Glossary
========

.. 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.

  Conditional Average Outcomes
    :math:`\mathbb{E}[Y_i(w) | X]` for each treatment variant :math:`w`.

  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 need to be a
    specific type of 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.