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@@ -103,7 +103,7 @@ difficulty making predictions near 0 and 1 because variance in the
 underlying base models will bias predictions that should be near zero or one
 away from these values. Because predictions are restricted to the interval
 [0,1], errors caused by variance tend to be one-sided near zero and one. For
-example, if a model should predict p = 0 for a case, the only way bagging
+example, if a model should predict :math:`p = 0` for a case, the only way bagging
 can achieve this is if all bagged trees predict zero. If we add noise to the
 trees that bagging is averaging over, this noise will cause some trees to
 predict values larger than 0 for this case, thus moving the average
@@ -146,7 +146,7 @@ Usage
 The :class:`CalibratedClassifierCV` class is used to calibrate a classifier.
 
 :class:`CalibratedClassifierCV` uses a cross-validation approach to ensure
-unbiased data is always used to fit the calibrator. The data is split into k
+unbiased data is always used to fit the calibrator. The data is split into :math:`k`
 `(train_set, test_set)` couples (as determined by `cv`). When `ensemble=True`
 (default), the following procedure is repeated independently for each
 cross-validation split:
@@ -157,13 +157,13 @@ cross-validation split:
    regressor) (when the data is multiclass, a calibrator is fit for every class)
 
 This results in an
-ensemble of k `(classifier, calibrator)` couples where each calibrator maps
+ensemble of :math:`k` `(classifier, calibrator)` couples where each calibrator maps
 the output of its corresponding classifier into [0, 1]. Each couple is exposed
 in the `calibrated_classifiers_` attribute, where each entry is a calibrated
 classifier with a :term:`predict_proba` method that outputs calibrated
 probabilities. The output of :term:`predict_proba` for the main
 :class:`CalibratedClassifierCV` instance corresponds to the average of the
-predicted probabilities of the `k` estimators in the `calibrated_classifiers_`
+predicted probabilities of the :math:`k` estimators in the `calibrated_classifiers_`
 list. The output of :term:`predict` is the class that has the highest
 probability.
 
@@ -244,12 +244,12 @@ subject to :math:`\hat{f}_i \geq \hat{f}_j` whenever
 :math:`f_i \geq f_j`. :math:`y_i` is the true
 label of sample :math:`i` and :math:`\hat{f}_i` is the output of the
 calibrated classifier for sample :math:`i` (i.e., the calibrated probability).
-This method is more general when compared to 'sigmoid' as the only restriction
+This method is more general when compared to `'sigmoid'` as the only restriction
 is that the mapping function is monotonically increasing. It is thus more
 powerful as it can correct any monotonic distortion of the un-calibrated model.
 However, it is more prone to overfitting, especially on small datasets [6]_.
 
-Overall, 'isotonic' will perform as well as or better than 'sigmoid' when
+Overall, `'isotonic'` will perform as well as or better than `'sigmoid'` when
 there is enough data (greater than ~ 1000 samples) to avoid overfitting [3]_.
 
 .. note:: Impact on ranking metrics like AUC
 
@@ -372,8 +372,7 @@ Thus, one can create the training/test sets using numpy indexing::
 Repeated K-Fold
 ^^^^^^^^^^^^^^^
 
-:class:`RepeatedKFold` repeats K-Fold n times. It can be used when one
-requires to run :class:`KFold` n times, producing different splits in
+:class:`RepeatedKFold` repeats :class:`KFold` :math:`n` times, producing different splits in
 each repetition.
 
 Example of 2-fold K-Fold repeated 2 times::
@@ -392,7 +391,7 @@ Example of 2-fold K-Fold repeated 2 times::
   [1 3] [0 2]
 
 
-Similarly, :class:`RepeatedStratifiedKFold` repeats Stratified K-Fold n times
+Similarly, :class:`RepeatedStratifiedKFold` repeats :class:`StratifiedKFold` :math:`n` times
 with different randomization in each repetition.
 
 .. _leave_one_out:
@@ -434,10 +433,10 @@ folds are virtually identical to each other and to the model built from the
 entire training set.
 
 However, if the learning curve is steep for the training size in question,
-then 5- or 10- fold cross validation can overestimate the generalization error.
+then 5 or 10-fold cross validation can overestimate the generalization error.
 
