Github user tillrohrmann commented on a diff in the pull request:
https://github.com/apache/flink/pull/1898#discussion_r63498396
--- Diff: docs/apis/batch/libs/ml/cross_validation.md ---
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+---
+mathjax: include
+title: Cross Validation
+
+# Sub navigation
+sub-nav-group: batch
+sub-nav-parent: flinkml
+sub-nav-title: Cross Validation
+---
+<!--
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+-->
+
+* This will be replaced by the TOC
+{:toc}
+
+## Description
+
+ A prevalent problem when utilizing machine learning algorithms is
*overfitting*, or when an algorithm "memorizes" the training data but does a
poor job extrapolating to out of sample cases. A common method for dealing with
the overfitting problem is to hold back some subset of data from the original
training algorithm and then measure the fit algorithm's performance on this
hold-out set. This is commonly known as *cross validation*. A model is trained
on one subset of data and then *validated* on another set of data.
+
+## Cross Validation Strategies
+
+There are several strategies for holding out data. FlinkML has convenience
methods for
+- Train-Test Splits
+- Train-Test-Holdout Splits
+- K-Fold Splits
+- Multi-Random Splits
+
+### Train-Test Splits
+
+The simplest method of splitting is the `trainTestSplit`. This split takes
a DataSet and a parameter *fraction*. The *fraction* indicates the portion of
the DataSet that should be allocated to the training set. This split also takes
two additional optional parameters, *precise* and *seed*.
+
+By default, the Split is done by randomly deciding weather or not an
observation is assigned to the training DataSet with probability = *fraction*.
When *precise* is `true` however, additional steps are taken to ensure the
training set is as close as possible to the length of the DataSet $\cdot$
*fraction*.
+
+The method returns a new `TrainTestDataSet` object which has a `.training`
attribute containing the training DataSet and a `.testing` attribute containing
the testing DataSet.
+
+
+### Train-Test-Holdout Splits
+
+In some cases, algorithms have been known to 'learn' the testing set. To
combat this issue, a train-test-hold out strategy introduces a secondary
holdout set, aptly called the *holdout* set.
+
+Traditionally, training and testing would be done to train an algorithms
as normal and then a final test of the algorithm on the holdout set would be
done. Ideally, prediction errors/model scores in the holdout set would not be
significantly different than those observed in the testing set.
+
+In a train-test-holdout strategy we sacrifice the sample size of the
initial fitting algorithm for increased confidence that our model is not
over-fit.
+
+When using `trainTestHoldout` splitter, the *fraction* `Double` is
replaced by a *fraction* array of length three. The first element coresponds to
the portion to be used for training, second for testing, and third for holdout.
The weights of this array are *relative*, e.g. an array `Array(3.0, 2.0, 1.0)`
would results in approximately 50% of the observations being in the training
set, 33% of the observations in the testing set, and 17% of the observations in
holdout set.
+
+### K-Fold Splits
+
+In a *k-fold* strategy, the DataSet is split into *k* equal subsets. Then
for each of the *k* subsets, a `TrainTestDataSet` is created where the subset
is the `.training` DataSet, and the remaining subsets are the `.testing` set.
+
+For each training set, an algorithm is trained and then is evaluated based
on the predictions based on the assosciated testing set. When an algorithm that
has consistent grades (e.g. prediction errors) across held out datasets we can
have some confidence that our approach (e.g. choice of algorithm / algorithm
parameters / number of iterations) is robust against overfitting.
+
+<a
href="https://en.wikipedia.org/wiki/Cross-validation_(statistics)#k-fold_cross-validation">K-Fold
Cross Validatation</a>
+
+### Multi-Random Splits
+
+The *multi-random* strategy can be thought of as a more general form of
the *train-test-holdout* strategy. In fact, `.trainTestHoldoutSplit` is simple
a wrapper for `multiRandomSplit` which also packages the datasets into a
`trainTestHoldoutDataSet` object.
+
+The first major difference, is that `multiRandomSplit` takes an array of
fractions of any length. E.g. one can create multiple holdout sets.
Alternatively, one could think of `kFoldSplit` as a wrapper for
`multiRandomSplit` (which it is), the difference being `kFoldSplit` creates
subsets of approximately equal size, where `multiRandomSplit` will create
subsets of any size.
+
+The second major difference is that `multiRandomSplit` returns an array of
DataSets, equal in size and proportion to the *fraction array* that it was
passed as an argument.
+
+## Parameters
+
+The various `Splitter` methods share many parameters.
+
+ <table class="table table-bordered">
+ <thead>
+ <tr>
+ <th class="text-left" style="width: 20%">Parameter</th>
+ <th class="text-center">Type</th>
+ <th class="text-center">Description</th>
+ <th class="text-right">Used by Method</th>
+ </tr>
+ </thead>
+
+ <tbody>
+ <tr>
+ <td><code>input</code></td>
+ <td><code>DataSet[Any]</code></td>
+ <td>DataSet to be split.</td>
+ <td>
+ <code>randomSplit</code><br>
+ <code>multiRandomSplit</code><br>
+ <code>kFoldSplit</code><br>
+ <code>trainTestSplit</code><br>
+ <code>trainTestHoldoutSplit</code>
+ </td>
+ </tr>
+ <tr>
+ <td><code>seed</code></td>
+ <td><code>Long</code></td>
+ <td>
+ <p>
+ Used for seeding the random number generator which sorts
DataSets into other DataSets.
+ </p>
+ </td>
+ <td>
+ <code>randomSplit</code><br>
+ <code>multiRandomSplit</code><br>
+ <code>kFoldSplit</code><br>
+ <code>trainTestSplit</code><br>
+ <code>trainTestHoldoutSplit</code>
+ </td>
+ </tr>
+ <tr>
+ <td><code>precise</code></td>
+ <td><code>Boolean</code></td>
+ <td>When true, make additional effort to make DataSets as close to
the prescribed proportions as possible.</td>
+ <td>
+ <code>randomSplit</code><br>
+ <code>trainTestSplit</code>
+ </td>
+ </tr>
+ <tr>
+ <td><code>fraction</code></td>
+ <td><code>Double</code></td>
+ <td>The portion of the `input` to assign to the first or
<code>.training</code> DataSet. Must be in the range (0,1)</td>
+ <td><code>randomSplit</code><br>
+ <code>trainTestSplit</code>
+ </td>
+ </tr>
+ <tr>
+ <td><code>fracArray</code></td>
+ <td><code>Array[Double]</code></td>
+ <td>An array that prescribes the proportions of the output datasets
(proportions need not sum to 1 or be within the range (0,1))</td>
+ <td>
+ <code>multiRandomSplit</code><br>
+ <code>trainTestHoldoutSplit</code>
+ </td>
+ </tr>
+ <tr>
+ <td><code>kFolds</code></td>
+ <td><code>Int</code></td>
+ <td>The number of subsets to break the <code>input</code> DataSet
into.</td>
+ <td><code>kFoldSplit</code></td>
+ </tr>
+
+ </tbody>
+</table>
+
+## Examples
+
+{% highlight scala %}
+// An input dataset- does not have to be of type LabeledVector
+val data: DataSet[LabeledVector] = ...
+
+// A Simple Train-Test-Split
+val dataTrainTest: TrainTestDataSet = Splitter.trainTestSplit(data, 0.6,
true )
--- End diff --
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