smoking (smoking): a two-level factor with levels no and yes.
• M. Work (strenuous mental work): a two-level factor with levels no and yes.
• P. Work (strenuous physical work): a two-level factor with levels no and yes.
• Pressure (systolic blood pressure): a two-level factor with levels <140 and >140.
• Proteins (ratio of beta and alpha lipoproteins): a two-level factor with levels <3 and >3.
• Family (family anamnesis of coronary heart disease): a two-level factor with levels neg and pos.

The hailfinder dataset contains the following 56 variables:

• N07muVerMo (10.7mu vertical motion): a four-level factor with levels StrongUp, WeakUp, Neutral and Down.
• SubjVertMo (subjective judgment of vertical motion): a four-level factor with levels StrongUp, WeakUp, Neutral and Down.
• QGVertMotion (quasigeostrophic vertical motion): a four-level factor with levels StrongUp, WeakUp, Neutral and Down.
• CombVerMo (combined vertical motion): a four-level factor with levels StrongUp, WeakUp, Neutral and Down.
• AreaMesoALS (area of meso-alpha): a four-level factor with levels StrongUp, WeakUp, Neutral and Down.
• SatContMoist (satellite contribution to moisture): a four-level factor with levels VeryWet, Wet, Neutral and Dry.
• ... (49 more variables are in the correspondent .html file)

The lizards dataset contains the following 3 variables:

• Species (the species of the lizard): a two-level factor with levels Sagrei and Distichus.
• Height (perch height): a two-level factor with levels high (greater than 4.75 feet) and low (lesser or equal to 4.75 feet).
• Diameter (perch diameter): a two-level factor with levels narrow (greater than 4 inches) and wide (lesser or equal to 4 inches).

Local statistical analysis has long been of interest to social and environmental scientists who analyze geographic data. Research into local spatial statistics experienced a step-change in the mid-1990s, which provided a large class of local statistical methods and models. The local Moran statistic is one commonly used local indicator of spatial association, able to detect both areas of similarity and observations that are very dissimilar from their surroundings. From this, many further local statistics have been developed to characterize spatial clusters and outliers. These statistics have seen limited adoption because they do not sufficiently model the relationships involved in confounded spatial data, where the analyst seeks to understand the local spatial structure of a given outcome variable that is influenced by one or more additional factors. Recent innovations used to do joint multivariate local analysis also do not model this kind of conditional local structure in data. This article provides tools to rigorously characterize confounded local inference and a new and different class of multivariate conditional local Moran statistics that can account for confounding. To do this, we return to the Moran scatterplot as the critical tool for local Moran-style covariance statistics. Extending this concept, a new method is available directly from a “Moran-form” multiple regression. We show the empirical and theoretical properties of this statistic, show how some existing heuristic approaches arise naturally from this framework, and show how the use of conditional inference can change interpretations in an empirical analysis of rent and housing stock in a rapidly changing neighborhood.

In studies of civil strife, the ecological fallacy seems to befall all large-$n$ studies and thus there has been a big push, by several researchers, in recent years to gather disaggregated, spatially explicit data. However, while such efforts are heroic and are likely to lead to better information, we find that the resulting data can not be analysed in conventional ways, if the estimation of causal effects is the goal. The reason is that such data brings about other dangers: the violation of the Stable Unit Treatment Value Assumption (SUTVA). To be specific, one ``treated'' group's enemy could hardly be its control. We get around this problem by changing the causal effect of interest and by carefully re-aggregating the lower level data so as to preserve its most salient information. Restricting our analysis to groups that are excluded from power, we find some tentative evidence that such groups are less likely to engage in conflict if they are more spatially integrated with other groups.

The database for this study (Briganti et al. 2018; the same for the Braun study analysis) was composed of 1973 French-speaking students in several universities or schools for higher education in the following fields: engineering (31%), medicine (18%), nursing school (16%), economic sciences (15%), physiotherapy, (4%), psychology (11%), law school (4%) and dietetics (1%). The subjects were 17 to 25 years old (M = 19.6 years, SD = 1.6 years), 57% were females and 43% were males. Even though the full dataset was composed of 1973 participants, only 1270 answered the full questionnaire: missing data are handled using pairwise complete observations in estimating a Gaussian Graphical Model, meaning that all available information from every subject are used.

