sebwrede commented on a change in pull request #1061:
URL: https://github.com/apache/systemds/pull/1061#discussion_r494152273



##########
File path: src/main/python/docs/source/guide/algorithms.rst
##########
@@ -26,18 +26,173 @@ Prerequisite:
 
 - :doc:`/getting_started/install`
 
+This example goes through an algorithm from the list of builtin algorithms 
that can be applied to a dataset.
+For simplicity the dataset used for this is `MNIST 
<http://yann.lecun.com/exdb/mnist/>`_,
+since it is commonly known and explored.
+
+If one wants to skip the explanation then the full script is available at the 
bottom of this page.
 
 Step 1: Get Dataset
 -------------------
 
-TODO
+SystemDS provides builtin for downloading and setup of the MNIST dataset.
+To setup this simply use::
 
-Step 2: Train model
--------------------
+    from systemds.examples.tutorials.mnist import DataManager
+    d = DataManager()
+    X = d.get_train_data()
+    Y = d.get_train_labels()
+
+Here the DataManager contains the code for downloading and setting up numpy 
arrays containing the data.
+
+Step 2: Reshape & Format
+------------------------
+
+Usually data does not come in formats that perfectly fits the algorithms, to 
make this tutorial more
+realistic some data preprocessing is required to change the input to fit.
+
+First the Training data, X, has multiple dimensions resulting in a shape 
(60000, 28, 28).
+The dimensions correspond to first the number of images 60000, then the number 
of row pixels, 28,
+and finally the column pixels, 28.
+
+To use this data for Logistic Regression we have to reduce the dimensions.
+The input X is the training data. 
+It require the data to have two dimensions, the first resemble the
+number of inputs, and the other the number of features.
+
+Therefore to make the data fit the algorithm we reshape the X dataset, like 
so::
+
+    X = X.reshape((60000, 28*28))
+
+This takes each row of pixels and append to each other making a single feature 
vector per image.
+
+The Y dataset also does not perfectly fit the Logistic Regression algorithm, 
this is because the labels
+for this dataset is values ranging from 0, to 9, each label correspond to the 
integer shown in the image.
+unfortunately the algorithm require the labels to be distinct integers from 1 
and upwards.
+
+Therefore we add 1 to each label such that the labels go from 1 to 10, like 
this::
+
+    Y = Y + 1
+
+With these steps we are now ready to train a simple logistic model.
+
+Step 3: Training
+----------------
+
+To start with, we setup a SystemDS context::
+
+    from systemds.context import SystemDSContext
+    sds = SystemDSContext()
+
+Then setup the data::
+
+    from systemds.matrix import Matrix
+    X_ds = Matrix(sds, X)
+    Y_ds = Matrix(sds, Y)
+
+to reduce the training time and verify everything works, it is usually good to 
reduce the amount of data,
+to train on a smaller sample to start with::
+
+    sample_size = 1000
+    X_ds = Matrix(sds, X[:sample_size])
+    Y_ds = Matrix(sds, Y[:sample_size])
+
+And now everything is ready for our algorithm::
+
+    from systemds.operator.algorithm import multiLogReg
+
+    bias = multiLogReg(X_ds, Y_ds)
+
+Note that nothing has been calculated yet, in SystemDS, since it only happens 
when you call compute::
+
+    bias_r = bias.compute()
 
-TODO
+bias is a matrix, that if matrix multiplied with an instance returns a value 
distribution where, the highest value is the predicted type.
+This is the matrix that could be saved and used for predicting labels later.
 
