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Model evaluation

A set of Vertica machine learning functions evaluate the prediction data that is generated by trained models, or return information about the models themselves.

1: CONFUSION_MATRIX
2: CROSS_VALIDATE
3: ERROR_RATE
4: LIFT_TABLE
5: MSE
6: PRC
7: READ_TREE
8: RF_PREDICTOR_IMPORTANCE
9: ROC
10: RSQUARED

A set of Vertica machine learning functions evaluate the prediction data that is generated by trained models, or return information about the models themselves.

1 - CONFUSION_MATRIX

Computes the confusion matrix of a table with observed and predicted values of a response variable.

Computes the confusion matrix of a table with observed and predicted values of a response variable. CONFUSION_MATRIX produces a table with the following dimensions:

Rows: Number of classes
Columns: Number of classes + 2

Syntax

CONFUSION_MATRIX ( targets, predictions [ USING PARAMETERS num_classes = num-classes ] OVER()

Arguments

targets: An input column that contains the true values of the response variable.
predictions: An input column that contains the predicted class labels.

Arguments targets and predictions must be set to input columns of the same data type, one of the following: INTEGER, BOOLEAN, or CHAR/VARCHAR. Depending on their data type, these columns identify classes as follows:

INTEGER: Zero-based consecutive integers between 0 and (num-classes-1) inclusive, where num-classes is the number of classes. For example, given the following input column values— {0, 1, 2, 3, 4}—Vertica assumes five classes.

Note
If input column values are not consecutive, Vertica interpolates the missing values. Thus, given the following input values— {0, 1, 3, 5, 6,}— Vertica assumes seven classes.
BOOLEAN: Yes or No
CHAR/VARCHAR: Class names. If the input columns are of type CHAR/VARCHAR columns, you must also set parameter num_classes to the number of classes.
Note

Vertica computes the number of classes as the union of values in both input columns. For example, given the following sets of values in the targets and predictions input columns, Vertica counts four classes:
```
{'milk', 'soy milk', 'cream'}
{'soy milk', 'almond milk'}
```

Parameters

num_classes

An integer > 1, specifies the number of classes to pass to the function.

You must set this parameter if the specified input columns are of type CHAR/VARCHAR. Otherwise, the function processes this parameter according to the column data types:

INTEGER: By default set to 2, you must set this parameter correctly if the number of classes is any other value.
BOOLEAN: By default set to 2, cannot be set to any other value.

Examples

This example computes the confusion matrix for a logistic regression model that classifies cars in the mtcars data set as automatic or manual transmission. Observed values are in input column obs, while predicted values are in input column pred. Because this is a binary classification problem, all values are either 0 or 1.

In the table returned, all 19 cars with a value of 0 in column am are correctly predicted by PREDICT_LOGISTIC_REGRESSION as having a value of 0. Of the 13 cars with a value of 1 in column am, 12 are correctly predicted to have a value of 1, while 1 car is incorrectly classified as having a value of 0:

=> SELECT CONFUSION_MATRIX(obs::int, pred::int USING PARAMETERS num_classes=2) OVER()
    FROM (SELECT am AS obs, PREDICT_LOGISTIC_REG(mpg, cyl, disp,drat, wt, qsec, vs, gear, carb
             USING PARAMETERS model_name='myLogisticRegModel')AS PRED
             FROM mtcars) AS prediction_output;

actual_class | predicted_0 | predicted_1 |        comment
-------------+-------------+-------------+------------------------------------------
0            |          19 |           0 |
1            |           0 |          13 | Of 32 rows, 32 were used and 0 were ignored
(2 rows)

2 - CROSS_VALIDATE

Performs k-fold cross validation on a learning algorithm using an input relation, and grid search for hyper parameters.

Performs k-fold cross validation on a learning algorithm using an input relation, and grid search for hyper parameters. The output is an average performance indicator of the selected algorithm. This function supports SVM classification, naive bayes, and logistic regression.

This is a meta-function. You must call meta-functions in a top-level SELECT statement.

