[DOCS] Adds regression analytics resources and examples to the data frame analytics APIs and the evaluation API (#46176)

* [DOCS] Adds regression analytics resources and examples to the data frame analytics APIs.
Co-Authored-By: Benjamin Trent <ben.w.trent@gmail.com>
Co-Authored-By: Tom Veasey <tveasey@users.noreply.github.com>

docs/reference/ml/df-analytics/apis/dfanalyticsresources.asciidoc

@@ -12,7 +12,8 @@
 
 `analysis`::
   (object) The type of analysis that is performed on the `source`. For example: 
-  `outlier_detection`. For more information, see <<dfanalytics-types>>.
+  `outlier_detection` or `regression`. For more information, see 
+  <<dfanalytics-types>>.
   
 `analyzed_fields`::
   (object) You can specify both `includes` and/or `excludes` patterns. If 
@@ -98,15 +99,13 @@ PUT _ml/data_frame/analytics/loganalytics
 ==== Analysis objects
 
 {dfanalytics-cap} resources contain `analysis` objects. For example, when you
-create a {dfanalytics-job}, you must define the type of analysis it performs. 
-Currently, `outlier_detection` is the only available type of analysis, however, 
-other types will be added, for example `regression`.
-  
+create a {dfanalytics-job}, you must define the type of analysis it performs.
+
 [discrete]
 [[oldetection-resources]]
 ==== {oldetection-cap} configuration objects 
 
-An {oldetection} configuration object has the following properties:
+An `outlier_detection` configuration object has the following properties:
 
 `compute_feature_influence`::
   (boolean) If `true`, the feature influence calculation is enabled. Defaults to 
@@ -123,7 +122,7 @@ An {oldetection} configuration object has the following properties:
   recommend to use the ensemble method. Available methods are `lof`, `ldof`, 
   `distance_kth_nn`, `distance_knn`.
   