 Step 3: Validate
 ----------------
 
-TODO
+To see what accuracy the model achieves, we have to load in the test dataset 
as well.
+
+this can also be extracted from our builtin MNIST loader, to keep the tutorial 
short the operations are combined::
+
+    Xt = Matrix(sds, d.get_test_data().reshape((10000, 28*28)))
+    Yt = Matrix(sds, d.get_test_labels()) + 1
+
+The above loads the test data, and reshapes the X data the same way the 
training data was reshaped.
+
+Finally we verify the accuracy by calling::
+
+    from systemds.operator.algorithm import multiLogRegPredict
+    [m, y_pred, acc] = multiLogRegPredict(Xt, bias, Yt).compute()
+    print(acc)
+
+There are three outputs from the multiLogRegPredict call.
+
+m, is the mean probability of correctly classifying each label.
+y_pred, is the predictions made using the model, bias, trained.
+acc, is the accuracy achieved by the model.
+
+If the subset of the training data is used then you could expect an accuracy 
of 85% in this example
+using 1000 pictures of the training data.
+
+Step 4: Tuning
+--------------
+
+Now that we have a working baseline we can start tuning parameters.
+
+But first it is valuable to know how much of a difference in performance there 
is on the training data, vs the test data.
+This gives an indication of if we have exhausted the learning potential of the 
training data.
+
+To see how our accuracy is on the training data we use the Predict function 
again, but with our training data::
+
+    [m, y_pred, acc] = multiLogRegPredict(X_ds, bias, Y_ds).compute()
+    print(acc)
+
+In this specific case we achieve 100% accuracy on the training data, 
indicating that we have fit the training data,
+and have nothing more to learn from the data as it is now.
+
+To improve further we have to increase the training data, here for example we 
increase it
+from our sample of 1k to the full training dataset of 60k, in this example the 
maxi is set to reduce the number of iterations the algorithm takes,
+to again reduce training time::
+
+    X_ds = Matrix(sds, X)
+    Y_ds = Matrix(sds, Y)
+
+    bias = multiLogReg(X_ds, Y_ds, maxi=30)
+
+    [_, _, train_acc] = multiLogRegPredict(X_ds, bias, Y_ds).compute()
+    [_, _, test_acc] = multiLogRegPredict(Xt, bias, Yt).compute()
+    print(train_acc  "  " test_acc)
+
+With this change the accuracy achieved changes from the previous value to 92%. 
This is still low on this dataset as can be seen on `MNIST 
<http://yann.lecun.com/exdb/mnist/>`_.
+But this is a basic implementation, that can be replaced by a variety of 
algorithm and techniques.

Review comment:
       But this is a basic implementation that can be replaced by a variety of 
algorithms and techniques.

##########
File path: src/main/python/docs/source/guide/algorithms.rst
##########
@@ -26,18 +26,173 @@ Prerequisite:
 
 - :doc:`/getting_started/install`
 
+This example goes through an algorithm from the list of builtin algorithms 
that can be applied to a dataset.
+For simplicity the dataset used for this is `MNIST 
<http://yann.lecun.com/exdb/mnist/>`_,
+since it is commonly known and explored.
+
+If one wants to skip the explanation then the full script is available at the 
bottom of this page.
 
 Step 1: Get Dataset
 -------------------
 
-TODO
+SystemDS provides builtin for downloading and setup of the MNIST dataset.
+To setup this simply use::
 
-Step 2: Train model
--------------------
+    from systemds.examples.tutorials.mnist import DataManager
+    d = DataManager()
+    X = d.get_train_data()
+    Y = d.get_train_labels()
+
+Here the DataManager contains the code for downloading and setting up numpy 
arrays containing the data.
+
+Step 2: Reshape & Format
+------------------------
+
+Usually data does not come in formats that perfectly fits the algorithms, to 
make this tutorial more
+realistic some data preprocessing is required to change the input to fit.
+
+First the Training data, X, has multiple dimensions resulting in a shape 
(60000, 28, 28).
+The dimensions correspond to first the number of images 60000, then the number 
of row pixels, 28,
+and finally the column pixels, 28.
+
+To use this data for Logistic Regression we have to reduce the dimensions.
+The input X is the training data. 
+It require the data to have two dimensions, the first resemble the
+number of inputs, and the other the number of features.
+
+Therefore to make the data fit the algorithm we reshape the X dataset, like 
so::
+
+    X = X.reshape((60000, 28*28))
+
+This takes each row of pixels and append to each other making a single feature 
vector per image.
+
+The Y dataset also does not perfectly fit the Logistic Regression algorithm, 
this is because the labels
+for this dataset is values ranging from 0, to 9, each label correspond to the 
integer shown in the image.
+unfortunately the algorithm require the labels to be distinct integers from 1 
and upwards.
+
+Therefore we add 1 to each label such that the labels go from 1 to 10, like 
this::
+
+    Y = Y + 1
+
+With these steps we are now ready to train a simple logistic model.
+
+Step 3: Training
+----------------
+
+To start with, we setup a SystemDS context::
+
+    from systemds.context import SystemDSContext
+    sds = SystemDSContext()
+
+Then setup the data::
+
+    from systemds.matrix import Matrix
+    X_ds = Matrix(sds, X)
+    Y_ds = Matrix(sds, Y)
+
+to reduce the training time and verify everything works, it is usually good to 
reduce the amount of data,
+to train on a smaller sample to start with::
+
+    sample_size = 1000
+    X_ds = Matrix(sds, X[:sample_size])
+    Y_ds = Matrix(sds, Y[:sample_size])
+
+And now everything is ready for our algorithm::
+
+    from systemds.operator.algorithm import multiLogReg
+
+    bias = multiLogReg(X_ds, Y_ds)
+
+Note that nothing has been calculated yet, in SystemDS, since it only happens 
when you call compute::
+
+    bias_r = bias.compute()
 