The feature set is composed of 28 items meant to assess the four following components: fantasy, perspective taking, empathic concern and personal distress. In the questionnaire, the items are mixed; reversed items (items 3, 4, 7, 12, 13, 14, 15, 18, 19) are present. Items are scored from 0 to 4, where “0” means “Doesn’t describe me very well” and “4” means “Describes me very well”; reverse-scoring is calculated afterwards. The questionnaires were anonymized. The reanalysis of the database in this retrospective study was approved by the ethical committee of the Erasmus Hospital.

Size: A dataset of size 1973*28

Number of features: 28

Ground truth: No

Type of Graph: Mixed graph

The following gives the description of the variables:

More information about the dataset is contained in empathy_description.html file.

Causal Inference Platform Market Outlook

According to our latest research, the global causal inference platform market size reached USD 1.24 billion in 2024, reflecting a robust surge in adoption across multiple industries. The market is anticipated to expand at a compelling CAGR of 26.9% during the forecast period, with the market size projected to reach approximately USD 10.78 billion by 2033. This exceptional growth trajectory is underpinned by the increasing demand for advanced analytics solutions that can extract actionable insights from complex data, enabling organizations to make data-driven decisions with higher confidence.

The primary growth factor propelling the causal inference platform market is the exponential increase in the volume and complexity of data generated across sectors such as healthcare, finance, retail, and manufacturing. As organizations strive to move beyond traditional correlation-based analytics, the need for platforms that can accurately determine causality has become paramount. Causal inference platforms are uniquely positioned to address this need, providing sophisticated statistical methodologies and machine learning algorithms that distinguish causation from mere correlation. This capability is critical for organizations seeking to optimize operations, improve customer experiences, and minimize risks, thereby fueling the widespread adoption of these platforms.

Another significant driver is the rapid advancement of artificial intelligence (AI) and machine learning technologies, which have made causal inference platforms more accessible, scalable, and user-friendly. The integration of causal inference capabilities into existing data analytics ecosystems allows enterprises to unlock deeper insights, automate decision-making processes, and accelerate innovation. Furthermore, the growing emphasis on explainable AI and regulatory compliance is compelling organizations to adopt solutions that offer transparency and traceability in their analytical models. This trend is particularly evident in regulated industries such as healthcare and finance, where understanding the underlying causes of outcomes is essential for both operational effectiveness and legal compliance.

The increasing collaboration between academia, research institutions, and commercial enterprises is also fueling the growth of the causal inference platform market. Academic advancements in causal inference methodologies are rapidly being translated into commercial applications, enabling a continuous cycle of innovation. Additionally, government organizations are investing in causal inference platforms to enhance policy-making, public health initiatives, and economic planning. The convergence of these factors is creating a fertile environment for the causal inference platform market to thrive, with vendors continuously enhancing their offerings to meet the evolving needs of diverse end-users.

Regionally, North America dominates the causal inference platform market, driven by the presence of leading technology companies, high adoption of advanced analytics, and substantial investments in AI research. Europe follows closely, benefiting from a robust regulatory framework and a strong focus on data-driven innovation. The Asia Pacific region is emerging as a high-growth market, fueled by rapid digital transformation, expanding research activities, and increasing investments in AI infrastructure. Latin America and the Middle East & Africa are also witnessing steady growth, supported by government initiatives and the gradual modernization of enterprise IT environments. This global momentum underscores the transformative potential of causal inference platforms across industries and geographies.

Component Analysis

The component segment of the causal inference platform market is bifurcated into software and services, each playing a pivotal role in the market’s expansion. Software solutions constitute the backbone of causal inference platforms, providing users with advanced statistical modeling, simulation, and visualization

This dataset contains triples curated from Wikidata surrounding news events with causal relations, and is released as part of our WWW'23 paper, "Event Prediction using Case-Based Reasoning over Knowledge Graphs".

Starting from a set of classes that we consider to be types of "events", we queried Wikidata to collect entities that were an instanceOf an event class and that were connected to another such event entity by a causal triple (https://www.wikidata.org/wiki/Wikidata:List_of_properties/causality). For all such cause-effect event pairs, we then collected a 3-hop neighborhood of outgoing triples.

This replication file contains data and source code to replicate the results in "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models" by Yiqing Xu

The paper discusses the doubly robust estimator for missing data and causal inference models.