Causal AI: A Theoretical Introduction

Explore Pearl's causal hierarchy, moving from associations to interventions to counterfactuals, and learn the techniques needed to answer questions at each layer of causal reasoning.

Explore layer one of the ladder of causation, focusing on observed associations and conditional probabilities p(y|x) within subpopulations. Understand how correlation without causation explains ice cream sales and drownings.

Explore layer one methods that uncover associations and patterns in data—supervised and unsupervised learning, clustering, and Bayesian networks—and see why they support prediction but require causal graphs for intervention.

Explore layer two: the do operator enables interventions to reveal causal effects, distinguish interventional from observational distributions, and estimate average treatment effects.

Explore layer two techniques that use observational data to infer causation, requiring causal assumptions and extra knowledge to identify and remove biases via a causal Bayesian network.

Explore layer three of causal reasoning by imagining counterfactual parallel worlds and comparing outcomes to estimate individual treatment effects for personalized decisions.

Build and apply a structural causal model to answer layer three counterfactual questions about salary, education, and work experience, using abduction, action, and the do operator.

Using structural causal models, the do operator intervenes by replacing the variable’s structural equation to enforce a chosen value, as in setting college degree to one.

Navigate the ladder of causation—from associations to interventions and counterfactuals—and see how the do operator clarifies causal effects.

Explore causal DAGs and Pearl's framework to connect independence patterns with causal effects, using observational data to reduce bias in distinguishing correlation from causation.

Explore causal DAG concepts: nodes as random variables and directed edges encoding direct causes. Learn observed vs unobserved nodes, and key notions like parents, descendants, and directed paths, with examples.

Apply the do-operator within causal DAGs to intervene, disrupt natural mechanisms, and measure the resulting consequences, clarifying how randomization removes spurious associations and biases.

Explore graph independence and information flows in causal graphs, learn how conditioning blocks paths to separate spurious from causal associations along directed paths.

Examine graph patterns: forks, chains, and colliders that show when variables are independent in causal graphs, and how conditioning biases estimates through confounders, mediators, or colliders.

Discover how blocking paths and d-separation determine when x and y are graphically independent by conditioning on a set, using chains, forks, and colliders.

Explore how blocking paths yields graphical independence and, under the causal Markov condition and d-separation, translates to statistical independence.

Explore causal graphs that encode chains, forks, and colliders to reveal flows. See how conditioning blocks or opens paths and how identification, causal Markov, and minimality map dependencies to statistics.

Explore how causal graphs link associations to causal relationships, learn to block spurious paths with forks and colliders, and determine identification of causal effects from observational data.

Explore estimands, estimators, and estimates, and learn how conditional ignorability enables identifying causal effects in observational data through the adjustment formula and the role of an adjustment set Z.

Explore how causal quantities rest on probabilities, linking observational and interventional distributions, and show how identification techniques rewrite probability terms to remove the dual operator.

Identify the backdoor adjustment to block all backdoor paths in causal graphs using a conditioning set Z with no descendants of the cause.

Master front door adjustment to identify causal effects when backdoor control fails due to unobserved confounders. See how a mediator enables three-step identification from x to z to y.

Explore do-calculus as the foundational identification technique for causal inference, covering its three rules, do-operator transformations, and applicability to front-door and back-door criteria.

Study how positivity and unconfoundedness interact in causal inference, showing how conditioning on covariates can reduce data and threaten reliable estimates.

Identify causal estimands from observational data using do calculus, back-door and front-door criteria, and conditional ignorability, then use adjustment sets to plan estimation while balancing positivity.

Learn how identification selects adjustment variables, use a causal graph to form a valid adjustment set, and estimate an unbiased causal effect from observational data.

Explore how the average treatment effect hides individual heterogeneity and how conditional average treatment effects illuminate subgroup responses and individual treatment effects for targeted interventions.

Learn how the s-learner uses a single model to estimate the average treatment effect by predicting outcomes with t=1 and t=0, leveraging covariates Z.

The t-learner fits two separate models for treated and control groups, predicts outcomes by covariate z, and averages differences to estimate treatment effect, highlighting data efficiency and bias toward zero.

The X-learner uses a two-stage training to predict mu terms from covariates, combines lambda models with H0 and H1, and uses propensity score weights to estimate the average treatment effect.

Pair treated and control units by covariate similarity to estimate the average treatment effect, using exact or nearest-neighbor matching and propensity scores.

Explore inverse probability weighting with propensity scores to reweight outcomes, apply stabilized weights, balance covariates, and create a balanced pseudo population for causal effect estimation.

Discover how systematic and random errors shape causal estimates, and how including or excluding variables like confounders or colliders influences bias and estimate precision, with confidence intervals.

Explore the second part of causal inference estimation, compare estimation techniques including machine learning models and propensity scores, and highlight how causal graphs determine adjustment sets.

Learn to obtain causal graphs using domain knowledge, causal discovery algorithms, and observational data; use directed acyclic graphs to identify adjustments and variables for the Perylene average causal effect estimator.

Build causal graphs from domain knowledge—expert insights, studies, and experiments reveal potential cause and effect links. Acknowledge biases and complement with causal discovery algorithms for objective edges.

Explore causal discovery algorithms and their four categories—constraint-based, score-based, function-based, and continuous optimization-based—used to infer edges and directions in causal graphs from data, with discussions of challenges and popular methods.

Explore the main assumptions behind causal discovery, including the causal Markov condition and faithfulness, and how they map statistical independencies to graph structure while noting causal sufficiency and acyclicity constraints.

Constraint-based causal discovery uses independence tests to infer conditional independencies and map them to causal graphs, with the PC algorithm revealing colliders, forks, chains, and Markov equivalence classes.

Explore score-based causal discovery with greedy equivalent search, identifying causal graphs by maximizing a score function like BIC across a graph space, and obtaining a Markov equivalence class.

Explore function based causal discovery with lingam, a linear non-Gaussian acyclic model that identifies causal direction by exploiting independence of residuals and non-Gaussian errors.

Discover continuous optimization based methods for causal discovery. Learn how gradient-based optimization and the augmented lagrangian approach enforce acyclicity in a single adjacency matrix A.

Combine hybrid algorithms with domain expertise to build and iteratively validate a causal graph, incorporating prior knowledge for robust real-world solutions.

Review the two main techniques for obtaining a causal graph from domain knowledge and explore popular causal discovery algorithms and their challenges.

Explore the key challenges in causal AI and learn practical techniques to tackle them, plus fresh considerations and a roadmap to advance your causal journey.

Explore core challenges in causal AI, including limited validation without ground truth, estimator selection with synthetic data, and validating causal graphs through partial identification and sensitivity analysis.

Explore the scope of causal AI, including binary and continuous treatments, time series considerations, and estimator limits like the t-learner, plus book recommendations for foundational study.