-TODO
+bias is a matrix, that if matrix multiplied with an instance returns a value 
distribution where, the highest value is the predicted type.
+This is the matrix that could be saved and used for predicting labels later.
 
 Step 3: Validate
 ----------------
 
-TODO
+To see what accuracy the model achieves, we have to load in the test dataset 
as well.
+
+this can also be extracted from our builtin MNIST loader, to keep the tutorial 
short the operations are combined::
+
+    Xt = Matrix(sds, d.get_test_data().reshape((10000, 28*28)))
+    Yt = Matrix(sds, d.get_test_labels()) + 1
+
+The above loads the test data, and reshapes the X data the same way the 
training data was reshaped.
+
+Finally we verify the accuracy by calling::
+
+    from systemds.operator.algorithm import multiLogRegPredict
+    [m, y_pred, acc] = multiLogRegPredict(Xt, bias, Yt).compute()
+    print(acc)
+
+There are three outputs from the multiLogRegPredict call.
+
+m, is the mean probability of correctly classifying each label.
+y_pred, is the predictions made using the model, bias, trained.
+acc, is the accuracy achieved by the model.
+
+If the subset of the training data is used then you could expect an accuracy 
of 85% in this example
+using 1000 pictures of the training data.
+
+Step 4: Tuning
+--------------
+
+Now that we have a working baseline we can start tuning parameters.
+
+But first it is valuable to know how much of a difference in performance there 
is on the training data, vs the test data.
+This gives an indication of if we have exhausted the learning potential of the 
training data.
+
+To see how our accuracy is on the training data we use the Predict function 
again, but with our training data::
+
+    [m, y_pred, acc] = multiLogRegPredict(X_ds, bias, Y_ds).compute()
+    print(acc)
+
+In this specific case we achieve 100% accuracy on the training data, 
indicating that we have fit the training data,
+and have nothing more to learn from the data as it is now.
+
+To improve further we have to increase the training data, here for example we 
increase it
+from our sample of 1k to the full training dataset of 60k, in this example the 
maxi is set to reduce the number of iterations the algorithm takes,
+to again reduce training time::
+
+    X_ds = Matrix(sds, X)
+    Y_ds = Matrix(sds, Y)
+
+    bias = multiLogReg(X_ds, Y_ds, maxi=30)
+
+    [_, _, train_acc] = multiLogRegPredict(X_ds, bias, Y_ds).compute()
+    [_, _, test_acc] = multiLogRegPredict(Xt, bias, Yt).compute()
+    print(train_acc  "  " test_acc)

Review comment:
       This is invalid syntax. I think it should be: 
   `print(train_acc, "   ", test_acc)`

##########
File path: src/main/python/docs/source/guide/algorithms.rst
##########
@@ -26,18 +26,173 @@ Prerequisite:
 
 - :doc:`/getting_started/install`
 
+This example goes through an algorithm from the list of builtin algorithms 
that can be applied to a dataset.
+For simplicity the dataset used for this is `MNIST 
<http://yann.lecun.com/exdb/mnist/>`_,
+since it is commonly known and explored.
+
+If one wants to skip the explanation then the full script is available at the 
bottom of this page.
 
