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A Survey of Learning Causality with Data: Problems and Methods
Ruocheng Guo, Lu Cheng, Jundong Li, P. Richard Hahn, Huan Liu
TL;DR
The paper asks how abundant data alter the learning of causal effects and relations. It answers through a comprehensive, data-organized survey of traditional and frontier causal methods and their connections to machine learning. The survey concludes that existing causal-learning research lays a foundation for addressing big-data challenges while leaving important problems open.
Problem
The survey addresses how convenient access to copious data changes the possibilities and challenges of learning causal effects and relations.
Method
The paper provides a comprehensive, structured review organized by data types, causal problems, methods, and connections to machine learning.
Results
The survey shows that existing efforts build a foundation for data-driven learning of causal effects and relations and connect causal and predictive problem solving.
Takeaways & Limitations
Learning causality with data offers substantial potential, while using causal knowledge to improve machine-learning algorithms remains an open research area.
Takeaways & Limitations
Many observational-data problems remain open, including anomalies, treatment entanglement, complex treatments, and temporal observations.
Abstract
from arXiv · showhide
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.
1 INTRODUCTION
The survey examines how big data changes learning causal effects and relations, offering a structured review of methods, data types, and connections to machine learning. It highlights both new opportunities and challenges, including high dimensionality, unmeasured confounding, and dataset bias.
- Motivation: Big data may help address causal questions by providing many measurable features and extensive datasets, but high dimensionality and poorly understood dataset bias create new challenges.The survey illustrates these issues with questions about whether Yelp reviews drive restaurant customers or merely reflect popularity.
- Causal questions: The survey distinguishes causal inference, which estimates effects under interventions, from causal discovery, which identifies variables that could change another variable.Both questions imagine modifying variables and rerunning the data-generating process.
- Scope and organization: It reviews causal inference methods for i.i.d., non-i.i.d., and unobserved-confounding settings, alongside causal discovery methods for i.i.d. and time-series data.The survey also connects causality with supervised and semi-supervised learning, domain adaptation, and reinforcement learning.
- Data: The survey focuses on observational data because such data are pervasive in big-data applications, while interventional data explicitly set at least one variable.It notes that observational variables are determined by their causes, whereas interventions alter that process.
- Evaluation: Ground truth for average causal effects can come from randomized experiments, whereas individual causal effects often require simulations because counterfactual outcomes are unavailable.This distinction affects how causal learning methods are evaluated in practice.
- Contribution: Unlike previous surveys, this work organizes methods around data types and the causal questions they support, aiming to bridge machine learning, data mining, and causal learning.Its coverage includes traditional and frontier methods as well as open problems.
2 PRELIMINARIES
The survey introduces structural causal models and causal graphs as frameworks for representing causal relations, interventions, and assumptions. It distinguishes interventional distributions from observational associations and shows how confounding complicates causal-effect identification.
- Potential outcomes: The potential-outcome framework represents treatment effects using treated and untreated potential outcomes, with strong ignorability combining unconfoundedness and overlap.Under unconfoundedness, conditioning on suitable observed features supports causal identification; overlap requires P(t = 1|x) ∈(0, 1).
- Structural causal models: Structural causal models combine causal graphs with structural equations to represent causal relations among variables.Directed edges encode causal effects, while structural equations quantify them using observed variables and exogenous noise.
- Causal graphs: Causal graphs use directed acyclic structures in which d-separation and blocked paths encode conditional-independence relationships.A node is blocked under specified conditioning conditions, and a set d-separates two variables when it blocks all paths between them.
- Interventions: Intervention do(t′) sets the treatment to t′ and removes arrows entering it, producing the interventional distribution P(y|do(t′)).This formalizes rerunning the data-generating process after modifying the treatment and supports causal-effect queries.
- Causal effects: Causal effects compare outcomes under different interventions, whereas observational P(y|t) may differ from interventional P(y|do(t)) because of confounding.The back-door path t ← x → y is given as a source of confounding bias; randomized assignment avoids such paths.
3 LEARNING CAUSAL EFFECTS
This section defines learning causal effects as estimating how outcomes change under treatment modifications and reviews population-level and heterogeneous effects. It emphasizes that average effects can obscure meaningful differences across subpopulations.
- Problem definition: Learning causal effects quantifies how the expected outcome changes when treatment changes from control c to treatment t.The survey frames this through treatment-effect quantities such as E[y|t] − E[y|c].
- Treatment-effect targets: Average treatment effect summarizes effects for a target population, while conditional treatment effect depends on features defining a subpopulation.The relevant population may be the whole population, a known or unknown subgroup, or an individual.
- Heterogeneous effects: ATE can be misleading when a population contains heterogeneous groups with different causal effects.The survey gives restaurant location as an example where Yelp ratings may matter more in big cities than small towns.
- Heterogeneous effects: CATE estimation learns a function mapping features and binary treatment to subgroup-specific treatment effects.The quality of the learned function can be evaluated with mean squared error, also called PEHE for estimated individual effects.
3.1 Traditional Methods without Unobserved Confounders
Traditional methods assume observed covariates can block confounding and use regression, matching, propensity scores, or covariate balancing to estimate causal effects. Their validity depends on assumptions such as unconfoundedness and overlap.
