Cover of Causal Inference for Data Science

What you will learn in Causal Inference for Data Science

by Aleix Ruiz de Villa

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Chapter by chapter

Chapter 1: Introducing causality

1.1 How causal inference works · 1.1.1 Step 1: Determine the type of data · 1.1.2 Step 2: Understand your problem · 1.1.3 Step 3: Create a model · 1.1.4 Step 4: Share your model · 1.1.5 Step 5: Apply causal inference techniques · 1.2 Contrasts between causal models and the predictive models of machine learning · 1.3 Experimental studies · 1.3.1 Motivating example: Deploying a new website · 1.3.2 A/B testing · 1.3.3 Randomized controlled trials · 1.3.4 Steps to perform an A/B test · 1.3.5 Limitations of A/B testing and RCTs · 1.4 Observational studies · 1.4.1 Simulating synthetic data · 1.4.2 Causal effects under confounding · 1.5 Reviewing basic statistical concepts · 1.5.1 Empirical distributions and data-generating distributions · 1.5.2 A refresher on conditional probabilities and expectations · 1.6 Further reading · 1.7 Chapter quiz · 1.8 Summary

What you learn in chapter 1 →

Chapter 2: First steps: Working with confounders

2.1 Learning the basic elements of causal inference through Simpson’s paradox · 2.1.1 What’s the problem? · 2.1.2 Develop your intuition: How to approach the problem · 2.1.3 Solving Simpson’s paradox · 2.2 Generalizing to other problems · 2.2.1 Describing the problem with a graph · 2.2.2 Articulating what we would like to know · 2.2.3 Finding the way to calculate the causal effect · 2.2.4 Articulating what we would like to know: The language of interventions · 2.2.5 Finding the way to calculate the causal effect: The adjustment formula · 2.2.6 How does the treatment work in each situation? The positivity assumption · 2.3 Interventions and RCTs · 2.4 First contact with the structural approach · 2.4.1 Simulating the kidney stone example · 2.4.2 Interventions in the structural approach · 2.5 When to apply the adjustment formula · 2.5.1 RCT or A/B test · 2.5.2 Confounders · 2.5.3 Unobserved confounders · 2.5.4 Mediators · 2.5.5 Many confounders · 2.5.6 Outcome predictive variables · 2.5.7 Treatment predictive variables · 2.5.8 Conditional Intervention · 2.5.9 Combining all the previous situations · 2.5.10 Summarizing the differences between intervening and applying the adjustment formula · 2.6 So, what’s the plan? · 2.7 Lessons learned · 2.8 Chapter quiz · 2.9 Summary

What you learn in chapter 2 →

Chapter 3: Applying causal inference

3.1 When and why to use graphs in causal inference analysis · 3.2 Steps to formulate your problem using graphs · 3.2.1 List all the variables · 3.2.2 Create your graph · 3.2.3 State your assumptions · 3.2.4 State your objectives · 3.2.5 Check the positivity assumption · 3.3 Other examples · 3.3.1 Recommender systems · 3.3.2 Pricing · 3.3.3 Simulations · 3.4 Further reading · 3.5 Chapter quiz · 3.6 Summary

What you learn in chapter 3 →

Chapter 4: How machine learning and causal inference can help each other

4.1 What does supervised learning do? · 4.1.1 When should causal inference be used vs. supervised learning? · 4.1.2 The goal of data fitting · 4.1.3 When the future and the past behave the same way · 4.1.4 When do causal inference and supervised learning coincide? · 4.1.5 Predictive error is a false friend · 4.1.6 Validation of interventions · 4.2 How does supervised learning participate in causal inference? · 4.2.1 Empirical and generating distributions in the adjustment formula · 4.2.2 The flexibility of the adjustment formula · 4.2.3 The adjustment formula for continuous distributions · 4.2.4 Algorithms for calculating the adjustment formula · 4.2.5 Cross–fitting: Avoiding overfitting · 4.3 Other applications of causal inference in machine learning · 4.3.1 Reinforcement learning · 4.3.2 Fairness · 4.3.3 Spurious correlations · 4.3.4 Natural language processing · 4.3.5 Explainability · 4.4 Further reading · 4.5 Chapter quiz · 4.6 Summary