-As a general rule, most authors, and empirical evidence, suggest that 5- or 10-
-fold cross validation should be preferred to LOO.
+As a general rule, most authors and empirical evidence suggest that 5 or 10-fold
+cross validation should be preferred to LOO.
 
 .. dropdown:: References
 
@@ -553,10 +552,10 @@ relative class frequencies are approximately preserved in each fold.
 
 .. _stratified_k_fold:
 
-Stratified k-fold
+Stratified K-fold
 ^^^^^^^^^^^^^^^^^
 
-:class:`StratifiedKFold` is a variation of *k-fold* which returns *stratified*
+:class:`StratifiedKFold` is a variation of *K-fold* which returns *stratified*
 folds: each set contains approximately the same percentage of samples of each
 target class as the complete set.
 
@@ -648,10 +647,10 @@ parameter.
 
 .. _group_k_fold:
 
-Group k-fold
+Group K-fold
 ^^^^^^^^^^^^
 
-:class:`GroupKFold` is a variation of k-fold which ensures that the same group is
+:class:`GroupKFold` is a variation of K-fold which ensures that the same group is
 not represented in both testing and training sets. For example if the data is
 obtained from different subjects with several samples per-subject and if the
 model is flexible enough to learn from highly person specific features it
 
@@ -7,7 +7,7 @@ Kernel ridge regression
 .. currentmodule:: sklearn.kernel_ridge
 
 Kernel ridge regression (KRR) [M2012]_ combines :ref:`ridge_regression`
-(linear least squares with l2-norm regularization) with the `kernel trick
+(linear least squares with :math:`L_2`-norm regularization) with the `kernel trick
 <https://en.wikipedia.org/wiki/Kernel_method>`_. It thus learns a linear
 function in the space induced by the respective kernel and the data. For
 non-linear kernels, this corresponds to a non-linear function in the original
@@ -16,7 +16,7 @@ space.
 The form of the model learned by :class:`KernelRidge` is identical to support
 vector regression (:class:`~sklearn.svm.SVR`). However, different loss
 functions are used: KRR uses squared error loss while support vector
-regression uses :math:`\epsilon`-insensitive loss, both combined with l2
+regression uses :math:`\epsilon`-insensitive loss, both combined with :math:`L_2`
 regularization. In contrast to :class:`~sklearn.svm.SVR`, fitting
 :class:`KernelRidge` can be done in closed-form and is typically faster for
 medium-sized datasets. On the other hand, the learned model is non-sparse and
@@ -31,7 +31,7 @@ plotted, where both complexity/regularization and bandwidth of the RBF kernel
 have been optimized using grid-search. The learned functions are very
 similar; however, fitting :class:`KernelRidge` is approximately seven times
 faster than fitting :class:`~sklearn.svm.SVR` (both with grid-search).
-However, prediction of 100000 target values is more than three times faster
+However, prediction of 100,000 target values is more than three times faster
 with :class:`~sklearn.svm.SVR` since it has learned a sparse model using only
 approximately 1/3 of the 100 training datapoints as support vectors.
 
 
@@ -173,11 +173,11 @@ In this scenario, the empirical sample covariance is a poor
 estimator, and shrinkage helps improving the generalization performance of
 the classifier.
 Shrinkage LDA can be used by setting the ``shrinkage`` parameter of
-the :class:`~discriminant_analysis.LinearDiscriminantAnalysis` class to 'auto'.
+the :class:`~discriminant_analysis.LinearDiscriminantAnalysis` class to `'auto'`.
 This automatically determines the optimal shrinkage parameter in an analytic
 way following the lemma introduced by Ledoit and Wolf [2]_. Note that
-currently shrinkage only works when setting the ``solver`` parameter to 'lsqr'
-or 'eigen'.
+currently shrinkage only works when setting the ``solver`` parameter to `'lsqr'`
+or `'eigen'`.
 
