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# LinearRegression 

### Companion object LinearRegression

#### class LinearRegression extends Regressor[Vector, LinearRegression, LinearRegressionModel] with LinearRegressionParams with DefaultParamsWritable with Logging

Linear regression.

The learning objective is to minimize the specified loss function, with regularization. This supports two kinds of loss:

• squaredError (a.k.a squared loss)
• huber (a hybrid of squared error for relatively small errors and absolute error for relatively large ones, and we estimate the scale parameter from training data)

This supports multiple types of regularization:

• none (a.k.a. ordinary least squares)
• L2 (ridge regression)
• L1 (Lasso)
• L2 + L1 (elastic net)

The squared error objective function is:

\begin{align} \min_{w}\frac{1}{2n}{\sum_{i=1}^n(X_{i}w - y_{i})^{2} + \lambda\left[\frac{1-\alpha}{2}{||w||_{2}}^{2} + \alpha{||w||_{1}}\right]} \end{align}

The huber objective function is:

\begin{align} \min_{w, \sigma}\frac{1}{2n}{\sum_{i=1}^n\left(\sigma + H_m\left(\frac{X_{i}w - y_{i}}{\sigma}\right)\sigma\right) + \frac{1}{2}\lambda {||w||_2}^2} \end{align}

where

\begin{align} H_m(z) = \begin{cases} z^2, & \text {if } |z| < \epsilon, \\ 2\epsilon|z| - \epsilon^2, & \text{otherwise} \end{cases} \end{align}

Note: Fitting with huber loss only supports none and L2 regularization.

Annotations
@Since( "1.3.0" )
Source
LinearRegression.scala
Ordering
1. Grouped
2. Alphabetic
3. By Inheritance
Inherited
1. LinearRegression
2. DefaultParamsWritable
3. MLWritable
4. LinearRegressionParams
5. HasLoss
6. HasAggregationDepth
7. HasSolver
8. HasWeightCol
9. HasStandardization
10. HasFitIntercept
11. HasTol
12. HasMaxIter
13. HasElasticNetParam
14. HasRegParam
15. Regressor
16. Predictor
17. PredictorParams
18. HasPredictionCol
19. HasFeaturesCol
20. HasLabelCol
21. Estimator
22. PipelineStage
23. Logging
24. Params
25. Serializable
26. Serializable
27. Identifiable
28. AnyRef
29. Any
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Visibility
1. Public
2. All

### Instance Constructors

1. new LinearRegression()
Annotations
@Since( "1.4.0" )
2. new LinearRegression(uid: String)
Annotations
@Since( "1.3.0" )

### Value Members

1. final def !=(arg0: Any): Boolean
Definition Classes
AnyRef → Any
2. final def ##(): Int
Definition Classes
AnyRef → Any
3. final def \$[T](param: Param[T]): T

An alias for getOrDefault().

An alias for getOrDefault().

Attributes
protected
Definition Classes
Params
4. final def ==(arg0: Any): Boolean
Definition Classes
AnyRef → Any
5. final val aggregationDepth

Param for suggested depth for treeAggregate (>= 2).

Param for suggested depth for treeAggregate (>= 2).

Definition Classes
HasAggregationDepth
6. final def asInstanceOf[T0]: T0
Definition Classes
Any
7. final def clear(param: Param[_]): LinearRegression.this.type

Clears the user-supplied value for the input param.

Clears the user-supplied value for the input param.

Definition Classes
Params
8. def clone()
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws( ... ) @native()
9. def copy(extra: ParamMap)

Creates a copy of this instance with the same UID and some extra params.

Creates a copy of this instance with the same UID and some extra params. Subclasses should implement this method and set the return type properly. See defaultCopy().

Definition Classes
LinearRegressionPredictorEstimatorPipelineStageParams
Annotations
@Since( "1.4.0" )
10. def copyValues[T <: Params](to: T, extra: ParamMap = ParamMap.empty): T

Copies param values from this instance to another instance for params shared by them.