Behavior type

Volatile

Syntax

CROSS_VALIDATE ( 'algorithm', 'input-relation', 'response-column', 'predictor-columns'
        [ USING PARAMETERS
              [exclude_columns = 'excluded-columns']
           [, cv_model_name = 'model']
           [, cv_metrics = 'metrics']
           [, cv_fold_count = num-folds]
           [, cv_hyperparams = 'hyperparams']
           [, cv_prediction_cutoff = prediction-cutoff] ] )

Arguments

algorithm

Name of the algorithm training function, one of the following:

input-relation

The table or view that contains data used for training and testing. If the input relation is defined in Hive, use SYNC_WITH_HCATALOG_SCHEMA to sync the hcatalog schema, and then run the machine learning function.

response-column

Name of the input column that contains the response.

predictor-columns

Comma-separated list of columns in the input relation that represent independent variables for the model, or asterisk (*) to select all columns. If you select all columns, the argument list for parameter exclude_columns must include response-column, and any columns that are invalid as predictor columns.

Parameters

exclude_columns

Comma-separated list of columns from predictor-columns to exclude from processing.

cv_model_name

The name of a model that lets you retrieve results of the cross validation process. If you omit this parameter, results are displayed but not saved. If you set this parameter to a model name, you can retrieve the results with summary functions GET_MODEL_ATTRIBUTE and GET_MODEL_SUMMARY

cv_metrics

The metrics used to assess the algorithm, specified either as a comma-separated list of metric names or in a JSON array. In both cases, you specify one or more of the following metric names:

accuracy (default)
error_rate
TP: True positive, the number of cases of class 1 predicted as class 1
FP: False positive, the number of cases of class 0 predicted as class 1
TN: True negative, the number of cases of class 0 predicted as class 0
FN: False negative, the number of cases of class 1 predicted as class 0
TPR or recall: True positive rate, the correct predictions among class 1
FPR: False positive rate, the wrong predictions among class 0
TNR: True negative rate, the correct predictions among class 0
FNR: False negative rate, the wrong predictions among class 1
PPV or precision: The positive predictive value, the correct predictions among cases predicted as class 1
NPV: Negative predictive value, the correct predictions among cases predicted as class 0
MSE: Mean squared error
MAE: Mean absolute error
rsquared: coefficient of determination
explained_variance

fscore

(1 + beta˄2) * precison * recall / (beta˄2 * precision + recall)

beta equals 1 by default

auc_roc: AUC of ROC using the specified number of bins, by default 100
auc_prc: AUC of PRC using the specified number of bins, by default 100
counts: Shortcut that resolves to four other metrics: TP, FP, TN, and FN
count: Valid only in JSON syntax, counts the number of cases labeled by one class (case-class-label) but predicted as another class (predicted-class-label):
```
cv_metrics='[{"count":[case-class-label, predicted-class-label]}]'
```

cv_fold_count

The number of folds to split the data.

Default: 5

cv_hyperparams

A JSON string that describes the combination of parameters for use in grid search of hyper parameters. The JSON string contains pairs of the hyper parameter name. The value of each hyper parameter can be specified as an array or sequence. For example:

{"param1":[value1,value2,...], "param2":{"first":first_value, "step":step_size, "count":number_of_values} }

Hyper parameter names and string values should be quoted using the JSON standard. These parameters are passed to the training function.

cv_prediction_cutoff

The cutoff threshold that is passed to the prediction stage of logistic regression, a FLOAT between 0 and 1, exclusive

Default: 0.5

Model attributes

call_string

The value of all input arguments that were specified at the time CROSS_VALIDATE was called.

run_average

The average across all folds of all metrics specified in parameter cv_metrics, if specified; otherwise, average accuracy.

fold_info

The number of rows in each fold:

fold_id: The index of the fold.
row_count: The number of rows held out for testing in the fold.

counters

All counters for the function, including:

accepted_row_count: The total number of rows in the input_relation, minus the number of rejected rows.
rejected_row_count: The number of rows of the input_relation that were skipped because they contained an invalid value.
feature_count: The number of features input to the machine learning model.

run_details

Information about each run, where a run means training a single model, and then testing that model on the one held-out fold:

fold_id: The index of the fold held out for testing.
iteration_count: The number of iterations used in model training on non-held-out folds.
accuracy: All metrics specified in parameter cv_metrics, or accuracy if cv_metrics is not provided.
error_rate: All metrics specified in parameter cv_metrics, or accuracy if the parameter is omitted.

