Fixed typos and formatting problems.

Author: victorprincipe

examples/FeatureSelection.py

@@ -19,7 +19,7 @@
 
 # %%
 #
-# For this, we will use the provided csd dataset, which has 100 features to select from.
+# For this, we will use the provided CSD dataset, which has 100 features to select from.
 
 X, y = load_csd_1000r(return_X_y=True)
 X = StandardFlexibleScaler(column_wise=False).fit_transform(X)
@@ -69,7 +69,7 @@
 # Non-iterative feature selection with CUR + PCovR
 # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 #
-# Computing a non-iterative CUR is more efficient, although can resultin poorer
+# Computing a non-iterative CUR is more efficient, although can result in poorer
 # performance for larger datasets. you can also use a greater number of
 # eigenvectors to compute the feature importance by varying ``k``, but ``k`` should
 # not exceed the number of targets, for optimal results.

examples/OrthogonalRegressionNonAnalytic.py

@@ -42,8 +42,8 @@
 
 # %%
 #
-# These are coordinates of a 3-dimensional cube. We treat the points of the cube as samples
-# and the 3 dimensions as features x y z
+# Below are coordinates of a 3-dimensional cube. We treat the points of the cube as samples
+# and the 3 dimensions as features x, y, and z.
 
 cube = np.array(
     [
@@ -61,13 +61,13 @@
 
 # %%
 #
-# the x y coordinates of the cube
+# The x y coordinates of the cube are obtained as follows:
 
 xy_plane_projected_cube = cube[:, [0, 1]]
 
 # %%
 #
-# a square prism with a scaling applied on the z axis
+# A square prism, with scaling applied on the z axis, can be defined as such:
 
 
 def z_scaled_square_prism(z_scaling):
@@ -207,7 +207,7 @@ def z_scaled_square_prism(z_scaling):
 # %%
 #
 # The projection allows an optimal reconstruction of the cube while when not using a
-# projection the orthogonal condition does not allow the same reconstruction
+# projection the orthogonal condition does not allow the same reconstruction.
 
 
 fig, ax_xy = plt.subplots(figsize=(7.5, 4))

examples/PCovR-WHODataset.py

@@ -22,7 +22,7 @@
 # %%
 #
 # Load the Dataset
-# ----------------
+# ^^^^^^^^^^^^^^^^
 
 
 df = load_who_dataset()["data"]
@@ -47,7 +47,7 @@
 
 # %%
 #
-# We are taking the logarithm of the population  and GDP to avoid extreme distributions
+# Below, we take the logarithm of the population and GDP to avoid extreme distributions
 
 log_scaled = ["SP.POP.TOTL", "NY.GDP.PCAP.CD"]
 for ls in log_scaled:
@@ -80,7 +80,10 @@
 # Train the Different Linear DR Techniques
 # ----------------------------------------
 #
-# Best Error for Linear Regression
+# Below, we obtain the regression errors using a variety of linear DR techniques.
+#
+# Linear Regression
+# ^^^^^^^^^^^^^^^^^
 
 RidgeCV(cv=5, alphas=np.logspace(-8, 2, 20), fit_intercept=False).fit(
     X_train, y_train
@@ -153,8 +156,10 @@
 
 
 # %%
+# Below, we obtain the regression errors using a variety of kernel DR techniques.
 #
-# Best Error for Kernel Regression
+# Kernel Regression
+# ^^^^^^^^^^^^^^^^^
 
 gs.best_score_
 

examples/PCovR.py

@@ -23,7 +23,7 @@
 
 # %%
 #
-# For this, we will use the :func:`sklearn.datasets.load_diabetes` dataset from sklearn.
+# For this, we will use the :func:`sklearn.datasets.load_diabetes` dataset from ``sklearn``.
 
 X, y = load_diabetes(return_X_y=True)
 y = y.reshape(X.shape[0], -1)
@@ -37,6 +37,7 @@
 # %%
 #
 # Computing a simple PCovR and making a fancy plot of the results
+# ---------------------------------------------------------------
 
 mixing = 0.5
 pcovr = PCovR(
@@ -71,7 +72,8 @@
 
 # %%
 #
-# Surveying Many Mixing Parameters
+# Surveying many Mixing Parameters
+# --------------------------------
 
 n_alpha = 5
 
@@ -165,4 +167,4 @@
 # you are comparing before constructing a kernel, for example, whether the analysis is
 # to be based on whole structures or individual atomic environments. For more detail,
 # see Appendix C of `Helfrecht 2020 <https://iopscience.iop.org/article/10.1088/2632-2153/aba9ef>`_
-# or regarding kernels involving gradients `Musil 2021 <https://arxiv.org/pdf/2101.08814.pdf>`_.
+# or, regarding kernels involving gradients, `Musil 2021 <https://arxiv.org/pdf/2101.08814.pdf>`_.

examples/PCovR_Regressors.py

@@ -16,7 +16,7 @@
 
 # %%
 #
-# For this, we will use the :func:`sklearn.datasets.load_diabetes` dataset from sklearn.
+# For this, we will use the :func:`sklearn.datasets.load_diabetes` dataset from ``sklearn``.
 
 mixing = 0.5
 

examples/PlotGFRE.py

@@ -15,7 +15,7 @@
 different, but have the same 3-body features. For more details about the dataset
 please refer to `Pozdnyakov 2020 <https://doi.org/10.1103/PhysRevLett.125.166001>`_.
 
-The skmatter dataset already contains the 3 and 4-body features computed with
+The ``skmatter`` dataset already contains the 3 and 4-body features computed with
 `librascal <https://github.com/lab-cosmo/librascal>`_ so we can load it and
 compare it with the GFRE/GFRD.
 """

examples/PlotLFRE.py

@@ -128,7 +128,7 @@
 
 # %%
 #
-# The environments span a manifold which is described by the coordinates :math`v/\pi` and
+# The environments span a manifold which is described by the coordinates :math:`v/\pi` and
 # :math:`u/\pi` (please refer to `Pozdnyakov 2020 <https://doi.org/10.1103/PhysRevLett.125.166001>`_
 # for a concrete understanding of the manifold). The LFRE is presented for each environment
 # in the manifold in the two contour plots. It can be seen that the reconstruction error