What you learn in chapter 4 →

Chapter 5: Finding comparable cases with propensity scores

5.1 Developing your intuition about the propensity scores · 5.1.1 Finding matches for estimating causal effects · 5.1.2 But is there a match? · 5.1.3 Why matching can be hard · 5.1.4 How propensity scores can be used to calculate the ATE · 5.2 Basic notions of propensity scores · 5.2.1 Which cases are we working with? · 5.2.2 What are the propensity scores? · 5.2.3 The positivity assumption is … an assumption · 5.3 Propensity scores in practice · 5.3.1 Data preparation · 5.3.2 Calculating the propensity scores · 5.3.3 Assess the positivity assumption · 5.3.4 Calculating ATEs drawn from the propensity scores · 5.4 Calculating propensity score adjustment: An exercise · 5.4.1 Exercise steps · 5.5 Further reading · 5.6 Chapter quiz · 5.7 Summary

What you learn in chapter 5 →

Chapter 6: Direct and indirect effects with linear models

6.1 Estimating causal effects with linear models · 6.1.1 Simulating a pricing problem: A walkthrough · 6.1.2 Direct and indirect effects · 6.2 Understanding causal dynamics through linear models · 6.2.1 The analogy of a gas flowing through pipes · 6.2.2 How correlation flows through a graph · 6.2.3 Calculating causation and correlation from the arrows' coefficients · 6.2.4 Linear models and the “do” operator · 6.3 Chapter quiz · 6.4 Summary

What you learn in chapter 6 →

Chapter 7: Dealing with complex graphs

7.1 Altering the correlation between two variables conditioning on a third one · 7.1.1 Arrival time example of conditional independence · 7.1.2 Mathematical example of conditional independence · 7.1.3 Breaking a causal model into independent modules · 7.1.4 The bricks of DAGs: Factorizing probability distributions · 7.1.5 What’s the d-separation about? · 7.1.6 Defining d-separation · 7.2 Back-door criterion · 7.2.1 The importance of the back-door criterion · 7.3 Good and bad controls · 7.3.1 Good controls · 7.3.2 Neutral controls · 7.3.3 Bad controls · 7.4 Revisiting previous chapters · 7.4.1 Efficient controls · 7.4.2 Propensity score · 7.4.3 Again: Don’t include variables in your model just because they make the model more accurate · 7.4.4 Should you adjust for income? · 7.4.5 Linear models · 7.5 An advanced tool for identifying causal effects: The do-calculus · 7.6 Further reading · 7.7 Chapter quiz · 7.8 Summary

What you learn in chapter 7 →

Chapter 8: Advanced tools with the DoubleML library

8.1 Double machine learning · 8.1.1 FWL theorem: The predecessor of DML · 8.1.2 Nonlinear models with DML · 8.1.3 DML in practice · 8.1.4 Heterogeneous treatment effects · 8.2 Confidence intervals · 8.2.1 Simulating new datasets with bootstrapping · 8.2.2 Analytical formulas for confidence intervals · 8.3 Doubly robust estimators · 8.3.1 AIPW in practice · 8.4 Further reading · 8.5 Chapter quiz · 8.6 Summary

What you learn in chapter 8 →

Chapter 9: Instrumental variables

9.1 Understanding IVs through an example · 9.1.1 The example’s DAG · 9.1.2 IV assumptions · 9.1.3 IVs in RCTs · 9.2 Estimating the causal effect with IVs · 9.2.1 Applying IVs with linear models · 9.2.2 Applying IVs for partially linear models · 9.2.3 An alternative formula for the IV method · 9.2.4 The lack of a general formula for the general IV graph · 9.3 Instrumental variables in practice · 9.3.1 Two-stage least squares (2SLS) algorithm · 9.3.2 Weak instruments · 9.3.3 IVs with DoubleML · 9.4 References · 9.5 Chapter quiz · 9.6 Summary

