Causal Inference · 134

Glossary

The technical terms of this track, with short definitions (and the Persian term where available). Each term links to the lesson where it is introduced.

abduction, action, prediction: Pearl's three steps for a counterfactual in an SCM: update the noise terms with the evidence, change the model by the intervention, and compute the outcome in the modified model. Introduced in: Lesson 9
additive noise model: A model $Y := f(X) + U$ with $U \perp\!\!\!\perp X$ . For nonlinear $f$ (or non-Gaussian $U$ ) the reverse model usually does not fit, so the direction can be learned. Introduced in: Lesson 10
adjustment formula (standardization): The weighted average of the subgroup outcomes with the weights of the whole population, $\sum_z \mathbb{E}[Y \mid T = t, Z = z]\, P(Z = z)$ . It gives the causal effect when $Z$ contains all confounders. Introduced in: Lesson 1
algorithmic recourse: A set of actions that a person can take to change a model's decision, chosen with a causal model so that the downstream effects of the actions are taken into account. Introduced in: Lesson 9
association: Two variables are associated (dependent) when knowing one changes the distribution of the other. Correlation measures only the linear part of an association. Introduced in: Lesson 1
average treatment effect (ATE): The mean effect in the population, $\tau_{\mathrm{ATE}} = \mathbb{E}[Y(1) - Y(0)]$ . Introduced in: Lesson 2
average treatment effect on the treated (ATT): The mean effect among the units that received the treatment, $\tau_{\mathrm{ATT}} = \mathbb{E}[Y(1) - Y(0) \mid T = 1]$ . Introduced in: Lesson 2
backdoor criterion: A set $Z$ satisfies it relative to $(T, Y)$ if no node in $Z$ is a descendant of $T$ and $Z$ blocks every backdoor path. Then $P(y \mid \mathrm{do}(t)) = \sum_z P(y \mid t, z) P(z)$ . Introduced in: Lesson 4
backdoor path: A path from $T$ to $Y$ that starts with an arrow into $T$ , $T \leftarrow \dots Y$ . Open backdoor paths carry non-causal association. Introduced in: Lesson 3
bandwidth: The width $h$ of the window around the cutoff that the local regression uses. A small $h$ gives less bias and more variance. Introduced in: Lesson 7
blocked path: A path is blocked by $Z$ if it has a chain or fork node in $Z$ , or a collider that is not in $Z$ and has no descendant in $Z$ . Introduced in: Lesson 3
causal and anticausal learning: Causal learning predicts an effect from its causes ( $X \to Y$ ); anticausal learning predicts a cause from its effects ( $Y \to X$ ). The direction decides which shifts are likely and whether unlabeled data can help. Introduced in: Lesson 11
causal discovery: Learning the causal graph from data, usually under assumptions such as the causal Markov property, faithfulness and no hidden confounders. Introduced in: Lesson 10
causal effect: The change in an outcome $Y$ that is produced by changing a treatment $T$ while everything else that is not caused by $T$ stays as it is. Introduced in: Lesson 1
causal forest: A random forest of honest causal trees whose leaves estimate treatment effects; it estimates $\tau(x)$ as a weighted local effect (generalized random forests). Introduced in: Lesson 8
causal graph: A directed graph whose nodes are variables and whose arrows mean "is a direct cause of". It draws the causal assumptions of a study. Introduced in: Lesson 1
chain, fork, collider: The three shapes of three nodes on a path: chain $A \to B \to C$ , fork $A \leftarrow B \to C$ , collider $A \to B \leftarrow C$ . Conditioning on $B$ blocks a chain or fork and opens a collider. Introduced in: Lesson 3
collider: A variable with two arrows pointing into it on a path, $A \to C \leftarrow B$ . Conditioning on a collider (or on its descendant) creates an association between $A$ and $B$ . Introduced in: Lesson 1
collider bias (Berkson's paradox): A spurious association between two independent causes, created by conditioning or selecting on their common effect. Introduced in: Lesson 3
compliance types: Groups defined by the potential treatments $T(1), T(0)$ : compliers (1, 0), always-takers (1, 1), never-takers (0, 0) and defiers (0, 1). Introduced in: Lesson 6
conditional average treatment effect (CATE): The mean effect for units with covariates $x$ , $\tau(x) = \mathbb{E}[Y(1) - Y(0) \mid X = x]$ . Introduced in: Lesson 8
conditional exchangeability: Treatment is independent of the potential outcomes within levels of the covariates, $(Y(0), Y(1)) \perp\!\!\!\perp T \mid X$ . Also called "no unmeasured confounding" or ignorability. Introduced in: Lesson 2