-`n_neighbors`::
+  `n_neighbors`::
   (integer) Defines the value for how many nearest neighbors each method of 
   {oldetection} will use to calculate its {olscore}. When the value is not set, 
   different values will be used for different ensemble members. This helps 
@@ -140,3 +139,122 @@ An {oldetection} configuration object has the following properties:
   before computing outlier scores: (x_i - mean(x_i)) / sd(x_i). Defaults to 
   `true`. For more information, see 
   https://en.wikipedia.org/wiki/Feature_scaling#Standardization_(Z-score_Normalization)[this wiki page about standardization].
+
+
+[discrete]
+[[regression-resources]]
+==== {regression-cap} configuration objects
+
+[source,console]
+--------------------------------------------------
+PUT _ml/data_frame/analytics/house_price_regression_analysis
+{
+  "source": {
+    "index": "houses_sold_last_10_yrs" <1>
+  },
+  "dest": {
+    "index": "house_price_predictions" <2>
+  },
+  "analysis": 
+    {
+      "regression": { <3>
+        "dependent_variable": "price" <4>
+      }
+    }
+}
+--------------------------------------------------
+// TEST[skip:TBD]
+
+<1> Training data is taken from source index `houses_sold_last_10_yrs`.
+<2> Analysis results will be output to destination index 
+`house_price_predictions`.
+<3> The regression analysis configuration object.
+<4> Regression analysis will use field `price` to train on. As no other 
+parameters have been specified it will train on 100% of eligible data, store its 
+prediction in destination index field `price_prediction` and use in-built 
+hyperparameter optimization to give minimum validation errors.
+
+
+[float]
+[[regression-resources-standard]]
+===== Standard parameters
+
+`dependent_variable`::
+  (Required, string) Defines which field of the {dataframe} is to be predicted. 
+  This parameter is supplied by field name and must match one of the fields in 
+  the index being used to train. If this field is missing from a document, then 
+  that document will not be used for training, but a prediction with the trained 
+  model will be generated for it. The data type of the field must be numeric. It 
+  is also known as continuous target variable.
+
+`prediction_field_name`::
+ (Optional, string) Defines the name of the prediction field in the results. 
+ Defaults to `<dependent_variable>_prediction`.
+ 
+`training_percent`::
+ (Optional, integer) Defines what percentage of the eligible documents that will 
+ be used for training. Documents that are ignored by the analysis (for example 
+ those that contain arrays) won’t be included in the calculation for used 
+ percentage. Defaults to `100`.
+
+
+[float]
+[[regression-resources-advanced]]
+===== Advanced parameters
+
+Advanced parameters are for fine-tuning {reganalysis}. They are set 
+automatically by <<ml-hyperparameter-optimization,hyperparameter optimization>> 
+to give minimum validation error. It is highly recommended to use the default 
+values unless you fully understand the function of these parameters. If these 
+parameters are not supplied, their values are automatically tuned to give 
+minimum validation error.
+
+`eta`::
+ (Optional, double) The shrinkage applied to the weights. Smaller values result 
+ in larger forests which have better generalization error. However, the smaller 
+ the value the longer the training will take. For more information, see 
+ https://en.wikipedia.org/wiki/Gradient_boosting#Shrinkage[this wiki article] 
+ about shrinkage.
+ 
+`feature_bag_fraction`::
+ (Optional, double) Defines the fraction of features that will be used when 
+ selecting a random bag for each candidate split. 
+ 
+`maximum_number_trees`::
+ (Optional, integer) Defines the maximum number of trees the forest is allowed 
+ to contain. The maximum value is 2000.
+
+`gamma`::
+ (Optional, double) Regularization parameter to prevent overfitting on the 
+ training dataset. Multiplies a linear penalty associated with the size of 
+ individual trees in the forest. The higher the value the more training will 
+ prefer smaller trees. The smaller this parameter the larger individual trees 
+ will be and the longer train will take.
+ 
+`lambda`::
+ (Optional, double) Regularization parameter to prevent overfitting on the 
+ training dataset. Multiplies an L2 regularisation term which applies to leaf 
+ weights of the individual trees in the forest. The higher the value the more 
+ training will attempt to keep leaf weights small. This makes the prediction 
+ function smoother at the expense of potentially not being able to capture 
+ relevant relationships between the features and the {depvar}. The smaller this 
+ parameter the larger individual trees will be and the longer train will take.
+
+
+[[ml-hyperparameter-optimization]]
+===== Hyperparameter optimization
+
+If you don't supply {regression} parameters, hyperparameter optimization will be 
+performed by default to set a value for the undefined parameters. The starting 
+point is calculated for data dependent parameters by examining the loss on the 
+training data. Subject to the size constraint, this operation provides an upper 
+bound on the improvement in validation loss.
+
+A fixed number of rounds is used for optimization which depends on the number of 
+parameters being optimized. The optimitazion starts with random search, then 
+Bayesian Optimisation is performed that is targeting maximum expected 
+improvement. If you override any parameters, then the optimization will 
+calculate the value of the remaining parameters accordingly and use the value 
+you provided for the overridden parameter. The number of rounds are reduced 
+respectively. The validation error is estimated in each round by using 4-fold 
+cross validation.

docs/reference/ml/df-analytics/apis/evaluate-dfanalytics.asciidoc

@@ -27,15 +27,11 @@ information, see {stack-ov}/security-privileges.html[Security privileges] and
 [[ml-evaluate-dfanalytics-desc]]
 ==== {api-description-title}
 
-This API evaluates the executed analysis on an index that is already annotated
-with a field that contains the results of the analytics (the `ground truth`)
-for each {dataframe} row.
+The API packages together commonly used evaluation metrics for various types of 
+machine learning features. This has been designed for use on indexes created by 
+{dfanalytics}. Evaluation requires both a ground truth field and an analytics 
+result field to be present.
 