What you learn in chapter 9 →

Chapter 10: Potential outcomes framework

10.1 What is a potential outcome? · 10.1.1 Individual outcomes · 10.1.2 Population outcomes · 10.1.3 Causal effects · 10.1.4 PO assumptions · 10.2 How do POs relate to DAGs? · 10.2.1 The first law of causal inference · 10.2.2 Expressing PO assumptions with DAGs · 10.2.3 Counterfactuals · 10.3 Adjustment formula with potential outcomes · 10.4 IVs with potential outcomes · 10.5 Chapter quiz · 10.6 Summary

What you learn in chapter 10 →

Chapter 11: The effect of a time-related event

11.1 Which types of data will we use? · 11.2 Regression discontinuity design · 11.2.1 Data simulation · 11.2.2 RDD terminology · 11.2.3 Assumptions · 11.2.4 Effect estimation · 11.2.5 RDD in practice · 11.3 Synthetic controls · 11.3.1 Data simulation · 11.3.2 Synthetic controls terminology · 11.3.3 Assumptions · 11.3.4 Effect estimation · 11.3.5 Synthetic controls in practice · 11.3.6 Selecting training and predicting time periods · 11.4 Differences in differences · 11.4.1 Data simulation · 11.4.2 DiD terminology · 11.4.3 Assumptions · 11.4.4 Effect estimation · 11.4.5 In practice · 11.5 Chapter quiz · 11.6 Method comparison · 11.7 References · 11.8 Summary