confounder: A common cause of the treatment and the outcome, $T \leftarrow X \to Y$ . It creates an association between $T$ and $Y$ that is not an effect of $T$ . Introduced in: Lesson 1
confounding bias: The difference between the associational difference $\mathbb{E}[Y \mid T = 1] - \mathbb{E}[Y \mid T = 0]$ and the causal effect, caused by common causes of $T$ and $Y$ . Introduced in: Lesson 1
consistency (causal): The assumption that the observed outcome equals the potential outcome of the received treatment: $Y_i = Y_i(T_i)$ . Introduced in: Lesson 2
controlled direct effect (CDE): The effect of $T$ on $Y$ when the mediator is set to a fixed value $m$ for everyone: $\mathbb{E}[Y(1, m) - Y(0, m)]$ . Introduced in: Lesson 9
counterfactual: A potential outcome under a treatment that the unit did not receive, for example $Y_i(0)$ for a treated unit. Introduced in: Lesson 2
counterfactual fairness: A predictor is counterfactually fair if its prediction for an individual would stay the same in the counterfactual world where the protected attribute had a different value. Introduced in: Lesson 9
covariate shift, label shift, concept shift: Covariate shift: $P(x)$ changes and $P(y \mid x)$ stays. Label shift: $P(y)$ changes and $P(x \mid y)$ stays. Concept shift: $P(y \mid x)$ changes. Introduced in: Lesson 11
CPDAG: Completed partially directed acyclic graph: the graph that represents a Markov equivalence class. Directed edges are shared by all members; undirected edges differ between them. Introduced in: Lesson 10
cross-fitting: Split the data into $K$ folds; fit the nuisance models on $K - 1$ folds and evaluate them on the held-out fold, for every fold. It removes overfitting bias from the final estimate. Introduced in: Lesson 5
cross-world assumption: An assumption that relates potential outcomes under different treatments for the same unit, such as $Y(1, m) \perp\!\!\!\perp M(0)$ . No experiment can check it; natural effects need it. Introduced in: Lesson 9
d-separation: Sets $A$ and $B$ are d-separated by $Z$ in $G$ , $A \perp_G B \mid Z$ , when every path between them is blocked by $Z$ . In an SCM, d-separation implies conditional independence. Introduced in: Lesson 3
difference-in-differences (DiD): The change over time in the treated group minus the change in the control group. It estimates the effect on the treated in the post period under parallel trends. Introduced in: Lesson 7
directed acyclic graph (DAG): A directed graph with no directed cycles: you can never follow the arrows back to the start node. Introduced in: Lesson 3
distribution shift: The test distribution differs from the training distribution. A causal view asks which mechanism of the data-generating process changed. Introduced in: Lesson 11
do-calculus: Pearl's three rules that insert or delete observations and actions in $P(y \mid \mathrm{do}(t), z)$ when d-separation holds in a modified graph. They are complete for identification. Introduced in: Lesson 4
do-operator: $\mathrm{do}(T = t)$ means: set $T$ to $t$ by an outside intervention. It replaces the assignment of $T$ in the SCM and removes the arrows into $T$ . Introduced in: Lesson 4
double machine learning (DML): Estimate the effect from residuals: regress $Y - \hat\ell(X)$ on $T - \hat m(X)$ , with the nuisances fitted by ML and cross-fitting. Neyman orthogonality makes the result insensitive to small nuisance errors. Introduced in: Lesson 8
doubly robust estimator (AIPW): An estimator that combines outcome regressions and the propensity score. It is consistent if either model is correct, and its error is of the order of the product of the two errors. Introduced in: Lesson 5
DR-learner: A meta-learner that regresses the doubly robust (AIPW) pseudo-outcome on $X$ to estimate $\tau(x)$ . Introduced in: Lesson 8
E-value: The minimum risk ratio that an unmeasured confounder must have with both treatment and outcome to explain away an observed risk ratio $RR > 1$ : $RR + \sqrt{RR(RR - 1)}$ . Introduced in: Lesson 5
effective sample size (ESS): For weights $w_i$ , $\mathrm{ESS} = (\sum_i w_i)^2 / \sum_i w_i^2$ : the number of equally weighted units that give the same precision. Large weights make it small. Introduced in: Lesson 5
estimand, estimator, estimate: The estimand is the quantity we want (for example the ATE), the estimator is the recipe that turns data into a number, and the estimate is the number it gives. Introduced in: Lesson 2
