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change tabbing in rst files to sphinx-design
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‎doc/guide/algorithms.rst

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@@ -10,30 +10,30 @@ Algorithm DML1
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The algorithm ``dml_procedure='dml1'`` can be summarized as
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1. **Inputs:** Choose a model (PLR, PLIV, IRM, IIVM), provide data :math:`(W_i)_{i=1}^{N}`, a Neyman-orthogonal score function :math:`\psi(W; \theta, \eta)` and specify machine learning method(s) for the nuisance function(s) :math:`\eta`.
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2. **Train ML predictors on folds:** Take a :math:`K`-fold random partition :math:`(I_k)_{k=1}^{K}` of observation indices :math:`[N] = \lbrace 1, \ldots, N\rbrace` such that the size of each fold :math:`I_k` is :math:`n=N/K`. For each :math:`k \in [K] = \lbrace 1, \ldots, K\rbrace`, construct a high-quality machine learning estimator
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#. **Inputs:** Choose a model (PLR, PLIV, IRM, IIVM), provide data :math:`(W_i)_{i=1}^{N}`, a Neyman-orthogonal score function :math:`\psi(W; \theta, \eta)` and specify machine learning method(s) for the nuisance function(s) :math:`\eta`.
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.. math::
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#. **Train ML predictors on folds:** Take a :math:`K`-fold random partition :math:`(I_k)_{k=1}^{K}` of observation indices :math:`[N] = \lbrace 1, \ldots, N\rbrace` such that the size of each fold :math:`I_k` is :math:`n=N/K`. For each :math:`k \in [K] = \lbrace 1, \ldots, K\rbrace`, construct a high-quality machine learning estimator
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.. math::
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\hat{\eta}_{0,k} = \hat{\eta}_{0,k}\big((W_i)_{i\not\in I_k}\big)
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\hat{\eta}_{0,k} = \hat{\eta}_{0,k}\big((W_i)_{i\not\in I_k}\big)
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of :math:`\eta_0`, where :math:`x \mapsto \hat{\eta}_{0,k}(x)` depends only on the subset of data :math:`(W_i)_{i\not\in I_k}`.
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of :math:`\eta_0`, where :math:`x \mapsto \hat{\eta}_{0,k}(x)` depends only on the subset of data :math:`(W_i)_{i\not\in I_k}`.
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3. **Estimate causal parameter:** For each :math:`k \in [K]`, construct the estimator :math:`\check{\theta}_{0,k}` as the solution to the equation
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#. **Estimate causal parameter:** For each :math:`k \in [K]`, construct the estimator :math:`\check{\theta}_{0,k}` as the solution to the equation
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.. math::
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.. math::
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\frac{1}{n} \sum_{i \in I_k} \psi(W_i; \check{\theta}_{0,k}, \hat{\eta}_{0,k}) = 0.
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\frac{1}{n} \sum_{i \in I_k} \psi(W_i; \check{\theta}_{0,k}, \hat{\eta}_{0,k}) = 0.
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The estimate of the causal parameter is obtain via aggregation
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The estimate of the causal parameter is obtain via aggregation
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.. math::
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.. math::
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\tilde{\theta}_0 = \frac{1}{K} \sum_{k=1}^{K} \check{\theta}_{0,k}.
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\tilde{\theta}_0 = \frac{1}{K} \sum_{k=1}^{K} \check{\theta}_{0,k}.
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4. **Outputs:** The estimate of the causal parameter :math:`\tilde{\theta}_0` as well as the values of the evaluated score function are returned.
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#. **Outputs:** The estimate of the causal parameter :math:`\tilde{\theta}_0` as well as the values of the evaluated score function are returned.
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Algorithm DML2
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@@ -44,17 +44,17 @@ The algorithm ``dml_procedure='dml2'`` can be summarized as
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2. **Train ML predictors on folds:** Take a :math:`K`-fold random partition :math:`(I_k)_{k=1}^{K}` of observation indices :math:`[N] = \lbrace 1, \ldots, N\rbrace` such that the size of each fold :math:`I_k` is :math:`n=N/K`. For each :math:`k \in [K] = \lbrace 1, \ldots, K\rbrace`, construct a high-quality machine learning estimator
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.. math::
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.. math::
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\hat{\eta}_{0,k} = \hat{\eta}_{0,k}\big((W_i)_{i\not\in I_k}\big)
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\hat{\eta}_{0,k} = \hat{\eta}_{0,k}\big((W_i)_{i\not\in I_k}\big)
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of :math:`\eta_0`, where :math:`x \mapsto \hat{\eta}_{0,k}(x)` depends only on the subset of data :math:`(W_i)_{i\not\in I_k}`.
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of :math:`\eta_0`, where :math:`x \mapsto \hat{\eta}_{0,k}(x)` depends only on the subset of data :math:`(W_i)_{i\not\in I_k}`.
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3. **Estimate causal parameter:** Construct the estimator for the causal parameter :math:`\tilde{\theta}_0` as the solution to the equation
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.. math::
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.. math::
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\frac{1}{N} \sum_{k=1}^{K} \sum_{i \in I_k} \psi(W_i; \tilde{\theta}_0, \hat{\eta}_{0,k}) = 0.
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\frac{1}{N} \sum_{k=1}^{K} \sum_{i \in I_k} \psi(W_i; \tilde{\theta}_0, \hat{\eta}_{0,k}) = 0.
