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
$$ \begin{align} H_m(z) = \begin{cases} z^2, & \text {if } |z| < \epsilon, \\ 2\epsilon|z| - \epsilon^2, & \text{otherwise} \end{cases} \end{align} $$
Since 3.1.0, it supports stacking instances into blocks and using GEMV for better performance. The block size will be 1.0 MB, if param maxBlockSizeInMB is set 0.0 by default.
Note: Fitting with huber loss only supports none and L2 regularization.
- Annotations
 - @Since( "1.3.0" )
 - Source
 - LinearRegression.scala
 
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        aggregationDepth: IntParam
      
      
      
Param for suggested depth for treeAggregate (>= 2).
Param for suggested depth for treeAggregate (>= 2).
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        clear(param: Param[_]): LinearRegression.this.type
      
      
      
Clears the user-supplied value for the input param.
Clears the user-supplied value for the input param.
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        copy(extra: ParamMap): LinearRegression
      
      
      
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
 - LinearRegression → Predictor → Estimator → PipelineStage → Params
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        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 toparamMap. 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
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 extra params to be copied to the target's
paramMap- returns
 the target instance with param values copied
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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.
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        elasticNetParam: DoubleParam
      
      
      
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
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        epsilon: DoubleParam
      
      
      
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
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        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
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Explains all params of this instance.
Explains all params of this instance. See
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extractParamMapwith no extra values.extractParamMapwith no extra values.- Definition Classes
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        extractParamMap(extra: ParamMap): 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.
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        featuresCol: Param[String]
      
      
      
Param for features column name.
Param for features column name.
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        def
      
      
        fit(dataset: Dataset[_]): LinearRegressionModel
      
      
      
Fits a model to the input data.
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        fit(dataset: Dataset[_], paramMaps: Seq[ParamMap]): Seq[LinearRegressionModel]
      
      
      
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
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        def
      
      
        fit(dataset: Dataset[_], paramMap: ParamMap): LinearRegressionModel
      
      
      
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
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        def
      
      
        fit(dataset: Dataset[_], firstParamPair: ParamPair[_], otherParamPairs: ParamPair[_]*): LinearRegressionModel
      
      
      
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
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        fitIntercept: BooleanParam
      
      
      
Param for whether to fit an intercept term.
Param for whether to fit an intercept term.
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Optionally returns the user-supplied value of a param.
Optionally returns the user-supplied value of a param.
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Gets the default value of a parameter.
Gets the default value of a parameter.
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        getElasticNetParam: Double
      
      
      
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        getMaxBlockSizeInMB: Double
      
      
      
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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.
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Gets a param by its name.
Gets a param by its name.
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Tests whether the input param has a default value set.
Tests whether the input param has a default value set.
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Tests whether this instance contains a param with a given name.
Tests whether this instance contains a param with a given name.
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Checks whether a param is explicitly set or has a default value.
Checks whether a param is explicitly set or has a default value.
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Checks whether a param is explicitly set.
Checks whether a param is explicitly set.
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Param for label column name.
Param for label column name.
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        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" )
 
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        final 
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        maxBlockSizeInMB: DoubleParam
      
      
      
Param for Maximum memory in MB for stacking input data into blocks.
Param for Maximum memory in MB for stacking input data into blocks. Data is stacked within partitions. If more than remaining data size in a partition then it is adjusted to the data size. Default 0.0 represents choosing optimal value, depends on specific algorithm. Must be >= 0..
- Definition Classes
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        final 
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        maxIter: IntParam
      
      
      
Param for maximum number of iterations (>= 0).
Param for maximum number of iterations (>= 0).
- Definition Classes
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        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.
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        predictionCol: Param[String]
      
      
      
Param for prediction column name.
Param for prediction column name.
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        final 
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        regParam: DoubleParam
      
      
      
Param for regularization parameter (>= 0).
Param for regularization parameter (>= 0).
- Definition Classes
 - HasRegParam
 
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        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
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        final 
        def
      
      
        set(paramPair: ParamPair[_]): LinearRegression.this.type
      
      
      
Sets a parameter in the embedded param map.
Sets a parameter in the embedded param map.
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        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
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        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
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        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" )
 
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        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
 
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        final 
        def
      
      
        setDefault[T](param: Param[T], value: T): LinearRegression.this.type
      
      
      
Sets a default value for a param.
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        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" )
 
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        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" )
 
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        def
      
      
        setFeaturesCol(value: String): LinearRegression
      
      
      
- Definition Classes
 - Predictor
 
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        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" )
 
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        def
      
      
        setLabelCol(value: String): LinearRegression
      
      
      