Copies param values from this instance to another instance for params shared by them.

This handles default Params and explicitly set Params separately. Default Params are copied from and to defaultParamMap, and explicitly set Params are copied from and to paramMap. Warning: This implicitly assumes that this Params instance and the target instance share the same set of default Params.

to

the target instance, which should work with the same set of default Params as this source instance

extra

extra params to be copied to the target's paramMap

returns

the target instance with param values copied

Attributes
protected
Definition Classes
Params
11. final def defaultCopy[T <: Params](extra: ParamMap): T

Default implementation of copy with extra params.

Default implementation of copy with extra params. It tries to create a new instance with the same UID. Then it copies the embedded and extra parameters over and returns the new instance.

Attributes
protected
Definition Classes
Params
12. final val elasticNetParam

Param for the ElasticNet mixing parameter, in range [0, 1].

Param for the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty.

Definition Classes
HasElasticNetParam
13. final val epsilon

The shape parameter to control the amount of robustness.

The shape parameter to control the amount of robustness. Must be > 1.0. At larger values of epsilon, the huber criterion becomes more similar to least squares regression; for small values of epsilon, the criterion is more similar to L1 regression. Default is 1.35 to get as much robustness as possible while retaining 95% statistical efficiency for normally distributed data. It matches sklearn HuberRegressor and is "M" from A robust hybrid of lasso and ridge regression. Only valid when "loss" is "huber".

Definition Classes
LinearRegressionParams
Annotations
@Since( "2.3.0" )
14. final def eq(arg0: AnyRef): Boolean
Definition Classes
AnyRef
15. def equals(arg0: Any): Boolean
Definition Classes
AnyRef → Any
16. def explainParam(param: Param[_]): String

Explains a param.

Explains a param.

param

input param, must belong to this instance.

returns

a string that contains the input param name, doc, and optionally its default value and the user-supplied value

Definition Classes
Params
17. def explainParams(): String

Explains all params of this instance.

Explains all params of this instance. See explainParam().

Definition Classes
Params
18. def extractInstances(dataset: Dataset[_], validateInstance: (Instance) ⇒ Unit): RDD[Instance]

Extract labelCol, weightCol(if any) and featuresCol from the given dataset, and put it in an RDD with strong types.

Extract labelCol, weightCol(if any) and featuresCol from the given dataset, and put it in an RDD with strong types. Validate the output instances with the given function.

Attributes
protected
Definition Classes
PredictorParams
19. def extractInstances(dataset: Dataset[_]): RDD[Instance]

Extract labelCol, weightCol(if any) and featuresCol from the given dataset, and put it in an RDD with strong types.

Extract labelCol, weightCol(if any) and featuresCol from the given dataset, and put it in an RDD with strong types.

Attributes
protected
Definition Classes
PredictorParams
20. def extractLabeledPoints(dataset: Dataset[_])

Extract labelCol and featuresCol from the given dataset, and put it in an RDD with strong types.

Extract labelCol and featuresCol from the given dataset, and put it in an RDD with strong types.

Attributes
protected
Definition Classes
Predictor
21. final def extractParamMap()

extractParamMap with no extra values.

extractParamMap with no extra values.

Definition Classes
Params
22. final def extractParamMap(extra: ParamMap)

Extracts the embedded default param values and user-supplied values, and then merges them with extra values from input into a flat param map, where the latter value is used if there exist conflicts, i.e., with ordering: default param values less than user-supplied values less than extra.

Extracts the embedded default param values and user-supplied values, and then merges them with extra values from input into a flat param map, where the latter value is used if there exist conflicts, i.e., with ordering: default param values less than user-supplied values less than extra.

Definition Classes
Params
23. final val featuresCol: Param[String]

Param for features column name.

Param for features column name.

Definition Classes
HasFeaturesCol
24. def finalize(): Unit
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
25. def fit(dataset: Dataset[_])

Fits a model to the input data.

Fits a model to the input data.