Privileges

Non-superusers:

SELECT privileges on the input relation
CREATE and USAGE privileges on the default schema where machine learning algorithms generate models. If cv_model_name is provided, the cross validation results are saved as a model in the same schema.

Specifying metrics in JSON

Parameter cv_metrics can specify metrics as an array of JSON objects, where each object specifies a metric name . For example, the following expression sets cv_metrics to two metrics specified as JSON objects, accuracy and error_rate:

cv_metrics='["accuracy", "error_rate"]'

In the next example, cv_metrics is set to two metrics, accuracy and TPR (true positive rate). Here, the TPR metric is specified as a JSON object that takes an array of two class label arguments, 2 and 3:

cv_metrics='[ "accuracy", {"TPR":[2,3] } ]'

Metrics specified as JSON objects can accept parameters. In the following example, the fscore metric specifies parameter beta, which is set to 0.5:

cv_metrics='[ {"fscore":{"beta":0.5} } ]'

Parameter support can be especially useful for certain metrics. For example, metrics auc_roc and auc_prc build a curve, and then compute the area under that curve. For ROC, the curve is formed by plotting metrics TPR against FPR; for PRC, PPV (precision) against TPR (recall). The accuracy of such curves can be increased by setting parameter num_bins to a value greater than the default value of 100. For example, the following expression computes AUC for an ROC curve built with 1000 bins:

cv_metrics='[{"auc_roc":{"num_bins":1000}}]'

Using metrics with Multi-class classifier functions

All supported metrics are defined for binary classifier functions LOGISTIC_REG and SVM_CLASSIFIER. For multi-class classifier functions such as NAIVE_BAYES, these metrics can be calculated for each one-versus-the-rest binary classifier. Use arguments to request the metrics for each classifier. For example, if training data has integer class labels, you can set cv_metrics with the precision (PPV) metric as follows:

cv_metrics='[{"precision":[0,4]}]'

This setting specifies to return two columns with precision computed for two classifiers:

Column 1: classifies 0 versus not 0
Collumn 2: classifies 4 versus not 4

If you omit class label arguments, the class with index 1 is used. Instead of computing metrics for individual one-versus-the-rest classifiers, the average is computed in one of the following styles: macro, micro, or weighted (default). For example, the following cv_metrics setting returns the average weighted by class sizes:

cv_metrics='[{"precision":{"avg":"weighted"}}]'

AUC-type metrics can be similarly defined for multi-class classifiers. For example, the following cv_metrics setting computes the area under the ROC curve for each one-versus-the-rest classifier, and then returns the average weighted by class sizes.

cv_metrics='[{"auc_roc":{"avg":"weighted", "num_bins":1000}}]'

Examples

=> SELECT CROSS_VALIDATE('svm_classifier', 'mtcars', 'am', 'mpg'
      USING PARAMETERS cv_fold_count= 6,
                       cv_hyperparams='{"C":[1,5]}',
                       cv_model_name='cv_svm',
                       cv_metrics='accuracy, error_rate');
         CROSS_VALIDATE
----------------------------
 Finished

===========
run_average
===========
C  |accuracy      |error_rate
---+--------------+----------
1 | 0.75556       |  0.24444
5 | 0.78333       |  0.21667
(1 row)

3 - ERROR_RATE

Using an input table, returns a table that calculates the rate of incorrect classifications and displays them as FLOAT values.

Using an input table, returns a table that calculates the rate of incorrect classifications and displays them as FLOAT values. ERROR_RATE returns a table with the following dimensions:

Rows: Number of classes plus one row that contains the total error rate across classes
Columns: 2

Syntax

ERROR_RATE ( targets, predictions [ USING PARAMETERS num_classes = num-classes ] ) OVER()

Arguments

targets: An input column that contains the true values of the response variable.
predictions: An input column that contains the predicted class labels.