event study: A DiD regression with one coefficient per period relative to the treatment start. Pre-treatment coefficients near zero support (but do not prove) parallel trends. Introduced in: Lesson 7
exchangeability: Treatment is independent of the potential outcomes, $(Y(0), Y(1)) \perp\!\!\!\perp T$ . A randomized experiment guarantees it. Introduced in: Lesson 2
exclusion restriction: The IV assumption that the instrument has no path to the outcome except through the treatment. Data cannot check it. Introduced in: Lesson 6
faithfulness: The assumption that every conditional independence in the distribution comes from d-separation in the graph; no independence is created by exact cancellation of effects. Introduced in: Lesson 3
FCI algorithm: Fast causal inference: a version of the PC algorithm that allows hidden confounders and selection; its output is a partial ancestral graph (PAG). Introduced in: Lesson 10
first stage and reduced form: The first stage $\gamma$ is the effect of $Z$ on $T$ ; the reduced form $\rho$ is the effect of $Z$ on $Y$ . The IV (Wald) estimate is $\hat\tau_{\mathrm{IV}} = \hat\rho / \hat\gamma$ . Introduced in: Lesson 6
Fisher randomization test: A test of the sharp null: recompute the test statistic under every possible (or many random) treatment assignments and compare the observed value with this distribution. Introduced in: Lesson 2
Fisher's z test: A test of zero partial correlation for Gaussian data: $\sqrt{n - |S| - 3}\,\tfrac12 \ln\frac{1 + r}{1 - r}$ is approximately standard normal under independence. Introduced in: Lesson 10
frontdoor criterion: A set $M$ that intercepts all directed paths from $T$ to $Y$ , has no open backdoor path from $T$ , and has all its backdoor paths to $Y$ blocked by $T$ . It identifies the effect even with a hidden confounder of $T$ and $Y$ . Introduced in: Lesson 4
fundamental problem of causal inference: For every unit we observe at most one potential outcome, so individual effects are never observed directly. Causal inference is a missing-data problem. Introduced in: Lesson 2
fuzzy RDD: A regression discontinuity where crossing the cutoff changes the probability of treatment but not from 0 to 1. The jump in $Y$ divided by the jump in $T$ is an IV estimate of a LATE at the cutoff. Introduced in: Lesson 7
g-formula (outcome regression): Identification by standardization, $\tau_{\mathrm{ATE}} = \mathbb{E}_X[\mu_1(X) - \mu_0(X)]$ with $\mu_t(x) = \mathbb{E}[Y \mid T = t, X = x]$ . It holds under consistency, conditional exchangeability and positivity. Introduced in: Lesson 5
greedy equivalence search (GES): A score-based discovery algorithm that adds and then removes edges between equivalence classes to improve a score such as BIC. Introduced in: Lesson 10
Group DRO: Group distributionally robust optimization: train to minimize the worst loss over predefined groups instead of the average loss. Introduced in: Lesson 11
honesty (honest trees): Using one part of the sample to choose the splits of a tree and another part to estimate the effects in its leaves. It gives valid confidence intervals. Introduced in: Lesson 8
ID algorithm: An algorithm (Tian and Pearl; Shpitser and Pearl) that decides whether $P(y \mid \mathrm{do}(t))$ is identified in a graph with hidden variables and, if it is, returns the formula. Introduced in: Lesson 4
identified: A causal quantity is identified when it can be written as a function of the observed distribution, so it is the same in all models that agree with the graph and the data. Introduced in: Lesson 4
individual treatment effect (ITE): The effect for one unit, $\tau_i = Y_i(1) - Y_i(0)$ . It cannot be observed, because each unit receives only one treatment. Introduced in: Lesson 2
instrumental variable: A variable $Z$ that affects the treatment (relevance), is independent of the hidden confounders (independence), and affects the outcome only through the treatment (exclusion restriction). Introduced in: Lesson 6
intention-to-treat (ITT) effect: The effect of being assigned (or encouraged) to the treatment, whether or not the unit took it. It is the reduced form. Introduced in: Lesson 6
interference: The outcome of one unit depends on the treatments of other units, for example in social networks or two-sided markets. It breaks SUTVA. Introduced in: Lesson 2
interventional distribution: The distribution $P(y \mid \mathrm{do}(t))$ of the outcome in the modified model where $T$ is set to $t$ . In general it differs from $P(y \mid t)$ . Introduced in: Lesson 4
