From e105f75fadeaf7ef4b3e69f8a6a3194c22a06942 Mon Sep 17 00:00:00 2001
From: Kevin Klein <7267523+kklein@users.noreply.github.com>
Date: Wed, 3 Apr 2024 10:18:09 +0200
Subject: [PATCH] Create first version of glossary (#16)
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Co-authored-by: Francesc Martí Escofet <154450563+FrancescMartiEscofetQC@users.noreply.github.com>
---
 docs/glossary.rst | 112 +++++++++++++++++++++++++++-------------------
 1 file changed, 66 insertions(+), 46 deletions(-)

diff --git a/docs/glossary.rst b/docs/glossary.rst
index c39e3d7..7d88afd 100644
--- a/docs/glossary.rst
+++ b/docs/glossary.rst
@@ -1,49 +1,69 @@
 Glossary
 ========
 
-.. list-table::
-   :widths: 25 50 25
-   :header-rows: 1
-
-   * - Term
-     - Definition
-     - Reference
-   * - Base model
-     - TODO
-     - TODO
-   * - Conditional Average Treatment Effect (CATE)
-     - TODO
-     - TODO
-   * - Double Machine Learning
-     - TODO
-     - TODO
-   * - Heterogeneous Treatment Effect (HTE)
-     - TODO
-     - TODO
-   * - MetaLearner
-     - TODO
-     - TODO
-   * - Nuisance model
-     - TODO
-     - TODO
-   * - Observational data
-     - TODO
-     - TODO
-   * - Outcome model
-     - TODO
-     - TODO
-   * - Potential Outcomes
-     - TODO
-     - TODO
-   * - Propensity model
-     - TODO
-     - TODO
-   * - Propensity score
-     - TODO
-     - TODO
-   * - Randomized Control Trial (RCT)
-     - TODO
-     - TODO
-   * - Treatment model
-     - TODO
-     - TODO
+.. glossary::
+
+  Base model
+    A prediction model used within a MetaLearner. See
+    `Kuenzel et al. (2019) <https://arxiv.org/pdf/1706.03461.pdf>`_.
+
+  Conditional Average Treatment Effect (CATE)
+    :math:`\tau(X) = \mathbb{E}[Y(1) - Y(0)|X]` in the binary case and
+    :math:`\tau_{i,j}(X) = \mathbb{E}[Y(i) - Y(j)|X]` if more than two
+    variants exist.
+    See `Athey et al. (2016) <https://arxiv.org/abs/1607.00698>`_,
+    Chapter 10.
+
+  Covariates
+    The features :math:`X` based on which a CATE is estimated.
+
+  Double Machine Learning
+    Similar to the R-Learner, the Double Machine Learning blueprint
+    relies on estimating two nuisance models in its first stage: a
+    propensity model as well as an outcome model. Unlike the
+    R-Learner, the last-stage or treatment effect model might not
+    be any estimator.
+    See `Chernozhukov et al. (2016) <https://arxiv.org/abs/1608.00060>`_.
+
+  Heterogeneous Treatment Effect (HTE)
+    Synonym for CATE.
+
+  MetaLearner
+    CATE model which relies on arbitrary prediction estimators
+    (regressors or classifiers) for the actual estimation.
+    See `Kuenzel et al. (2019) <https://arxiv.org/pdf/1706.03461.pdf>`_.
+
+  Nuisance model
+    A first-stage model in a MetaLearner.
+    See `Nie et al. (2019) <https://arxiv.org/pdf/1712.04912.pdf>`_.
+
+  Observational data
+    Experiment data collected outside of a RCT, i.e. treatment
+    assignments can depend on covariates or potential outcomes.
+    See `Athey et al. (2016) <https://arxiv.org/abs/1607.00698>`_.
+
+  Outcome model
+    A model estimating the outcome based on covariates,
+    i.e. :math:`\mathbb{E}[Y|X]`.
+
+  Potential outcomes
+    Outcomes under various variants, e.g. :math:`Y(0)` and
+    :math:`Y(1)`, in Rubin-Causal Model (RCM).
+    See `Holland et al. (1986) <https://www.cs.columbia.edu/~blei/fogm/2023F/readings/Holland1986.pdf>`_.
+
+  Propensity model
+    A model estimating the propensity score.
+
+  Propensity score
+    The probability of receiving a certain treatment/variant, conditioning
+    on covariates: :math:`\Pr[W_i = w | X]`.
+    See `Rosenbaum et al. (1983) <https://academic.oup.com/biomet/article/70/1/41/240879?login=false>`_.
+
+  Randomized Control Trial (RCT)
+    An experiment in which the treatment assignment is independent
+    of the covariates :math:`X`.
+    See `Athey et al. (2016) <https://arxiv.org/abs/1607.00698>`_.
+
+  Treatment effect model
+    A second-stage model in a MetaLearner which models the
+    treatment effects as a function of covariates.