INTEGER: Zero-based consecutive integers between 0 and (num-classes-1) inclusive, where num-classes is the number of classes. For example, given the following input column values— {0, 1, 2, 3, 4}—Vertica assumes five classes.

Note
If input column values are not consecutive, Vertica interpolates the missing values. Thus, given the following input values— {0, 1, 3, 5, 6,}— Vertica assumes seven classes.
BOOLEAN: Yes or No
CHAR/VARCHAR: Class names. If the input columns are of type CHAR/VARCHAR columns, you must also set parameter num_classes to the number of classes.
Note

Vertica computes the number of classes as the union of values in both input columns. For example, given the following sets of values in the targets and predictions input columns, Vertica counts four classes:
```
{'milk', 'soy milk', 'cream'}
{'soy milk', 'almond milk'}
```

Parameters

num_classes

An integer > 1, specifies the number of classes to pass to the function.

You must set this parameter if the specified input columns are of type CHAR/VARCHAR. Otherwise, the function processes this parameter according to the column data types:

INTEGER: By default set to 2, you must set this parameter correctly if the number of classes is any other value.
BOOLEAN: By default set to 2, cannot be set to any other value.

Privileges

Non-superusers: model owner, or USAGE privileges on the model

Examples

This example shows how to execute the ERROR_RATE function on an input table named mtcars. The response variables appear in the column obs, while the prediction variables appear in the column pred. Because this example is a classification problem, all response variable values and prediction variable values are either 0 or 1, indicating binary classification.

In the table returned by the function, the first column displays the class id column. The second column displays the corresponding error rate for the class id. The third column indicates how many rows were successfully used by the function and whether any rows were ignored.

=> SELECT ERROR_RATE(obs::int, pred::int USING PARAMETERS num_classes=2) OVER()
    FROM (SELECT am AS obs, PREDICT_LOGISTIC_REG (mpg, cyl, disp, drat, wt, qsec, vs, gear, carb
                USING PARAMETERS model_name='myLogisticRegModel', type='response') AS pred
             FROM mtcars) AS prediction_output;
 class |     error_rate     |                   comment
-------+--------------------+---------------------------------------------
     0 |                  0 |
     1 | 0.0769230797886848 |
       |            0.03125 | Of 32 rows, 32 were used and 0 were ignored
(3 rows)

4 - LIFT_TABLE

Returns a table that compares the predictive quality of a machine learning model.

Returns a table that compares the predictive quality of a machine learning model. This function is also known as a lift chart.

Syntax

LIFT_TABLE ( targets, probabilities
        [ USING PARAMETERS [num_bins = num-bins] [, main_class = class-name ] ] )
OVER()

Arguments

targets

An input column that contains the true values of the response variable, one of the following data types: INTEGER, BOOLEAN, or CHAR/VARCHAR. Depending on the column data type, the function processes column data as follows:

INTEGER: Uses the input column as containing the true value of the response variable.
BOOLEAN: Resolves Yes to 1, 0 to No.
CHAR/VARCHAR: Resolves the value specified by parameter main_class to 1, all other values to 0.

Note

If the input column is of data type INTEGER or BOOLEAN, the function ignores parameter main_class.

probabilities

A FLOAT input column that contains the predicted probability of response being the main class, set to 1 if targets is of type INTEGER.

Parameters

num_bins

An integer value that determines the number of decision boundaries. Decision boundaries are set at equally spaced intervals between 0 and 1, inclusive. The function computes the table at each num-bin + 1 point.

Default: 100

main_class

Used only if targets is of type CHAR/VARCHAR, specifies the class to associate with the probabilities argument.

Examples

Execute LIFT_TABLE on an input table mtcars.