What you learn in chapter 11 →

Concepts explained in this book

confounderConfounding is a causal-analysis problem in which variables create a noncausal association that makes it difficult to distinguish a treatment's effect from other influences on the outcome.
average treatment effect estimationThe average treatment effect is the population-average difference in outcomes that would result from two alternative treatments or interventions.
linear regressionLinear regression is a regression method that estimates a linear relationship between an outcome and one or more predictors.
causal inferenceA causal problem is a problem of determining whether and how one factor causes an outcome.
positivity assumptionThe positivity assumption is the condition that every treatment has a nonzero and non-unit probability of being assigned at every confounder value that occurs in the population.
causal adjustmentThe adjustment formula is a causal inference formula that identifies an effect by averaging outcome distributions conditional on treatment across the target population distribution of a confounding variable.
potential outcomes frameworkA potential outcome is the outcome that would result for a unit under a particular treatment or intervention level.
propensity scoreA propensity score is the conditional probability that a unit receives a treatment given its observed covariates.
structural causal modelA causal model is a conceptual representation of causal relationships that accounts for variables influencing both a cause and an effect.
effect of treatment on the treatedThe average treatment effect on the treated is the average difference between treated outcomes and their untreated potential outcomes among treated units.
causationCausality is a relationship in which changing one factor produces a change in another factor or outcome.
treatment effectThe change in an outcome caused by changing an exposure or treatment while holding the relevant causal context fixed.
direct effectA direct effect is the portion of a causal effect transmitted along a specified direct causal path from a cause to an outcome, excluding effects through mediators.
directed acyclic graphA directed acyclic graph is a graph with directed edges and no directed cycles, used in causal inference to represent variables and their causal relationships.
cross-fittingCross-fitting is a procedure that partitions data, trains models on complementary subsets, and evaluates predictions on held-out subsets to reduce overfitting in causal estimation.
total effectA total effect is the overall causal effect of a treatment or variable on an outcome, including all direct and mediated pathways.
indirect effectAn indirect effect is the causal influence of one variable on another that operates through one or more intervening variables.
double machine learningDouble machine learning is a causal estimation technique that combines machine-learning nuisance models with orthogonalized effect estimation to reduce bias from estimating those nuisance components.
d-separationD-separation is a graphical criterion stating that a conditioning set blocks the relevant paths between variables in a graph, implying their conditional independence under the graph's assumptions.
correlationCorrelation is a statistical association in which two variables vary together without by itself establishing that either causes the other.
supervised learningSupervised learning is a machine-learning approach that learns a mapping from inputs to labeled outputs.
accuracyAccuracy is the proportion of predictions that match the corresponding observed outcomes.
conditional expectationA conditional expectation is the expected value of a variable under a specified condition or given values of other variables.
DoubleMLDoubleML is an open-source software library for estimating causal effects with double machine learning and related methods in R and Python.
instrumental variableAn instrument is a variable that directly influences treatment while being unrelated to confounders and not directly influencing the outcome.
synthetic dataSynthetic data are artificially generated observations produced from a specified model rather than collected from real-world events.
colliderA collider is a variable that is causally influenced by two other variables and whose conditioning can induce or alter their association.
backdoor criterionThe back-door criterion is a graphical criterion for determining whether conditioning on a set of variables identifies a causal effect in a directed acyclic graph.
cross-validationCross-validation is a model-evaluation procedure that repeatedly partitions data into training and validation portions to estimate predictive performance.
conditional independenceConditional independence is a probabilistic property in which two variables are independent after restricting attention to specified values or information about another variable.
counterfactual outcomeA counterfactual is a representation of what would have happened to a unit or system under a treatment or condition different from the one actually observed.
unobserved confoundingAn unobserved confounder is a confounding variable that influences treatment and outcome but is not measured or available in the data.
adjustment setAn adjustment set is a set of variables conditioned on to block noncausal paths while preserving the causal paths between a treatment and an outcome.
overfittingOverfitting is the condition in which a model captures noise or idiosyncrasies in training data and consequently generalizes poorly to new data.
synthetic controlSynthetic control is a causal estimation method that constructs a predictive baseline from correlated time-series data to estimate what would have happened to a treated unit without the intervention.
conditional probabilityConditional probability is the probability of an event given that another event or condition is known to occur.
Simpson's paradoxSimpson’s paradox is a statistical phenomenon in which an association or trend observed across aggregated data reverses or differs after conditioning on a grouping variable.
observational dataObservational data are measurements collected without assigning or controlling the conditions under which observations occur.
T-learnerA T-learner is a causal estimation algorithm that fits separate outcome models for each treatment value and compares their predictions.
classifierClassification is a predictive modeling task for assigning an instance to one of a set of discrete classes.
regression coefficientA regression coefficient is a parameter quantifying the change in a modeled outcome associated with a one-unit change in a predictor while other predictors are held fixed.
causal arrowA causal arrow is a directed graph edge representing the direction of a causal relationship.
difference-in-differencesDifference in differences is a causal estimation method that compares changes over time between treated and comparison groups.