Definition Classes
PredictorEstimator
26. def fit(dataset: Dataset[_], paramMaps: Array[ParamMap])

Fits multiple models to the input data with multiple sets of parameters.

Fits multiple models to the input data with multiple sets of parameters. The default implementation uses a for loop on each parameter map. Subclasses could override this to optimize multi-model training.

dataset

input dataset

paramMaps

An array of parameter maps. These values override any specified in this Estimator's embedded ParamMap.

returns

fitted models, matching the input parameter maps

Definition Classes
Estimator
Annotations
@Since( "2.0.0" )
27. def fit(dataset: Dataset[_], paramMap: ParamMap)

Fits a single model to the input data with provided parameter map.

Fits a single model to the input data with provided parameter map.

dataset

input dataset

paramMap

Parameter map. These values override any specified in this Estimator's embedded ParamMap.

returns

fitted model

Definition Classes
Estimator
Annotations
@Since( "2.0.0" )
28. def fit(dataset: Dataset[_], firstParamPair: ParamPair[_], otherParamPairs: ParamPair[_]*)

Fits a single model to the input data with optional parameters.

Fits a single model to the input data with optional parameters.

dataset

input dataset

firstParamPair

the first param pair, overrides embedded params

otherParamPairs

other param pairs. These values override any specified in this Estimator's embedded ParamMap.

returns

fitted model

Definition Classes
Estimator
Annotations
@Since( "2.0.0" ) @varargs()
29. final val fitIntercept

Param for whether to fit an intercept term.

Param for whether to fit an intercept term.

Definition Classes
HasFitIntercept
30. final def get[T](param: Param[T]): Option[T]

Optionally returns the user-supplied value of a param.

Optionally returns the user-supplied value of a param.

Definition Classes
Params
31. final def getAggregationDepth: Int

Definition Classes
HasAggregationDepth
32. final def getClass(): Class[_]
Definition Classes
AnyRef → Any
Annotations
@native()
33. final def getDefault[T](param: Param[T]): Option[T]

Gets the default value of a parameter.

Gets the default value of a parameter.

Definition Classes
Params
34. final def getElasticNetParam: Double

Definition Classes
HasElasticNetParam
35. def getEpsilon: Double

Definition Classes
LinearRegressionParams
Annotations
@Since( "2.3.0" )
36. final def getFeaturesCol: String

Definition Classes
HasFeaturesCol
37. final def getFitIntercept: Boolean

Definition Classes
HasFitIntercept
38. final def getLabelCol: String

Definition Classes
HasLabelCol
39. final def getLoss: String

Definition Classes
HasLoss
40. final def getMaxIter: Int

Definition Classes
HasMaxIter
41. final def getOrDefault[T](param: Param[T]): T

Gets the value of a param in the embedded param map or its default value.

Gets the value of a param in the embedded param map or its default value. Throws an exception if neither is set.

Definition Classes
Params
42. def getParam(paramName: String): Param[Any]

Gets a param by its name.

Gets a param by its name.

Definition Classes
Params
43. final def getPredictionCol: String

Definition Classes
HasPredictionCol
44. final def getRegParam: Double

Definition Classes
HasRegParam
45. final def getSolver: String

Definition Classes
HasSolver
46. final def getStandardization: Boolean

Definition Classes
HasStandardization
47. final def getTol: Double

Definition Classes
HasTol
48. final def getWeightCol: String

Definition Classes
HasWeightCol
49. final def hasDefault[T](param: Param[T]): Boolean

Tests whether the input param has a default value set.

Tests whether the input param has a default value set.

Definition Classes
Params
50. def hasParam(paramName: String): Boolean

Tests whether this instance contains a param with a given name.

Tests whether this instance contains a param with a given name.