invariant causal prediction (ICP): A method that searches for the sets of features for which $P(y \mid x_S)$ is the same in all training environments; the causal parents are such a set. Introduced in: Lesson 11
inverse probability weighting (IPW): Weighting each unit by $1/e(X)$ if treated and $1/(1 - e(X))$ if control, so the weighted sample is a pseudo-population in which $T$ does not depend on $X$ . Introduced in: Lesson 5
inverse propensity scoring (IPS): The off-policy estimate $\hat V_{\mathrm{IPS}} = \frac1n \sum_i \frac{\pi(a_i \mid x_i)}{\pi_0(a_i \mid x_i)} r_i$ . It is unbiased under overlap but can have high variance. Introduced in: Lesson 11
ladder of causation: Pearl's three levels of causal questions: association (seeing, $P(y \mid t)$ ), intervention (doing, $P(y \mid \mathrm{do}(t))$ ) and counterfactuals (imagining what would have happened). Introduced in: Lesson 1
LiNGAM: Linear non-Gaussian acyclic model. With non-Gaussian noise, the full DAG (not only its equivalence class) is identifiable from observational data. Introduced in: Lesson 10
local average treatment effect (LATE): The average effect among compliers. Under the IV assumptions with monotonicity, the Wald ratio identifies the LATE, not the ATE. Introduced in: Lesson 6
local Markov property: Every variable is independent of its non-descendants given its parents. For a DAG it is equivalent to the factorization $P(v) = \prod_j P(v_j \mid \mathrm{pa}_j)$ . Introduced in: Lesson 3
logging policy: The policy $\pi_0(a \mid x)$ that chose the actions in the logged data. Its probabilities are the propensities used by IPS. Introduced in: Lesson 11
Lord's paradox: Two reasonable analyses of the same before-and-after data (change scores versus regression on the baseline) give different answers, because they answer different causal questions. Introduced in: Lesson 1
M-bias: Bias created by adjusting for a pre-treatment collider $Mb$ in the graph $T \leftarrow U_1 \to Mb \leftarrow U_2 \to Y$ . It shows that "adjust for all pre-treatment variables" can be wrong. Introduced in: Lesson 4
Markov blanket: The parents, children and other parents of the children of a node. Given its Markov blanket, the node is independent of all other variables. Introduced in: Lesson 3
Markov equivalence class: The set of DAGs that imply the same conditional independences. Two DAGs are Markov equivalent if they have the same skeleton and the same v-structures. Introduced in: Lesson 10
matching: Estimating the missing potential outcome of a unit by the outcome of one or more units with similar covariates in the other treatment group. Introduced in: Lesson 5
mediator: A variable $M$ on a causal path from treatment to outcome, $T \to M \to Y$ . Adjusting for it removes part of the effect we want to measure. Introduced in: Lesson 1
Meek's rules: Orientation rules that direct more edges of a partially directed graph without creating new v-structures or cycles. Introduced in: Lesson 10
Mendelian randomization: Using genetic variants, which are assigned at random at conception, as instruments for an exposure such as cholesterol level. Introduced in: Lesson 6
meta-learner: A recipe that builds a CATE estimator from ordinary regression models: the S-, T-, X-, DR- and R-learners. Introduced in: Lesson 8
modularity: The assumption that an intervention on one variable changes only its own assignment; the mechanisms of the other variables stay the same. Introduced in: Lesson 4
monotonicity (no defiers): The IV assumption $T_i(1) \ge T_i(0)$ for every unit: the instrument never pushes anyone away from the treatment. Introduced in: Lesson 6
mutilated graph: The graph after an intervention. $G_{\overline{T}}$ removes the arrows into $T$ ; $G_{\underline{T}}$ removes the arrows out of $T$ . Introduced in: Lesson 4
natural direct effect (NDE): The effect of changing $T$ while the mediator keeps the value it would take under control: $\mathbb{E}[Y(1, M(0)) - Y(0, M(0))]$ . Introduced in: Lesson 9
natural experiment: A situation where a rule, a policy or nature assigns a treatment in a way that is close to random for some units, so we can estimate an effect without running an experiment. Introduced in: Lesson 7
natural indirect effect (NIE): The effect of changing the mediator from $M(0)$ to $M(1)$ while $T$ is fixed at 1: $\mathbb{E}[Y(1, M(1)) - Y(1, M(0))]$ . Introduced in: Lesson 9