=> SELECT LIFT_TABLE(obs::int, prob::float USING PARAMETERS num_bins=2) OVER()
    FROM (SELECT am AS obs, PREDICT_LOGISTIC_REG(mpg, cyl, disp, drat, wt, qsec, vs, gear, carb
                                                    USING PARAMETERS model_name='myLogisticRegModel',
                                                    type='probability') AS prob
             FROM mtcars) AS prediction_output;
 decision_boundary | positive_prediction_ratio |       lift       |                   comment
-------------------+---------------------------+------------------+---------------------------------------------
                 1 |                         0 |              NaN |
               0.5 |                   0.40625 | 2.46153846153846 |
                 0 |                         1 |                1 | Of 32 rows, 32 were used and 0 were ignored
(3 rows)

The first column, decision_boundary, indicates the cut-off point for whether to classify a response as 0 or 1. For instance, for each row, if prob is greater than or equal to decision_boundary, the response is classified as 1. If prob is less than decision_boundary, the response is classified as 0.

The second column, positive_prediction_ratio, shows the percentage of samples in class 1 that the function classified correctly using the corresponding decision_boundary value.

For the third column, lift, the function divides the positive_prediction_ratio by the percentage of rows correctly or incorrectly classified as class 1.

5 - MSE

Returns a table that displays the mean squared error of the prediction and response columns in a machine learning model.

Syntax

MSE ( targets, predictions ) OVER()

Arguments

targets: The model response variable, of type FLOAT.
predictions: A FLOAT input column that contains predicted values for the response variable.

Examples

Execute the MSE function on input table faithful_testing. The response variables appear in the column obs, while the prediction variables appear in the column prediction.

=> SELECT MSE(obs, prediction) OVER()
   FROM (SELECT eruptions AS obs,
                PREDICT_LINEAR_REG (waiting USING PARAMETERS model_name='myLinearRegModel') AS prediction
         FROM faithful_testing) AS prediction_output;
        mse        |                   Comments
-------------------+-----------------------------------------------
 0.252925741352641 | Of 110 rows, 110 were used and 0 were ignored
(1 row)

6 - PRC

Returns a table that displays the points on a receiver precision recall (PR) curve.

Syntax

PRC ( targets, probabilities
       [ USING PARAMETERS
             [num_bins = num-bins]
             [, f1_score = return-score ]
             [, main_class = class-name ] )
OVER()

Arguments

targets

INTEGER: Uses the input column as containing the true value of the response variable.
BOOLEAN: Resolves Yes to 1, 0 to No.
CHAR/VARCHAR: Resolves the value specified by parameter main_class to 1, all other values to 0.

Note

If the input column is of data type INTEGER or BOOLEAN, the function ignores parameter main_class.

probabilities

A FLOAT input column that contains the predicted probability of response being the main class, set to 1 if targets is of type INTEGER.

Parameters

num_bins

Default: 100

f1_score

A Boolean that specifies whether to return a column that contains the f1 score—the harmonic average of the precision and recall measures, where an F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0.

Default: false

main_class

Used only if targets is of type CHAR/VARCHAR, specifies the class to associate with the probabilities argument.

Examples

Execute the PRC function on an input table named mtcars. The response variables appear in the column obs, while the prediction variables appear in column pred.

=> SELECT PRC(obs::int, prob::float USING PARAMETERS num_bins=2, f1_score=true) OVER()
    FROM (SELECT am AS obs,
                    PREDICT_LOGISTIC_REG (mpg, cyl, disp, drat, wt, qsec, vs, gear, carb
                          USING PARAMETERS model_name='myLogisticRegModel',
                                           type='probability') AS prob
             FROM mtcars) AS prediction_output;
decision_boundary | recall | precision |     f1_score      |     comment
------------------+--------+-----------+-------------------+--------------------------------------------
0                 |      1 |   0.40625 | 0.577777777777778 |
0.5               |      1 |         1 |                 1 | Of 32 rows, 32 were used and 0 were ignored
(2 rows)

The first column, decision_boundary, indicates the cut-off point for whether to classify a response as 0 or 1. For example, in each row, if the probability is equal to or greater than decision_boundary, the response is classified as 1. If the probability is less than decision_boundary, the response is classified as 0.

7 - READ_TREE

Reads the contents of trees within the random forest or XGBoost model.