- Definition Classes
 - Predictor
 
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        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" )
 
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        def
      
      
        setMaxBlockSizeInMB(value: Double): LinearRegression.this.type
      
      
      
Sets the value of param maxBlockSizeInMB.
Sets the value of param maxBlockSizeInMB. Default is 0.0, then 1.0 MB will be chosen.
- Annotations
 - @Since( "3.1.0" )
 
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        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" )
 
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        def
      
      
        setPredictionCol(value: String): LinearRegression
      
      
      
- Definition Classes
 - Predictor
 
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        def
      
      
        setRegParam(value: Double): LinearRegression.this.type
      
      
      
Set the regularization parameter.
Set the regularization parameter. Default is 0.0.
- Annotations
 - @Since( "1.3.0" )
 
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        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" )
 
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        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.
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        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" )
 
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        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" )
 
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        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" )
 
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        final 
        val
      
      
        standardization: BooleanParam
      
      
      
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
 
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        final 
        def
      
      
        synchronized[T0](arg0: ⇒ T0): T0
      
      
      
- Definition Classes
 - AnyRef
 
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        def
      
      
        toString(): String
      
      
      
- Definition Classes
 - Identifiable → AnyRef → Any
 
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        final 
        val
      
      
        tol: DoubleParam
      
      
      
Param for the convergence tolerance for iterative algorithms (>= 0).
Param for the convergence tolerance for iterative algorithms (>= 0).
- Definition Classes
 - HasTol
 
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        def
      
      
        train(dataset: Dataset[_]): LinearRegressionModel
      
      
      
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
 - LinearRegression → Predictor
 
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        def
      
      
        transformSchema(schema: StructType): 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
transformSchemaand raise an exception if any parameter value is invalid. Parameter value checks which do not depend on other parameters are handled byParam.validate().Typical implementation should first conduct verification on schema change and parameter validity, including complex parameter interaction checks.
- Definition Classes
 - Predictor → PipelineStage
 
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        def
      
      
        transformSchema(schema: StructType, logging: Boolean): StructType
      
      
      
:: 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()
 
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        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
 - LinearRegression → Identifiable
 - Annotations
 - @Since( "1.3.0" )
 
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        def
      
      
        validateAndTransformSchema(schema: StructType, fitting: Boolean, featuresDataType: DataType): StructType
      
      
      
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.,
VectorUDTfor vector features.- returns
 output schema
- Attributes
 - protected
 - Definition Classes
 - LinearRegressionParams → PredictorParams
 
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        final 
        def
      
      
        wait(): Unit
      
      
      
- Definition Classes
 - AnyRef
 - Annotations
 - @throws( ... )
 
 - 
      
      
      
        
      
    
      
        final 
        def
      
      
        wait(arg0: Long, arg1: Int): Unit
      
      
      
- Definition Classes
 - AnyRef
 - Annotations
 - @throws( ... )
 
 - 
      
      
      
        
      
    
      
        final 
        def
      
      
        wait(arg0: Long): Unit
      
      
      
- Definition Classes
 - AnyRef
 - Annotations
 - @throws( ... ) @native()
 
 - 
      
      
      
        
      
    
      
        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
 
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        def
      
      
        write: MLWriter
      
      
      
Returns an
MLWriterinstance for this ML instance.Returns an
MLWriterinstance for this ML instance.- Definition Classes
 - DefaultParamsWritable → MLWritable
 
 
Inherited from DefaultParamsWritable
Inherited from MLWritable
Inherited from LinearRegressionParams
Inherited from HasMaxBlockSizeInMB
Inherited from HasLoss
Inherited from HasAggregationDepth
Inherited from HasSolver
Inherited from HasWeightCol
Inherited from HasStandardization
Inherited from HasFitIntercept
Inherited from HasTol
Inherited from HasMaxIter
Inherited from HasElasticNetParam
Inherited from HasRegParam
Inherited from Regressor[Vector, LinearRegression, LinearRegressionModel]
Inherited from Predictor[Vector, LinearRegression, LinearRegressionModel]
Inherited from PredictorParams
Inherited from HasPredictionCol
Inherited from HasFeaturesCol
Inherited from HasLabelCol
Inherited from Estimator[LinearRegressionModel]
Inherited from PipelineStage
Inherited from Logging
Inherited from Params
Inherited from Serializable
Inherited from Serializable
Inherited from Identifiable
Inherited from AnyRef
Inherited from Any
Parameters
A list of (hyper-)parameter keys this algorithm can take. Users can set and get the parameter values through setters and getters, respectively.
Members
getExpertParam
setExpertParam
Parameter setters
Parameter getters
(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.