causal pathA causal path is a directed path through a causal graph whose edges consistently point from a source variable to a destination variable and represent a route of causal influence.
mediatorA mediating variable is a variable through which part or all of the causal influence of one variable on another operates.
domain knowledgeDomain knowledge is knowledge about the real-world subject matter, mechanisms, and context represented by a dataset or model.
bandwidth parameterA bandwidth is a positive radius that determines the neighborhood of observations receiving nonzero or substantial weight in a local regression.
kernel functionA kernel is a weighting function that assigns observation weights according to distance from a target point.
local linear regressionLocal linear regression estimates a locally linear relationship by fitting weighted linear models around each prediction point.
local polynomial regressionLocal polynomial regression estimates a local relationship by fitting weighted polynomial models around each prediction point.
rdrobustrdrobust is a software package for regression discontinuity estimation using robust local polynomial methods.
interventionAn intervention is an externally imposed change to a variable or system intended to reveal or alter causal effects.
exogenous variableAn exogenous variable is a variable whose variation is determined outside the modeled causal system and is not explained by its included predictors.
chainA chain is a three-node directed path in which the arrows point consecutively in the same direction, as in X→Y→Z or X←Y←Z.
descendantA descendant is a variable reachable from another variable by following one or more directed causal arrows.
root-n consistencyRoot-n consistency is convergence of an estimator to its target at a rate proportional to the inverse square root of the sample size.
treatment effect heterogeneityTreatment effect heterogeneity is variation in a treatment's causal effect across units, covariate levels, or subpopulations.
Central Limit TheoremThe central limit theorem states that, under suitable independence and finite-variance conditions, a normalized sample mean approaches a normal distribution as sample size grows.
training datasetA training dataset is the subset of observations used to fit a predictive or statistical model.
regression discontinuity designRegression discontinuity design is a causal estimation method that exploits an abrupt change in treatment assignment or exposure at a time or threshold cutoff.
covariateA covariate is an observed variable included as an input or conditioning variable in a statistical or causal model.
inverse propensity weightingInverse probability weighting estimates causal effects by weighting observations by the inverse probability of receiving their observed treatment.
k-nearest neighborsK-nearest neighbors is a prediction method that uses the outcomes of the closest training observations to predict an input's outcome.
logistic regressionLogistic regression is a statistical model that estimates the probability of a categorical, often binary, outcome using a logistic function of input variables.
covarianceCovariance is a measure of the joint variation of two random variables.
forkA fork is a three-node causal structure in which one central node is a common cause of two other nodes, as in X←Z→Y.
instrument relevanceInstrument relevance is the instrumental-variable assumption that an instrument has a nonzero effect on or association with the treatment variable.
do operatorThe do operator denotes an intervention that sets a variable to a specified value in a causal graph while replacing its usual assignment mechanism.
coefficient of determinationR squared is the coefficient of determination measuring the proportion of outcome variation explained by a model.
predictive errorPredictive error is the discrepancy between a model’s predicted outcome and the corresponding observed outcome.
fitting errorFitting error is a measure of the discrepancy between a model's predicted outcomes and the observed outcomes used to fit it.
ground-truth modelA ground-truth model is a data-generating model whose relationships and parameter values are treated as known for evaluating an analysis.
intervened graphAn intervened graph is a causal graph modified to represent an intervention by removing arrows into the intervened variable and fixing its value.
subpopulationA subpopulation is a subset of a broader population defined by shared characteristics or assignment conditions.
convergence rateA convergence rate describes how quickly an estimator or sequence approaches its limiting or expected value as sample size increases.
data efficiencyData efficiency is the ability of an estimation method to achieve a specified reliability or accuracy with relatively few observations.
spurious correlationA spurious correlation is a statistical association between variables that does not reflect a causal relationship between them.
confidence intervalA confidence interval is an interval estimate that expresses uncertainty about an unknown population parameter under a specified confidence procedure.
area under the curveThe area under the ROC curve is a threshold-independent measure of binary classification performance based on the receiver operating characteristic curve.
endogenous variableA variable within a causal model whose value is determined by relationships represented in the model and by associated exogenous variables.
parent variableA variable that directly determines or influences another variable in a causal graph or structural equation.
hyperparameter tuningHyperparameter tuning is the process of selecting model-training settings by evaluating candidate settings and choosing the best-performing configuration.
seasonality effectSeasonality is a recurring time-related pattern that causes measurements such as website traffic to vary across periods.
post-treatment periodThe post-treatment period is the time interval after an event or treatment during which the observed outcome is compared with its counterfactual.
pretreatment periodA pretreatment period is the time interval before an event or treatment during which baseline data are observed and training data may be collected.
dataset splitA train-test split partitions observations into a training subset for fitting a model and a test subset for evaluating its predictions.
s-learnerAn S-learner is a causal estimation algorithm that fits one outcome model containing the treatment and confounders and predicts outcomes under alternative treatment values.
socioeconomic contextSocioeconomic context is an aggregate latent context comprising economic and competitive factors that influence pricing and sales.
conditional distributionA conditional distribution is the probability distribution of a variable after conditioning on specified information.
factual outcomeA factual outcome is the outcome actually observed for a unit under the treatment or condition it received.
residual errorA residual is the difference between an observed value and its value predicted by a fitted model.