- Adjustment assumption: Adjustment methods assume observed covariates contain sufficient confounders to block all back-door paths.The survey groups adjustment approaches into regression adjustment, propensity-score methods, and covariate balancing.
- Regression adjustment: Regression adjustment estimates counterfactual outcomes by modeling outcome relationships conditional on features and treatment.A single model can estimate P(y|x,t), while separate potential-outcome models estimate P1(y|x) and P0(y|x).
- Matching and stratification: Matching and stratification treat comparable groups as synthetic randomized trials and estimate effects within strata.Perfect stratification requires units in a group to be indistinguishable apart from treatment and potential outcomes.
- Assumptions and limitations: Lack of overlap prevents naïve ATE estimation in strata containing only treated or only control instances.Strong ignorability includes P(t = 1|x) ∈(0, 1), while matching and weighting can mitigate the practical difficulty of perfect matches.
- Propensity scores: IPTW weights observations by the inverse probability of receiving their observed treatment to balance treatment groups.For a propensity score of 0.1, the treated instance receives weight 9 relative to control instances in the example.
- Advanced adjustment: Doubly robust and targeted estimators combine outcome regression with propensity-score modeling to estimate treatment effects.TMLE fits outcome and propensity models before updating the outcome estimator using factual outcomes.
- Covariate balancing: Covariate balancing learns weights that match moments between treatment groups rather than relying only on propensity-score reweighting.Entropy balancing learns control-group weights through a regression-based preprocessing objective.
3.2 Traditional Methods with Unobserved Confounders
Traditional methods address unobserved confounding by using alternative information, including instrumental variables, front-door mediators, and discontinuities in treatment assignment. These methods rely on explicit structural or assignment assumptions that determine when causal effects are identifiable.
- Instrumental Variable Methods: Instrumental-variable methods use a variable that affects treatment but influences the outcome only through treatment, blocking alternative paths to the outcome.Validity requires association with treatment and conditional independence from the outcome under intervention; observed confounders may need adjustment.
- Instrumental Variable Methods: 2SLS first predicts each treatment from instruments and confounders, then estimates outcomes from the predicted treatments and covariates.This extends the restrictive ratio estimator to settings with multiple instruments, treatments, or confounding paths between the instrument and outcome.
- Instrumental Variable Methods: More than 50% valid instruments can suffice for identifying causal effects, and identification may remain possible with more than 50% invalid instruments under additional conditions.The latter case does not require knowing which instruments are valid.
- Front-door Criterion: The front-door criterion identifies treatment effects with unobserved confounders when mediators block treatment-to-outcome paths and satisfy specified confounding conditions.Restaurant search ranking can serve as a mediator when affected by rating without the relevant confounding structure, but not when confounders also affect ranking.
- Regression Discontinuity Design: Regression discontinuity estimates effects at a treatment cutoff using a continuously modeled running variable, while Fuzzy RDD handles probabilistic treatment assignment around the cutoff.Sharp RDD requires continuity of the outcome function at the cutoff; high-order polynomial specifications can be misleading, and exact cutoffs may be unavailable in practice.
3.3 Advanced Methods for Learning Causal Effects from Big Data
Big-data causal methods apply representation learning, neural networks, and ensemble models to estimate effects from rich or dependent data. These approaches support latent-confounder representations, counterfactual prediction, heterogeneous effects, and non-i.i.d. settings, while retaining model-specific assumptions and trade-offs.
- Learning Causal Effects with Neural Networks: Neural causal methods learn feature or confounder representations to estimate causal effects from high-dimensional data.Balancing Counterfactual Regression, TARnet, and CEVAE seek representations that better approximate confounders than observed features.
- Learning Causal Effects with Neural Networks: CEVAE encodes each instance, treatment, and outcome into a latent Gaussian representation and decodes the data from that representation.Its variational objective combines reconstruction and latent-distribution terms.
- Learning Causal Effects with Neural Networks: CEVAE reconstructs a counterfactual outcome and covariates for each instance-treatment combination, enabling counterfactual inference after training.Comparisons on IHDP, Twins, and Jobs reported representation-learning methods as state-of-the-art for learning causal effects.
- Learning Heterogeneous Causal Effects with Ensembles: BART estimates heterogeneous effects by modeling potential outcomes as sums of Bayesian regression trees and taking the difference between treatment-specific predictions.Its advantages include capturing nonlinearity and discontinuity, requiring little hyperparameter tuning, and quantifying posterior uncertainty.
- Learning Heterogeneous Causal Effects with Ensembles: Causal forests recursively partition covariate space into leaves, estimate treatment effects within leaves, and average estimates across trees.The proposed causal forest provides asymptotically normal and consistent estimates of conditional average treatment effects.
- Dependencies and Experimental Data: Non-i.i.d. causal learning models interference and uses networks or temporal structures when one instance’s treatment or outcome depends on others.These approaches incorporate dependencies beyond ordinary features, treatments, and outcomes.