 Step 1: Get Dataset
 -------------------
 
-TODO
+SystemDS provides builtin for downloading and setup of the MNIST dataset.
+To setup this simply use::
 
-Step 2: Train model
--------------------
+    from systemds.examples.tutorials.mnist import DataManager
+    d = DataManager()
+    X = d.get_train_data()
+    Y = d.get_train_labels()
+
+Here the DataManager contains the code for downloading and setting up numpy 
arrays containing the data.
+
+Step 2: Reshape & Format
+------------------------
+
+Usually data does not come in formats that perfectly fits the algorithms, to 
make this tutorial more
+realistic some data preprocessing is required to change the input to fit.
+
+First the Training data, X, has multiple dimensions resulting in a shape 
(60000, 28, 28).
+The dimensions correspond to first the number of images 60000, then the number 
of row pixels, 28,
+and finally the column pixels, 28.
+
+To use this data for Logistic Regression we have to reduce the dimensions.
+The input X is the training data. 
+It require the data to have two dimensions, the first resemble the
+number of inputs, and the other the number of features.
+
+Therefore to make the data fit the algorithm we reshape the X dataset, like 
so::
+
+    X = X.reshape((60000, 28*28))
+
+This takes each row of pixels and append to each other making a single feature 
vector per image.
+
+The Y dataset also does not perfectly fit the Logistic Regression algorithm, 
this is because the labels
+for this dataset is values ranging from 0, to 9, each label correspond to the 
integer shown in the image.
+unfortunately the algorithm require the labels to be distinct integers from 1 
and upwards.
+
+Therefore we add 1 to each label such that the labels go from 1 to 10, like 
this::
+
+    Y = Y + 1
+
+With these steps we are now ready to train a simple logistic model.
+
+Step 3: Training
+----------------
+
+To start with, we setup a SystemDS context::
+
+    from systemds.context import SystemDSContext
+    sds = SystemDSContext()
+
+Then setup the data::
+
+    from systemds.matrix import Matrix
+    X_ds = Matrix(sds, X)
+    Y_ds = Matrix(sds, Y)
+
+to reduce the training time and verify everything works, it is usually good to 
reduce the amount of data,
+to train on a smaller sample to start with::
+
+    sample_size = 1000
+    X_ds = Matrix(sds, X[:sample_size])
+    Y_ds = Matrix(sds, Y[:sample_size])
+
+And now everything is ready for our algorithm::
+
+    from systemds.operator.algorithm import multiLogReg
+
+    bias = multiLogReg(X_ds, Y_ds)
+
+Note that nothing has been calculated yet, in SystemDS, since it only happens 
when you call compute::
+
+    bias_r = bias.compute()
 
-TODO
+bias is a matrix, that if matrix multiplied with an instance returns a value 
distribution where, the highest value is the predicted type.
+This is the matrix that could be saved and used for predicting labels later.
 
 Step 3: Validate
 ----------------
 
-TODO
+To see what accuracy the model achieves, we have to load in the test dataset 
as well.
+
+this can also be extracted from our builtin MNIST loader, to keep the tutorial 
short the operations are combined::
+
+    Xt = Matrix(sds, d.get_test_data().reshape((10000, 28*28)))
+    Yt = Matrix(sds, d.get_test_labels()) + 1
+
+The above loads the test data, and reshapes the X data the same way the 
training data was reshaped.
+
+Finally we verify the accuracy by calling::
+
+    from systemds.operator.algorithm import multiLogRegPredict
+    [m, y_pred, acc] = multiLogRegPredict(Xt, bias, Yt).compute()
+    print(acc)
+
+There are three outputs from the multiLogRegPredict call.
+
+m, is the mean probability of correctly classifying each label.
+y_pred, is the predictions made using the model, bias, trained.
+acc, is the accuracy achieved by the model.

Review comment:
       This is displayed as one line when opening in IntelliJ. Is there an 
option to make it appear as an actual list?




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