Syntax

READ_TREE ( USING PARAMETERS model_name = 'model-name' [, tree_id = tree-id] [, format = 'format'] )

Parameters

model_name

Identifies the model that is stored as a result of training, where model-name conforms to conventions described in Identifiers. It must also be unique among all names of sequences, tables, projections, views, and models within the same schema.

tree_id

The tree identifier, an integer between 0 and n-1, where n is the number of trees in the random forest or XGBoost model. If you omit this parameter, all trees are returned.

format

Output format of the returned tree, one of the following:

tabular: Returns a table with the twelve output columns.
graphviz: Returns DOT language source that can be passed to a graphviz tool and render a graphic visualization of the tree.

Privileges

Non-superusers: USAGE privileges on the model

Examples

Get tabular output from READ_TREE for a random forest model:

=> SELECT READ_TREE ( USING PARAMETERS model_name='myRFModel', tree_id=1 ,
format= 'tabular') LIMIT 2;
-[ RECORD 1 ]-------------+-------------------
tree_id                   | 1
node_id                   | 1
node_depth                | 0
is_leaf                   | f
is_categorical_split      | f
split_predictor           | petal_length
split_value               | 1.921875
weighted_information_gain | 0.111242236024845
left_child_id             | 2
right_child_id            | 3
prediction                |
probability/variance      |

-[ RECORD 2 ]-------------+-------------------
tree_id                   | 1
node_id                   | 2
node_depth                | 1
is_leaf                   | t
is_categorical_split      |
split_predictor           |
split_value               |
weighted_information_gain |
left_child_id             |
right_child_id            |
prediction                | setosa
probability/variance      | 1

Get graphviz-formatted output from READ_TREE:

=> SELECT READ_TREE ( USING PARAMETERS model_name='myRFModel', tree_id=1 ,
format= 'graphviz')LIMIT 1;

-[ RECORD 1 ]+-------------------------------------------------------------------
---------------------------------------------------------------------------------
tree_id      | 1
tree_digraph | digraph Tree{
1 [label="petal_length < 1.921875 ?", color="blue"];
1 -> 2 [label="yes", color="black"];
1 -> 3 [label="no", color="black"];
2 [label="prediction: setosa, probability: 1", color="red"];
3 [label="petal_length < 4.871875 ?", color="blue"];
3 -> 6 [label="yes", color="black"];
3 -> 7 [label="no", color="black"];
6 [label="prediction: versicolor, probability: 1", color="red"];
7 [label="prediction: virginica, probability: 1", color="red"];
}

This renders as follows:

8 - RF_PREDICTOR_IMPORTANCE

Measures the importance of the predictors in a random forest model using the Mean Decrease Impurity (MDI) approach.

Measures the importance of the predictors in a random forest model using the Mean Decrease Impurity (MDI) approach. The importance vector is normalized to sum to 1.

Syntax

RF_PREDICTOR_IMPORTANCE ( USING PARAMETERS model_name = 'model-name' [, tree_id = tree-id] )

Parameters

model_name: Identifies the model that is stored as a result of the training, where model-name must be of type rf_classifier or rf_regressor.
tree_id: Identifies the tree to process, an integer between 0 and n-1, where n is the number of trees in the forest. If you omit this parameter, the function uses all trees to measure importance values.

Privileges

Non-superusers: USAGE privileges on the model

Examples

This example shows how you can use the RF_PREDICTOR_IMPORTANCE function.

=> SELECT RF_PREDICTOR_IMPORTANCE ( USING PARAMETERS model_name = 'myRFModel');
 predictor_index | predictor_name | importance_value
-----------------+----------------+--------------------
               0 | sepal.length   | 0.106763318092655
               1 | sepal.width    | 0.0279536658041994
               2 | petal.length   | 0.499198722346586
               3 | petal.width    | 0.366084293756561
(4 rows)

9 - ROC

Returns a table that displays the points on a receiver operating characteristic curve.

Returns a table that displays the points on a receiver operating characteristic curve. The ROC function tells you the accuracy of a classification model as you raise the discrimination threshold for the model.