Neyman orthogonality: A property of an estimating equation: its derivative with respect to the nuisance functions is zero at the truth, so first-order nuisance errors do not bias the estimate. Introduced in: Lesson 8
NOTEARS: Continuous-optimization structure learning with the acyclicity constraint $\operatorname{tr}(e^{W \circ W}) - d = 0$ on the weighted adjacency matrix $W$ . Introduced in: Lesson 10
nuisance functions: Functions we must estimate on the way but do not care about in themselves, such as $e(x)$ , $\mu_t(x)$ and $\ell(x) = \mathbb{E}[Y \mid X = x]$ . Introduced in: Lesson 8
off-policy evaluation (OPE): Estimating the value $V(\pi)$ of a new target policy $\pi$ from data logged under another policy $\pi_0$ , without deploying $\pi$ . Introduced in: Lesson 11
outcome: The variable $Y$ on which we measure the effect of the treatment, for example recovery, a test score or a click. Introduced in: Lesson 1
parallel trends: The DiD assumption that, without treatment, the mean outcome of the treated group would have changed by the same amount as the mean of the control group. Introduced in: Lesson 7
partially linear model: The model $Y = \tau T + g(X) + \varepsilon$ with an unknown function $g$ , the basic setting of double ML. Introduced in: Lesson 8
PC algorithm: A constraint-based discovery algorithm: remove edges by conditional independence tests with growing conditioning sets, orient v-structures from the separating sets, then apply Meek's rules. Introduced in: Lesson 10
positivity (overlap): Every unit has a chance of each treatment: $0 < P(T = 1 \mid X = x) < 1$ for all $x$ in the population. Introduced in: Lesson 2
potential outcomes: The outcomes $Y_i(1)$ and $Y_i(0)$ that unit $i$ would have under treatment and under control. Only one of them is ever observed. Introduced in: Lesson 2
principle of independent mechanisms: The causal mechanism $P(\text{effect} \mid \text{cause})$ does not inform or change with the distribution of the cause $P(\text{cause})$ . Introduced in: Lesson 11
probability of necessity (PN): The probability that the outcome would not have happened without the treatment, given that both happened: $P(Y(0) = 0 \mid T = 1, Y = 1)$ . Introduced in: Lesson 9
probability of sufficiency (PS): The probability that the treatment would have produced the outcome, given that neither happened: $P(Y(1) = 1 \mid T = 0, Y = 0)$ . Introduced in: Lesson 9
propensity score: The probability of treatment given the covariates, $e(x) = P(T = 1 \mid X = x)$ . Units with the same $e(x)$ have the same distribution of $X$ in both groups (balancing property). Introduced in: Lesson 5
pseudo-population: The weighted sample created by inverse probability weights. In it, the covariates have the same distribution in the treated and control groups. Introduced in: Lesson 5
R-learner (R-loss): Estimates $\tau(x)$ by minimizing $\sum_i \big[(Y_i - \hat\ell(X_i)) - \tau(X_i)(T_i - \hat e(X_i))\big]^2$ plus a penalty (Robinson's transformation). Introduced in: Lesson 8
randomized controlled trial (RCT): An experiment in which a random mechanism, not the units or the researcher, assigns the treatment. A/B tests are randomized experiments in online products. Introduced in: Lesson 2
regression discontinuity design (RDD): Treatment is assigned when a running variable $R$ crosses a cutoff $c$ . The jump of $\mathbb{E}[Y \mid R = r]$ at $c$ estimates the effect for units at the cutoff. Introduced in: Lesson 7
response types: For binary $T$ and $Y$ , the four ways a unit can respond: always 1, never 1, helped ( $Y(1) = 1, Y(0) = 0$ ) and hurt ( $Y(1) = 0, Y(0) = 1$ ). Introduced in: Lesson 9
running variable: The score $R$ that decides treatment in a regression discontinuity design, for example a test score or an age. Introduced in: Lesson 7
S-learner and T-learner: The S-learner fits one model of $Y$ on $(X, T)$ and takes the difference of its predictions at $T = 1$ and $T = 0$ ; the T-learner fits separate models $\hat\mu_1$ and $\hat\mu_0$ and takes $\hat\mu_1(x) - \hat\mu_0(x)$ . Introduced in: Lesson 8
sample-ratio mismatch (SRM): The observed share of units in each arm differs from the planned share more than chance allows. It signals a bug in assignment or logging. Introduced in: Lesson 2
selection bias: In the decomposition of the naive difference, the term $\mathbb{E}[Y(0) \mid T = 1] - \mathbb{E}[Y(0) \mid T = 0]$ : the treated and control groups differ even without treatment. Introduced in: Lesson 2