average treatment effect on the controlThe average treatment effect on the control is the average causal effect among units that received the control condition.
distributional overlapDistributional overlap is the sharing of values or ranges by the distributions of two groups.
supportThe support of a probability distribution is the range of values that can occur with positive probability.
causal graphical modelA causal graphical model represents causal relationships among variables with a graph together with a probabilistic or structural model.
time seriesTime series data are observations indexed in temporal order, often collected at multiple time points.
random variableA random variable is a variable whose value is determined by the outcome of a random experiment.
DoubleMLPLRDoubleMLPLR is a DoubleML class that estimates causal effects with the partially linear regression method.
nuisance functionA nuisance function is a secondary function needed to estimate a target causal parameter but not itself the primary parameter of interest.
orthogonalizationOrthogonalization is a causal estimation technique that reduces the influence of nuisance-model estimation errors on a target parameter estimate.
score functionA score function is a function of data and parameters whose equation or expectation characterizes an estimator or causal parameter.
empirical distribution functionAn empirical distribution is a probability distribution formed from a finite sample by assigning equal probability weight to each observation.
randomizationRandomization is the random assignment of participants or units to experimental groups or treatment conditions.
covariate adjustmentCovariate adjustment is the process of accounting for differences in measured covariates when estimating a treatment effect.
independenceIndependence is a probabilistic property in which knowledge of one random variable does not change the probability distribution of another.
data-generating processA data-generation process is the physical mechanism or process responsible for creating observed data and its underlying probability distribution.
biasBias is systematic distortion of an estimated effect caused by differences in assignment or other factors associated with the outcome.
doubly robust estimationA doubly robust estimator is a causal parameter estimator that combines two estimators and can remain consistent when at least one underlying model is correctly specified.
ignorabilityThe ignorability assumption, also called exchangeability, is the condition that potential outcomes are independent of treatment assignment conditional on specified covariates.
consistency equationA consistency equation states that a unit's observed outcome equals the potential outcome corresponding to the treatment the unit actually received.
CausalImpactThe CausalImpact function is an R function that estimates an intervention's effect from pre-event and post-event time-series data.
evaluation periodAn evaluation period is the selected post-event interval over which an intervention's effect is assessed.
mean differenceA difference in means is a sample statistic obtained by subtracting the mean outcome for one group from the mean outcome for another group.
path blockingPath blocking is the technique of conditioning on variables so that a graph path cannot transmit statistical association between its endpoints.
causal assumptionA causal assumption is a condition about variables, relationships, or the data-generating process that is taken to hold when drawing causal conclusions.
direct formulaA direct formula is an explicit mathematical procedure for calculating a causal effect from observed group-time averages.
stable unit treatment value assumptionThe stable unit treatment value assumption (SUTVA) requires treatment versions to be well defined and one unit’s treatment not to affect another unit’s outcome.
conditional interventionA conditional intervention is an intervention whose effect is evaluated within a population selected by specified values of one or more variables.
intervention distributionA probability distribution over variables generated under an intervention that fixes a treatment value rather than under natural treatment assignment.
multicollinearityMulticollinearity is a regression condition in which predictors are highly correlated, making their individual effects difficult to distinguish and estimate precisely.
machine learningMachine learning is a field of methods that enables computers to learn patterns or predictive relationships from data.
augmented inverse probability weightingAugmented inverse probability weighting is a doubly robust causal estimation method that combines an outcome model with inverse-probability treatment weighting.
random group assignmentRandom treatment assignment allocates treatment independently of participants' or units' characteristics by chance.
path analysisPath analysis is a statistical technique that decomposes relationships among variables into contributions from specified causal paths.
well-defined intervention assumptionA well-defined intervention specifies a unique treatment version whose effect has a single unambiguous interpretation.
structural equationA structural equation specifies a variable as a function of its direct causes and unknown factors in a causal system.
weak instrumentA weak instrument is an instrumental variable that has a small effect on the treatment variable, causing the instrumental-variable estimator to have high variance and potential numerical instability.
study designThe plan specifying how an experiment assigns conditions, measures outcomes, and controls sources of bias.
hypothesisA testable proposition about a causal relationship between an intervention and an outcome.
statistical confidenceA quantified degree of statistical assurance that an estimated result reflects a non-random effect under specified assumptions.
interventional quantityAn interventional quantity is a probability or statistical quantity evaluated under a specified intervention rather than under natural assignment.
physical modelA physical model is a representation of real-world mechanisms and entities that reproduces system behavior under specified conditions.
recommender systemA recommender system is a software system that suggests items or actions to users based on available information about them and the items.
recommendationA recommendation is a suggested item, content choice, or action produced for a user or decision-maker.
Frisch–Waugh–Lovell theoremThe Frisch–Waugh–Lovell theorem states that the coefficient of a variable in a multiple linear regression equals the coefficient obtained by regressing residualized outcomes on residualized predictors.
FWL strategyThe FWL strategy estimates a regression coefficient by removing confounder-predicted components from both the treatment and outcome and regressing the resulting residuals on each other.
discountA discount is a reduction from the standard price offered to a customer.

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