Definition Classes
Params
51. def hashCode(): Int
Definition Classes
AnyRef → Any
Annotations
@native()
52. def initializeLogIfNecessary(isInterpreter: Boolean, silent: Boolean): Boolean
Attributes
protected
Definition Classes
Logging
53. def initializeLogIfNecessary(isInterpreter: Boolean): Unit
Attributes
protected
Definition Classes
Logging
54. final def isDefined(param: Param[_]): Boolean

Checks whether a param is explicitly set or has a default value.

Checks whether a param is explicitly set or has a default value.

Definition Classes
Params
55. final def isInstanceOf[T0]: Boolean
Definition Classes
Any
56. final def isSet(param: Param[_]): Boolean

Checks whether a param is explicitly set.

Checks whether a param is explicitly set.

Definition Classes
Params
57. def isTraceEnabled(): Boolean
Attributes
protected
Definition Classes
Logging
58. final val labelCol: Param[String]

Param for label column name.

Param for label column name.

Definition Classes
HasLabelCol
59. def log: Logger
Attributes
protected
Definition Classes
Logging
60. def logDebug(msg: ⇒ String, throwable: Throwable): Unit
Attributes
protected
Definition Classes
Logging
61. def logDebug(msg: ⇒ String): Unit
Attributes
protected
Definition Classes
Logging
62. def logError(msg: ⇒ String, throwable: Throwable): Unit
Attributes
protected
Definition Classes
Logging
63. def logError(msg: ⇒ String): Unit
Attributes
protected
Definition Classes
Logging
64. def logInfo(msg: ⇒ String, throwable: Throwable): Unit
Attributes
protected
Definition Classes
Logging
65. def logInfo(msg: ⇒ String): Unit
Attributes
protected
Definition Classes
Logging
66. def logName: String
Attributes
protected
Definition Classes
Logging
67. def logTrace(msg: ⇒ String, throwable: Throwable): Unit
Attributes
protected
Definition Classes
Logging
68. def logTrace(msg: ⇒ String): Unit
Attributes
protected
Definition Classes
Logging
69. def logWarning(msg: ⇒ String, throwable: Throwable): Unit
Attributes
protected
Definition Classes
Logging
70. def logWarning(msg: ⇒ String): Unit
Attributes
protected
Definition Classes
Logging
71. final val loss: Param[String]

The loss function to be optimized.

The loss function to be optimized. Supported options: "squaredError" and "huber". Default: "squaredError"

Definition Classes
LinearRegressionParams → HasLoss
Annotations
@Since( "2.3.0" )
72. final val maxIter

Param for maximum number of iterations (>= 0).

Param for maximum number of iterations (>= 0).

Definition Classes
HasMaxIter
73. final def ne(arg0: AnyRef): Boolean
Definition Classes
AnyRef
74. final def notify(): Unit
Definition Classes
AnyRef
Annotations
@native()
75. final def notifyAll(): Unit
Definition Classes
AnyRef
Annotations
@native()
76. lazy val params: Array[Param[_]]

Returns all params sorted by their names.

Returns all params sorted by their names. The default implementation uses Java reflection to list all public methods that have no arguments and return Param.

Definition Classes
Params
Note

Developer should not use this method in constructor because we cannot guarantee that this variable gets initialized before other params.

77. final val predictionCol: Param[String]

Param for prediction column name.

Param for prediction column name.

Definition Classes
HasPredictionCol
78. final val regParam

Param for regularization parameter (>= 0).

Param for regularization parameter (>= 0).

Definition Classes
HasRegParam
79. def save(path: String): Unit

Saves this ML instance to the input path, a shortcut of write.save(path).

Saves this ML instance to the input path, a shortcut of write.save(path).

Definition Classes
MLWritable
Annotations
@Since( "1.6.0" ) @throws( ... )
80. final def set(paramPair: ParamPair[_]): LinearRegression.this.type

Sets a parameter in the embedded param map.

Sets a parameter in the embedded param map.

Attributes
protected
Definition Classes
Params
81. final def set(param: String, value: Any): LinearRegression.this.type

Sets a parameter (by name) in the embedded param map.

Sets a parameter (by name) in the embedded param map.