selective labels: The outcome is observed only for some decisions, for example repayment only for approved loans. A model trained on such data learns from a selected sample. Introduced in: Lesson 11
sensitivity analysis: Asking how strong an unmeasured confounder must be to change the conclusion, for example with the E-value, the robustness value or Rosenbaum's $\Gamma$ . Introduced in: Lesson 5
sharp null hypothesis: Fisher's null that the treatment has no effect on any unit, $Y_i(1) = Y_i(0)$ for all $i$ . It is stronger than "the ATE is zero". Introduced in: Lesson 2
Simpson's paradox: An association that has one direction in every subgroup and the opposite direction in the pooled data. It needs different case mixes in the groups; the causal story decides which table answers the question. Introduced in: Lesson 1
skeleton: The undirected graph you get by removing the arrow heads of a DAG. Introduced in: Lesson 10
spurious feature (shortcut): A feature that predicts the label in the training data only through a non-causal path, for example the background in Waterbirds. Models that rely on it fail when the correlation changes. Introduced in: Lesson 11
standardized mean difference (SMD): The difference of a covariate's means between treated and control, divided by a pooled standard deviation. A common rule asks for $|\mathrm{SMD}| < 0.1$ after matching or weighting. Introduced in: Lesson 5
structural causal model (SCM): A set of assignments $V_j := f_j(\mathrm{pa}_j, U_j)$ , one per variable, with independent noise terms $U_j$ . Its graph $G$ has an arrow from each parent to its child. Introduced in: Lesson 3
SUTVA: Stable unit treatment value assumption: the treatment is well defined (one version) and there is no interference, so a unit's outcome does not depend on the treatments of other units. Introduced in: Lesson 2
synthetic control: An estimate of a treated unit's untreated path by a weighted average of donor units, with weights $w \ge 0$ , $\sum w = 1$ , chosen to match the pre-treatment path. Introduced in: Lesson 7
total effect: The full effect of $T$ on $Y$ through all paths, $\mathbb{E}[Y(1) - Y(0)]$ . With a mediator it is the sum of the natural direct and natural indirect effects. Introduced in: Lesson 9
treatment: The variable $T$ whose effect we want to know, for example a drug, a tutoring program or a new ranking model. In this track it is binary, $T \in \{0, 1\}$ , unless a lesson says otherwise. Introduced in: Lesson 1
trimming and overlap weights: Remedies for extreme propensity scores. Trimming drops units with $e(x)$ near 0 or 1; overlap weights $T(1 - e) + (1 - T)e$ target the population where both treatments are common. Both change the estimand. Introduced in: Lesson 5
truncated factorization: The distribution after $\mathrm{do}(T = t)$ : the product of $P(v_j \mid \mathrm{pa}_j)$ over all variables except $T$ , evaluated at $T = t$ . Introduced in: Lesson 4
two-stage least squares (2SLS): Regress the treatment on the instruments, then regress the outcome on the predicted treatment. With one instrument and one treatment it equals the Wald ratio. Introduced in: Lesson 6
two-way fixed effects (TWFE): A regression of $Y$ on unit effects, time effects and a treatment indicator. With staggered adoption and changing effects it can put negative weights on some group-time effects. Introduced in: Lesson 7
uplift curve and Qini curve: Curves that rank units by predicted effect and show the gain from treating the top fraction. They evaluate a CATE model on randomized held-out data. Introduced in: Lesson 8
v-structure (immorality): A collider $A \to C \leftarrow B$ where $A$ and $B$ are not adjacent. Independence tests can find its arrow directions. Introduced in: Lesson 10
varsortability: In many simulated data sets, variance grows along the causal order. Methods can then find the order from the scales alone; standardizing the data removes this shortcut. Introduced in: Lesson 10
Wald estimator: For a binary instrument: the difference in mean outcome between $Z = 1$ and $Z = 0$ , divided by the difference in treatment rate. Introduced in: Lesson 6
weak instrument: An instrument that moves the treatment only a little. Then 2SLS is biased toward OLS and its confidence intervals are wrong; a first-stage $F$ below about 10 is a warning. Introduced in: Lesson 6
worst-group accuracy: The lowest accuracy over predefined groups (for example label × spurious attribute). It measures robustness to shortcut learning better than average accuracy. Introduced in: Lesson 11