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4. **Outputs:** The estimate of the causal parameter :math:`\tilde{\theta}_0` as well as the values of the evaluate score function are returned.
@@ -73,89 +73,105 @@ As an example we consider a partially linear regression model (PLR)
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implemented in ``DoubleMLPLR``.
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The DML algorithm can be selected via parameter ``dml_procedure='dml1'`` vs. ``dml_procedure='dml2'``.
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.. tabbed:: Python
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.. tab-set::
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.. ipython:: python
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.. tab-item:: Python
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:sync: py
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import doubleml as dml
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from doubleml.datasets import make_plr_CCDDHNR2018
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from sklearn.ensemble import RandomForestRegressor
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from sklearn.base import clone
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.. ipython:: python
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np.random.seed(3141)
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learner = RandomForestRegressor(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2)
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ml_l = clone(learner)
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ml_m = clone(learner)
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data = make_plr_CCDDHNR2018(alpha=0.5, return_type='DataFrame')
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obj_dml_data = dml.DoubleMLData(data, 'y', 'd')
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dml_plr_obj = dml.DoubleMLPLR(obj_dml_data, ml_l, ml_m, dml_procedure='dml1')
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dml_plr_obj.fit();
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import doubleml as dml
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from doubleml.datasets import make_plr_CCDDHNR2018
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from sklearn.ensemble import RandomForestRegressor
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from sklearn.base import clone
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.. tabbed:: R
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np.random.seed(3141)
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learner = RandomForestRegressor(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2)
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ml_l = clone(learner)
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ml_m = clone(learner)
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data = make_plr_CCDDHNR2018(alpha=0.5, return_type='DataFrame')
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obj_dml_data = dml.DoubleMLData(data, 'y', 'd')
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dml_plr_obj = dml.DoubleMLPLR(obj_dml_data, ml_l, ml_m, dml_procedure='dml1')
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dml_plr_obj.fit();
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.. jupyter-execute::
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.. tab-item:: R
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:sync: r
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library(DoubleML)
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library(mlr3)
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library(mlr3learners)
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library(data.table)
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lgr::get_logger("mlr3")$set_threshold("warn")
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.. jupyter-execute::
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learner = lrn("regr.ranger", num.trees = 100, mtry = 20, min.node.size = 2, max.depth = 5)
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ml_l = learner$clone()
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ml_m = learner$clone()
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set.seed(3141)
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data = make_plr_CCDDHNR2018(alpha=0.5, return_type='data.table')
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obj_dml_data = DoubleMLData$new(data, y_col="y", d_cols="d")
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dml_plr_obj = DoubleMLPLR$new(obj_dml_data, ml_l, ml_m, dml_procedure="dml1")
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dml_plr_obj$fit()
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library(DoubleML)
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library(mlr3)
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library(mlr3learners)
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library(data.table)
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lgr::get_logger("mlr3")$set_threshold("warn")
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learner = lrn("regr.ranger", num.trees = 100, mtry = 20, min.node.size = 2, max.depth = 5)
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ml_l = learner$clone()
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ml_m = learner$clone()
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set.seed(3141)
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data = make_plr_CCDDHNR2018(alpha=0.5, return_type='data.table')
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obj_dml_data = DoubleMLData$new(data, y_col="y", d_cols="d")
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dml_plr_obj = DoubleMLPLR$new(obj_dml_data, ml_l, ml_m, dml_procedure="dml1")
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dml_plr_obj$fit()
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The ``fit()`` method of ``DoubleMLPLR``
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stores the estimate :math:`\tilde{\theta}_0` in its ``coef`` attribute.
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.. tabbed:: Python
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.. tab-set::
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.. tab-item:: Python
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:sync: py
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.. ipython:: python
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.. ipython:: python
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dml_plr_obj.coef
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dml_plr_obj.coef
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.. tabbed:: R
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.. tab-item:: R
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:sync: r
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.. jupyter-execute::
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.. jupyter-execute::
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dml_plr_obj$coef
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dml_plr_obj$coef
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Let :math:`k(i) = \lbrace k: i \in I_k \rbrace`.
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The values of the score function :math:`(\psi(W_i; \tilde{\theta}_0, \hat{\eta}_{0,k(i)}))_{i \in [N]}`
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are stored in the attribute ``psi``.
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.. tabbed:: Python
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.. tab-set::
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.. ipython:: python
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.. tab-item:: Python
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:sync: py
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dml_plr_obj.psi[:5]
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.. ipython:: python
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.. tabbed:: R
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dml_plr_obj.psi[:5]
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.. jupyter-execute::
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.. tab-item:: R
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dml_plr_obj$psi[1:5, ,1]
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.. jupyter-execute::
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dml_plr_obj$psi[1:5, ,1]
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For the DML1 algorithm, the estimates for the different folds
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:math:`\check{\theta}_{0,k}``, :math:`k \in [K]` are stored in attribute ``all_dml1_coef``.
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.. tabbed:: Python
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.. tab-set::
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.. tab-item:: Python
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:sync: py
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.. ipython:: python
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.. ipython:: python
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dml_plr_obj.all_dml1_coef
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dml_plr_obj.all_dml1_coef
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:sync: r
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.. jupyter-execute::
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.. jupyter-execute::
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dml_plr_obj$all_dml1_coef
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dml_plr_obj$all_dml1_coef
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‎doc/guide/basics.rst

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