Attributes
protected
Definition Classes
Params
82. final def set[T](param: Param[T], value: T): LinearRegression.this.type

Sets a parameter in the embedded param map.

Sets a parameter in the embedded param map.

Definition Classes
Params
83. def setAggregationDepth(value: Int): LinearRegression.this.type

Suggested depth for treeAggregate (greater than or equal to 2).

Suggested depth for treeAggregate (greater than or equal to 2). If the dimensions of features or the number of partitions are large, this param could be adjusted to a larger size. Default is 2.

Annotations
@Since( "2.1.0" )
84. final def setDefault(paramPairs: ParamPair[_]*): LinearRegression.this.type

Sets default values for a list of params.

Sets default values for a list of params.

Note: Java developers should use the single-parameter setDefault. Annotating this with varargs can cause compilation failures due to a Scala compiler bug. See SPARK-9268.

paramPairs

a list of param pairs that specify params and their default values to set respectively. Make sure that the params are initialized before this method gets called.

Attributes
protected
Definition Classes
Params
85. final def setDefault[T](param: Param[T], value: T): LinearRegression.this.type

Sets a default value for a param.

Sets a default value for a param.

param

param to set the default value. Make sure that this param is initialized before this method gets called.

value

the default value

Attributes
protected
Definition Classes
Params
86. def setElasticNetParam(value: Double): LinearRegression.this.type

Set the ElasticNet mixing parameter.

Set the ElasticNet mixing parameter. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty. For alpha in (0,1), the penalty is a combination of L1 and L2. Default is 0.0 which is an L2 penalty.

Note: Fitting with huber loss only supports None and L2 regularization, so throws exception if this param is non-zero value.

Annotations
@Since( "1.4.0" )
87. def setEpsilon(value: Double): LinearRegression.this.type

Sets the value of param epsilon.

Sets the value of param epsilon. Default is 1.35.

Annotations
@Since( "2.3.0" )
88. def setFeaturesCol(value: String)

Definition Classes
Predictor
89. def setFitIntercept(value: Boolean): LinearRegression.this.type

Set if we should fit the intercept.

Set if we should fit the intercept. Default is true.

Annotations
@Since( "1.5.0" )
90. def setLabelCol(value: String)

Definition Classes
Predictor
91. def setLoss(value: String): LinearRegression.this.type

Sets the value of param loss.

Sets the value of param loss. Default is "squaredError".

Annotations
@Since( "2.3.0" )
92. def setMaxIter(value: Int): LinearRegression.this.type

Set the maximum number of iterations.

Set the maximum number of iterations. Default is 100.

Annotations
@Since( "1.3.0" )
93. def setPredictionCol(value: String)

Definition Classes
Predictor
94. def setRegParam(value: Double): LinearRegression.this.type

Set the regularization parameter.

Set the regularization parameter. Default is 0.0.

Annotations
@Since( "1.3.0" )
95. def setSolver(value: String): LinearRegression.this.type

Set the solver algorithm used for optimization.

Set the solver algorithm used for optimization. In case of linear regression, this can be "l-bfgs", "normal" and "auto".

• "l-bfgs" denotes Limited-memory BFGS which is a limited-memory quasi-Newton optimization method.
• "normal" denotes using Normal Equation as an analytical solution to the linear regression problem. This solver is limited to LinearRegression.MAX_FEATURES_FOR_NORMAL_SOLVER.
• "auto" (default) means that the solver algorithm is selected automatically. The Normal Equations solver will be used when possible, but this will automatically fall back to iterative optimization methods when needed.

Note: Fitting with huber loss doesn't support normal solver, so throws exception if this param was set with "normal".

Annotations
@Since( "1.6.0" )
96. def setStandardization(value: Boolean): LinearRegression.this.type

Whether to standardize the training features before fitting the model.

Whether to standardize the training features before fitting the model. The coefficients of models will be always returned on the original scale, so it will be transparent for users. Default is true.