4 CAUSAL DISCOVERY: LEARNING CAUSAL RELATIONS
Causal discovery determines whether variables are causally related by learning candidate graphs from statistical dependencies, using constraint-based, score-based, functional, and hybrid methods. The survey reviews their assumptions, evaluation metrics, computational challenges, and performance on large data.
- Causal discovery examines whether modifying one variable changes another and commonly represents candidate causal relations with graphs.
- Evaluation Metrics: Evaluation compares learned graphs with ground truth using graph distances such as structural Hamming distance and classification metrics for adjacencies and arrowheads.SHD counts edge additions, removals, or reversals needed to transform the learned graph into the ground truth.
- Constraint-based Algorithms: Constraint-based algorithms use conditional-independence tests to learn graph skeletons and orient edges, but can require faithfulness and may leave causal directions unresolved.PC begins with a fully connected graph, removes edges using separating sets, and then determines edge directions.
- Score-based Algorithms: Score-based algorithms maximize a graph score instead of relying on conditional-independence tests, but exhaustive structural search is computationally intractable and requires heuristics.GES uses greedy insertion and deletion phases to reach a local maximum, while BIC combines likelihood with regularization.
- Hybrid Algorithms: Hybrid methods combine constraint-based skeleton learning with score-based edge orientation, as in MMHC, which targets scalability to thousands of variables.MMHC first applies MMPC to learn the skeleton and then uses Bayesian-scoring hill climbing to orient edges.
5 CONNECTIONS TO MACHINE LEARNING
The survey examines how causal knowledge and machine learning inform each other across supervised and semi-supervised learning, domain adaptation, and causal direction learning. It presents methods that use causal structure for prediction and predictive techniques for learning causal relations.
- Supervised Learning and Semi-supervised Learning: Causal questions connect to supervised and semi-supervised learning because some causal problems can be reduced to prediction problems.The survey also considers how labeled causal or anti-causal datasets can train models to recognize causal direction.
- Connections to Machine Learning: The survey identifies supervised and semi-supervised learning, domain adaptation, and reinforcement learning as three machine-learning connections to causal learning.It frames the connections in both directions: causal knowledge can improve machine learning, and machine learning can help learn causality.
- Supervised Learning and Semi-supervised Learning: Causal regularization penalizes features less likely to cause the label, encouraging predictive models to emphasize potentially causal features.A related regularizer uses sample weights and constraints to balance treatment groups and identify causal features.
- Supervised Learning and Semi-supervised Learning: In anti-causal settings, unlabeled data can improve prediction because the marginal distribution P(x) contains information about P(y|x).The survey notes that SSL can outperform supervised learning when P(x) and the generating function f are dependent under specified independence conditions.
- Supervised Learning and Semi-supervised Learning: Comparing estimation errors for P(y|x) and P(x|y) can reveal causal direction because SSL benefits the anti-causal direction more than the causal direction.The survey describes Gaussian-process regression and likelihood comparison as one implementation, while noting scalability challenges for high-dimensional, noisy, or non-i.i.d. data.
- Supervised Learning and Semi-supervised Learning: Massive data on (x,t) can support causal-effect estimation when only a small number of outcomes y are observed by supplying information about P(x,t).This is presented as a special semi-supervised learning problem for learning causal effects.
- Domain Adaptation: Domain adaptation relates to causal learning through invariant prediction, which assumes that causal relations remain stable across domains.Under an underlying structural causal model and suitable interventions, invariant subsets are used to estimate causes and support domain-generalized prediction.
- Domain Adaptation: Causal transportability reuses causal knowledge learned from experiments in different domains using observational data, while concept drift can require prior causal knowledge.These approaches address changes between source and target domains that can undermine ordinary predictive transfer.
6 CONCLUSIONS AND SOME OPEN PROBLEMS
The survey concludes that more data and machine learning broaden data-driven causal learning while also exposing unresolved challenges. It organizes the field around causal effects, causal relations, and their connections to predictive learning, then identifies open problems for observational data and causal machine learning.
- Conclusions: The survey reviews efforts to learn causality with more data and less prior knowledge than traditional studies.It presents these efforts as foundations for further work on causal effects and relations in big-data settings.
- Conclusions: The survey aims to show that causality and machine learning can contribute to better solutions for both causal and predictive problems.It specifically notes that machine-learning models can benefit from exploiting learned causal knowledge.
- Conclusions: The survey covers causal inference and causal discovery, using i.i.d., non-i.i.d., time-series, and data-with-unobserved-confounders settings.It also connects causal learning with supervised and semi-supervised learning, domain adaptation, and reinforcement learning.
- Open Problems: Open observational-data problems include anomalies, treatment entanglement, complex treatments such as images and text, and temporal observations.These are presented as unresolved directions for learning causality from observational data.
- Open Problems: Using causal knowledge to improve machine learning remains open, including causal interpretation of black-box deep learning and causality-aware robustness and fairness.The survey identifies these as potential research directions rather than settled solutions.
APPENDIX
The appendix provides open-source indexes of datasets and algorithms for learning causality, organized by problem and data type.
- Appendix: The authors create an open-source data index and algorithm index to support development, evaluation, and comparison of causal-learning methods.Both indexes are categorized by the problem and the type of data.