-Evaluation is typically done by calculating a set of metrics that capture various aspects of the quality of the results over the data for which you have the
-`ground truth`.
-
-For different types of analyses different metrics are suitable. This API
-packages together commonly used metrics for various analyses.
 
 [[ml-evaluate-dfanalytics-request-body]]
 ==== {api-request-body-title}
@@ -45,15 +41,20 @@ packages together commonly used metrics for various analyses.
   performed.
 
 `query`::
-  (Optional, object) Query used to select data from the index.
-  The {es} query domain-specific language (DSL). This value corresponds to the query
-  object in an {es} search POST body. By default, this property has the following
-  value: `{"match_all": {}}`.
+  (Optional, object) A query clause that retrieves a subset of data from the 
+  source index. See <<query-dsl>>.
 
 `evaluation`::
-  (Required, object) Defines the type of evaluation you want to perform. For example: 
-  `binary_soft_classification`. See <<ml-evaluate-dfanalytics-resources>>.
-  
+  (Required, object) Defines the type of evaluation you want to perform. See 
+  <<ml-evaluate-dfanalytics-resources>>.
++
+--
+Available evaluation types:
+* `binary_soft_classification`
+* `regression`
+--
+
+
 ////
 [[ml-evaluate-dfanalytics-results]]
 ==== {api-response-body-title}
@@ -74,6 +75,8 @@ packages together commonly used metrics for various analyses.
 [[ml-evaluate-dfanalytics-example]]
 ==== {api-examples-title}
 
+===== Binary soft classification
+
 [source,console]
 --------------------------------------------------
 POST _ml/data_frame/_evaluate
@@ -131,3 +134,40 @@ The API returns the following results:
   }
 }
 ----
+
+
+===== {regression-cap}
+
+[source,console]
+--------------------------------------------------
+POST _ml/data_frame/_evaluate
+{
+  "index": "house_price_predictions", <1>
+  "query": {
+      "bool": {
+        "filter": [
+          { "term":  { "ml.is_training": false } } <2>
+        ]
+      }
+  },
+  "evaluation": {
+    "regression": { 
+      "actual_field": "price", <3>
+      "predicted_field": "ml.price_prediction", <4>
+      "metrics": {  
+        "r_squared": {},
+        "mean_squared_error": {}                             
+      }
+    }
+  }
+}
+--------------------------------------------------
+// TEST[skip:TBD]
+
+<1> The output destination index from a {dfanalytics} {reganalysis}.
+<2> In this example, a test/train split (`training_percent`) was defined for the 
+{reganalysis}. This query limits evaluation to be performed on the test split 
+only. 
+<3> The ground truth value for the actual house price. This is required in order 
+to evaluate results.
+<4> The predicted value for house price calculated by the {reganalysis}.

docs/reference/ml/df-analytics/apis/evaluateresources.asciidoc

@@ -12,7 +12,19 @@ Evaluation configuration objects relate to the <<evaluate-dfanalytics>>.
 `evaluation`::
   (object) Defines the type of evaluation you want to perform. The value of this 
   object can be different depending on the type of evaluation you want to 
-  perform. For example, it can contain <<binary-sc-resources>>.
+  perform.
++
+--
+Available evaluation types:
+* `binary_soft_classification`
+* `regression`
+--
+  
+`query`::
+  (object) A query clause that retrieves a subset of data from the source index. 
+  See <<query-dsl>>. The evaluation only applies to those documents of the index 
+  that match the query.
+
 
 [[binary-sc-resources]]
 ==== Binary soft classification configuration objects
@@ -27,18 +39,18 @@ probability whether each row is an outlier.
 ===== {api-definitions-title}
 
 `actual_field`::
-  (string) The field of the `index` which contains the `ground 
-  truth`. The data type of this field can be boolean or integer. If the data 
-  type is integer, the value has to be either `0` (false) or `1` (true).
+  (string) The field of the `index` which contains the `ground truth`. 
+  The data type of this field can be boolean or integer. If the data type is 
+  integer, the value has to be either `0` (false) or `1` (true).
 