Annotations
@Since( "1.5.0" )
Note

With/without standardization, the models should be always converged to the same solution when no regularization is applied. In R's GLMNET package, the default behavior is true as well.

97. def setTol(value: Double): LinearRegression.this.type

Set the convergence tolerance of iterations.

Set the convergence tolerance of iterations. Smaller value will lead to higher accuracy with the cost of more iterations. Default is 1E-6.

Annotations
@Since( "1.4.0" )
98. def setWeightCol(value: String): LinearRegression.this.type

Whether to over-/under-sample training instances according to the given weights in weightCol.

Whether to over-/under-sample training instances according to the given weights in weightCol. If not set or empty, all instances are treated equally (weight 1.0). Default is not set, so all instances have weight one.

Annotations
@Since( "1.6.0" )
99. final val solver: Param[String]

The solver algorithm for optimization.

The solver algorithm for optimization. Supported options: "l-bfgs", "normal" and "auto". Default: "auto"

Definition Classes
LinearRegressionParams → HasSolver
Annotations
@Since( "1.6.0" )
100. final val standardization

Param for whether to standardize the training features before fitting the model.

Param for whether to standardize the training features before fitting the model.

Definition Classes
HasStandardization
101. final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
102. def toString(): String
Definition Classes
Identifiable → AnyRef → Any
103. final val tol

Param for the convergence tolerance for iterative algorithms (>= 0).

Param for the convergence tolerance for iterative algorithms (>= 0).

Definition Classes
HasTol
104. def train(dataset: Dataset[_])

Train a model using the given dataset and parameters.

Train a model using the given dataset and parameters. Developers can implement this instead of fit() to avoid dealing with schema validation and copying parameters into the model.

dataset

Training dataset

returns

Fitted model

Attributes
protected
Definition Classes
LinearRegressionPredictor
105. def transformSchema(schema: StructType)

Check transform validity and derive the output schema from the input schema.

Check transform validity and derive the output schema from the input schema.

We check validity for interactions between parameters during transformSchema and raise an exception if any parameter value is invalid. Parameter value checks which do not depend on other parameters are handled by Param.validate().

Typical implementation should first conduct verification on schema change and parameter validity, including complex parameter interaction checks.

Definition Classes
PredictorPipelineStage
106. def transformSchema(schema: StructType, logging: Boolean)

:: DeveloperApi ::

:: DeveloperApi ::

Derives the output schema from the input schema and parameters, optionally with logging.

This should be optimistic. If it is unclear whether the schema will be valid, then it should be assumed valid until proven otherwise.

Attributes
protected
Definition Classes
PipelineStage
Annotations
@DeveloperApi()
107. val uid: String

An immutable unique ID for the object and its derivatives.

An immutable unique ID for the object and its derivatives.

Definition Classes
LinearRegressionIdentifiable
Annotations
@Since( "1.3.0" )
108. def validateAndTransformSchema(schema: StructType, fitting: Boolean, featuresDataType: DataType)

Validates and transforms the input schema with the provided param map.

Validates and transforms the input schema with the provided param map.

schema

input schema

fitting

whether this is in fitting

featuresDataType

SQL DataType for FeaturesType. E.g., VectorUDT for vector features.

returns

output schema

Attributes
protected
Definition Classes
LinearRegressionParams → PredictorParams
109. final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
110. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
111. final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
@throws( ... ) @native()
112. final val weightCol: Param[String]

Param for weight column name.

Param for weight column name. If this is not set or empty, we treat all instance weights as 1.0.

Definition Classes
HasWeightCol
113. def write

Returns an MLWriter instance for this ML instance.

Returns an MLWriter instance for this ML instance.

Definition Classes
DefaultParamsWritableMLWritable

### Parameters

A list of (hyper-)parameter keys this algorithm can take. Users can set and get the parameter values through setters and getters, respectively.

### (expert-only) Parameters

A list of advanced, expert-only (hyper-)parameter keys this algorithm can take. Users can set and get the parameter values through setters and getters, respectively.