Syntax

ROC ( targets, probabilities
        [ USING PARAMETERS
              [num_bins = num-bins]
              [, AUC = output]
              [, main_class = class-name ] ) ] )
OVER()

Arguments

targets

INTEGER: Uses the input column as containing the true value of the response variable.
BOOLEAN: Resolves Yes to 1, 0 to No.
CHAR/VARCHAR: Resolves the value specified by parameter main_class to 1, all other values to 0.

Note

If the input column is of data type INTEGER or BOOLEAN, the function ignores parameter main_class.

probabilities

A FLOAT input column that contains the predicted probability of response being the main class, set to 1 if targets is of type INTEGER.

Parameters

num_bins

Default: 100

Greater values result in more precise approximations of the AUC.

AUC

A Boolean value that specifies whether to output the area under the curve (AUC) value.

Default: True

main_class

Used only if targets is of type CHAR/VARCHAR, specifies the class to associate with the probabilities argument.

Examples

Execute ROC on input table mtcars. Observed class labels are in column obs, predicted class labels are in column prob:

=> SELECT ROC(obs::int, prob::float USING PARAMETERS num_bins=5, AUC = True) OVER()
    FROM (SELECT am AS obs,
          PREDICT_LOGISTIC_REG (mpg, cyl, disp, drat, wt, qsec, vs, gear, carb
               USING PARAMETERS
                  model_name='myLogisticRegModel', type='probability') AS prob
   FROM mtcars) AS prediction_output;
 decision_boundary | false_positive_rate | true_positive_rate | AUC |comment
-------------------+---------------------+--------------------+-----+-----------------------------------
0                  |                   1 |                  1 |     |
0.5                |                   0 |                  1 |     |
1                  |                   0 |                  0 |   1 | Of 32 rows,32 were used and 0 were ignoreded
(3 rows)

The function returns a table with the following results:

decision_boundary indicates the cut-off point for whether to classify a response as 0 or 1. In each row, if prob is equal to or greater than decision_boundary, the response is classified as 1. If prob is less than decision_boundary, the response is classified as 0.
false_positive_rate shows the percentage of false positives (when 0 is classified as 1) in the corresponding decision_boundary.
true_positive_rate shows the percentage of rows that were classified as 1 and also belong to class 1.

10 - RSQUARED

Returns a table with the R-squared value of the predictions in a regression model.

Syntax

RSQUARED ( targets, predictions ) OVER()

Important

The OVER() clause must be empty.

Arguments

targets: A FLOAT response variable for the model.
predictions: A FLOAT input column that contains the predicted values for the response variable.

Examples

This example shows how to execute the RSQUARED function on an input table named faithful_testing. The observed values of the response variable appear in the column, obs, while the predicted values of the response variable appear in the column, pred.

=> SELECT RSQUARED(obs, prediction) OVER()
     FROM (SELECT eruptions AS obs,
                  PREDICT_LINEAR_REG (waiting
                                       USING PARAMETERS model_name='myLinearRegModel') AS prediction
           FROM faithful_testing) AS prediction_output;
        rsq        |                    comment
-------------------+-----------------------------------------------
 0.801392981147911 | Of 110 rows, 110 were used and 0 were ignored
(1 row)

Model evaluation

1 - CONFUSION_MATRIX

Syntax

Arguments

Note

Note

Parameters

Examples

2 - CROSS_VALIDATE

Behavior type

Syntax

Arguments

Parameters

Model attributes

Privileges

Specifying metrics in JSON

Using metrics with Multi-class classifier functions

Examples

3 - ERROR_RATE

Syntax

Arguments

Note

Note

Parameters

Privileges

Examples

4 - LIFT_TABLE

Syntax

Arguments

Note

Parameters

Examples

5 - MSE

Syntax

Arguments

Examples

6 - PRC

Syntax

Arguments

Note

Parameters

Examples

7 - READ_TREE

Syntax

Parameters

Privileges

Examples

See also

8 - RF_PREDICTOR_IMPORTANCE

Syntax

Parameters

Privileges

Examples

See also

9 - ROC

Syntax

Arguments

Note

Parameters

Examples

10 - RSQUARED

Syntax

Important

Arguments

Examples