 `predicted_probability_field`::
-  (string) The field of the `index` that defines the probability of whether the 
-  item belongs to the class in question or not. It's the field that contains the 
-  results of the analysis.
+  (string) The field of the `index` that defines the probability of 
+  whether the item belongs to the class in question or not. It's the field that 
+  contains the results of the analysis.
 
 `metrics`::
-  (object) Specifies the metrics that are used for the evaluation. Available 
-  metrics:
+  (object) Specifies the metrics that are used for the evaluation. 
+  Available metrics:
   
   `auc_roc`::
     (object) The AUC ROC (area under the curve of the receiver operating 
@@ -60,4 +72,27 @@ probability whether each row is an outlier.
     (`tp` - true positive, `fp` - false positive, `tn` - true negative, `fn` - 
     false negative) are calculated.
     Default value is {"at": [0.25, 0.50, 0.75]}.
-  
+
+    
+[[regression-evaluation-resources]]
+==== {regression-cap} evaluation objects
+
+{regression-cap} evaluation evaluates the results of a {regression} analysis 
+which outputs a prediction of values.
+
+
+[discrete]
+[[regression-evaluation-resources-properties]]
+===== {api-definitions-title}
+
+`actual_field`::
+  (string) The field of the `index` which contains the `ground truth`. The data 
+  type of this field must be numerical.
+  
+`predicted_field`::
+  (string) The field in the `index` that contains the predicted value, 
+  in other words the results of the {regression} analysis.
+  
+`metrics`::
+  (object) Specifies the metrics that are used for the evaluation. Available 
+  metrics are `r_squared` and `mean_squared_error`.

docs/reference/ml/df-analytics/apis/put-dfanalytics.asciidoc

@@ -121,6 +121,9 @@ and mappings.
 [[ml-put-dfanalytics-example]]
 ==== {api-examples-title}
 
+[[ml-put-dfanalytics-example-od]]
+===== {oldetection-cap} example
+
 The following example creates the `loganalytics` {dfanalytics-job}, the analysis 
 type is `outlier_detection`:
 
@@ -170,4 +173,65 @@ The API returns the following result:
 }
 ----
 // TESTRESPONSE[s/1562265491319/$body.$_path/]
-// TESTRESPONSE[s/"version": "8.0.0"/"version": $body.version/]
+// TESTRESPONSE[s/"version": "8.0.0"/"version": $body.version/]
+
+
+[[ml-put-dfanalytics-example-r]]
+===== {regression-cap} example
+
+The following example creates the `house_price_regression_analysis` {
+dfanalytics-job}, the analysis type is `regression`:
+
+[source,console]
+--------------------------------------------------
+PUT _ml/data_frame/analytics/house_price_regression_analysis
+{
+  "source": {
+    "index": "houses_sold_last_10_yrs"
+  },
+  "dest": {
+    "index": "house_price_predictions"
+  },
+  "analysis": 
+    {
+      "regression": {
+        "dependent_variable": "price"
+      }
+    }
+}
+--------------------------------------------------
+// TEST[skip:TBD]
+
+
+The API returns the following result:
+
+[source,console-result]
+----
+{
+  "id" : "house_price_regression_analysis",
+  "source" : {
+    "index" : [
+      "houses_sold_last_10_yrs"
+    ],
+    "query" : {
+      "match_all" : { }
+    }
+  },
+  "dest" : {
+    "index" : "house_price_predictions",
+    "results_field" : "ml"
+  },
+  "analysis" : {
+    "regression" : {
+      "dependent_variable" : "price",
+      "training_percent" : 100
+    }
+  },
+  "model_memory_limit" : "1gb",
+  "create_time" : 1567168659127,
+  "version" : "8.0.0"
+}
+----
+// TESTRESPONSE[s/1567168659127/$body.$_path/]
+// TESTRESPONSE[s/"version": "8.0.0"/"version": $body.version/]
+