 The ``shrinkage`` parameter can also be manually set between 0 and 1. In
 particular, a value of 0 corresponds to no shrinkage (which means the empirical
@@ -192,7 +192,7 @@ best choice. For example if the distribution of the data
 is normally distributed, the
 Oracle Approximating Shrinkage estimator :class:`sklearn.covariance.OAS`
 yields a smaller Mean Squared Error than the one given by Ledoit and Wolf's
-formula used with shrinkage="auto". In LDA, the data are assumed to be gaussian
+formula used with `shrinkage="auto"`. In LDA, the data are assumed to be gaussian
 conditionally to the class. If these assumptions hold, using LDA with
 the OAS estimator of covariance will yield a better classification
 accuracy than if Ledoit and Wolf or the empirical covariance estimator is used.
@@ -239,17 +239,17 @@ computing :math:`S` and :math:`V` via the SVD of :math:`X` is enough. For
 LDA, two SVDs are computed: the SVD of the centered input matrix :math:`X`
 and the SVD of the class-wise mean vectors.
 
-The 'lsqr' solver is an efficient algorithm that only works for
+The `'lsqr'` solver is an efficient algorithm that only works for
 classification. It needs to explicitly compute the covariance matrix
 :math:`\Sigma`, and supports shrinkage and custom covariance estimators.
 This solver computes the coefficients
 :math:`\omega_k = \Sigma^{-1}\mu_k` by solving for :math:`\Sigma \omega =
 \mu_k`, thus avoiding the explicit computation of the inverse
 :math:`\Sigma^{-1}`.
 
-The 'eigen' solver is based on the optimization of the between class scatter to
+The `'eigen'` solver is based on the optimization of the between class scatter to
 within class scatter ratio. It can be used for both classification and
-transform, and it supports shrinkage. However, the 'eigen' solver needs to
+transform, and it supports shrinkage. However, the `'eigen'` solver needs to
 compute the covariance matrix, so it might not be suitable for situations with
 a high number of features.
 
 
@@ -211,11 +211,11 @@ Computation methods
 ===================
 
 There are two main methods to approximate the integral above, namely the
-'brute' and 'recursion' methods. The `method` parameter controls which method
+`'brute'` and `'recursion'` methods. The `method` parameter controls which method
 to use.
 
-The 'brute' method is a generic method that works with any estimator. Note that
-computing ICE plots is only supported with the 'brute' method. It
+The `'brute'` method is a generic method that works with any estimator. Note that
+computing ICE plots is only supported with the `'brute'` method. It
 approximates the above integral by computing an average over the data `X`:
 
 .. math::
@@ -231,7 +231,7 @@ at :math:`x_{S}`. Computing this for multiple values of :math:`x_{S}`, one
 obtains a full ICE line. As one can see, the average of the ICE lines
 corresponds to the partial dependence line.
 
-The 'recursion' method is faster than the 'brute' method, but it is only
+The `'recursion'` method is faster than the `'brute'` method, but it is only
 supported for PDP plots by some tree-based estimators. It is computed as
 follows. For a given point :math:`x_S`, a weighted tree traversal is performed:
 if a split node involves an input feature of interest, the corresponding left
@@ -240,23 +240,23 @@ being weighted by the fraction of training samples that entered that branch.
 Finally, the partial dependence is given by a weighted average of all the
 visited leaves' values.
 
-With the 'brute' method, the parameter `X` is used both for generating the
+With the `'brute'` method, the parameter `X` is used both for generating the
 grid of values :math:`x_S` and the complement feature values :math:`x_C`.
 However with the 'recursion' method, `X` is only used for the grid values:
 implicitly, the :math:`x_C` values are those of the training data.
 
-By default, the 'recursion' method is used for plotting PDPs on tree-based
+By default, the `'recursion'` method is used for plotting PDPs on tree-based
 estimators that support it, and 'brute' is used for the rest.
 
 .. _pdp_method_differences:
 
 .. note::
 
     While both methods should be close in general, they might differ in some
-    specific settings. The 'brute' method assumes the existence of the
+    specific settings. The `'brute'` method assumes the existence of the
     data points :math:`(x_S, x_C^{(i)})`. When the features are correlated,
-    such artificial samples may have a very low probability mass. The 'brute'
-    and 'recursion' methods will likely disagree regarding the value of the
+    such artificial samples may have a very low probability mass. The `'brute'`
+    and `'recursion'` methods will likely disagree regarding the value of the
     partial dependence, because they will treat these unlikely
     samples differently. Remember, however, that the primary assumption for
     interpreting PDPs is that the features should be independent.