org.apache.spark.ml.regression

## Class LinearRegression

• All Implemented Interfaces:
java.io.Serializable, Logging, Params, HasAggregationDepth, HasElasticNetParam, HasFeaturesCol, HasFitIntercept, HasLabelCol, HasLoss, HasMaxIter, HasPredictionCol, HasRegParam, HasSolver, HasStandardization, HasTol, HasWeightCol, PredictorParams, LinearRegressionParams, DefaultParamsWritable, Identifiable, MLWritable

public class LinearRegression
extends Predictor<FeaturesType,Learner,M>
implements LinearRegressionParams, DefaultParamsWritable, 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| &lt; \epsilon, \\ 2\epsilon|z| - \epsilon^2, & \text{otherwise} \end{cases} \end{align}

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

Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
LinearRegression()
LinearRegression(String uid)
• ### Method Summary

All Methods
Modifier and Type Method and Description
LinearRegression copy(ParamMap extra)
Creates a copy of this instance with the same UID and some extra params.
static LinearRegression load(String path)
static int MAX_FEATURES_FOR_NORMAL_SOLVER()
When using LinearRegression.solver == "normal", the solver must limit the number of features to at most this number.
static MLReader<T> read()
LinearRegression setAggregationDepth(int value)
Suggested depth for treeAggregate (greater than or equal to 2).
LinearRegression setElasticNetParam(double value)
Set the ElasticNet mixing parameter.
LinearRegression setEpsilon(double value)
Sets the value of param epsilon.
LinearRegression setFitIntercept(boolean value)
Set if we should fit the intercept.
LinearRegression setLoss(String value)
Sets the value of param loss.
LinearRegression setMaxIter(int value)
Set the maximum number of iterations.
LinearRegression setRegParam(double value)
Set the regularization parameter.
LinearRegression setSolver(String value)
Set the solver algorithm used for optimization.
LinearRegression setStandardization(boolean value)
Whether to standardize the training features before fitting the model.
LinearRegression setTol(double value)
Set the convergence tolerance of iterations.
LinearRegression setWeightCol(String value)
Whether to over-/under-sample training instances according to the given weights in weightCol.
String uid()
An immutable unique ID for the object and its derivatives.
• ### Methods inherited from class org.apache.spark.ml.Predictor

fit, setFeaturesCol, setLabelCol, setPredictionCol, transformSchema
• ### Methods inherited from class org.apache.spark.ml.Estimator

fit, fit, fit, fit
• ### Methods inherited from class Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface org.apache.spark.ml.regression.LinearRegressionParams

epsilon, getEpsilon, loss, solver, validateAndTransformSchema
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasLabelCol

getLabelCol, labelCol
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasFeaturesCol

featuresCol, getFeaturesCol
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasPredictionCol

getPredictionCol, predictionCol
• ### Methods inherited from interface org.apache.spark.ml.param.Params

clear, copyValues, defaultCopy, defaultParamMap, explainParam, explainParams, extractParamMap, extractParamMap, get, getDefault, getOrDefault, getParam, hasDefault, hasParam, isDefined, isSet, paramMap, params, set, set, set, setDefault, setDefault, shouldOwn
• ### Methods inherited from interface org.apache.spark.ml.util.Identifiable

toString
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasRegParam

getRegParam, regParam
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasElasticNetParam

elasticNetParam, getElasticNetParam
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasMaxIter

getMaxIter, maxIter
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasTol

getTol, tol
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasFitIntercept

fitIntercept, getFitIntercept
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasStandardization

getStandardization, standardization
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasWeightCol

getWeightCol, weightCol
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasSolver

getSolver
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasAggregationDepth

aggregationDepth, getAggregationDepth
• ### Methods inherited from interface org.apache.spark.ml.param.shared.HasLoss

getLoss
• ### Methods inherited from interface org.apache.spark.ml.util.DefaultParamsWritable

write
• ### Methods inherited from interface org.apache.spark.ml.util.MLWritable

save
• ### Methods inherited from interface org.apache.spark.internal.Logging

initializeLogging, initializeLogIfNecessary, initializeLogIfNecessary, isTraceEnabled, log_, log, logDebug, logDebug, logError, logError, logInfo, logInfo, logName, logTrace, logTrace, logWarning, logWarning
• ### Constructor Detail

• #### LinearRegression

public LinearRegression(String uid)
• #### LinearRegression

public LinearRegression()
• ### Method Detail

public static LinearRegression load(String path)
• #### MAX_FEATURES_FOR_NORMAL_SOLVER

public static int MAX_FEATURES_FOR_NORMAL_SOLVER()
When using LinearRegression.solver == "normal", the solver must limit the number of features to at most this number. The entire covariance matrix X^T^X will be collected to the driver. This limit helps prevent memory overflow errors.
Returns:
(undocumented)

public static MLReader<T> read()
• #### uid

public String uid()
Description copied from interface: Identifiable
An immutable unique ID for the object and its derivatives.
Specified by:
uid in interface Identifiable
Returns:
(undocumented)
• #### setRegParam

public LinearRegression setRegParam(double value)
Set the regularization parameter. Default is 0.0.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setFitIntercept

public LinearRegression setFitIntercept(boolean value)
Set if we should fit the intercept. Default is true.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setStandardization

public LinearRegression setStandardization(boolean value)
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.

Parameters:
value - (undocumented)
Returns:
(undocumented)
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.

• #### setElasticNetParam

public LinearRegression setElasticNetParam(double value)
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.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setMaxIter

public LinearRegression setMaxIter(int value)
Set the maximum number of iterations. Default is 100.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setTol

public LinearRegression setTol(double value)
Set the convergence tolerance of iterations. Smaller value will lead to higher accuracy with the cost of more iterations. Default is 1E-6.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setWeightCol

public LinearRegression setWeightCol(String value)
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.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setSolver

public LinearRegression setSolver(String value)
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".

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setAggregationDepth

public LinearRegression setAggregationDepth(int value)
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.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setLoss

public LinearRegression setLoss(String value)
Sets the value of param loss. Default is "squaredError".

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### setEpsilon

public LinearRegression setEpsilon(double value)
Sets the value of param epsilon. Default is 1.35.

Parameters:
value - (undocumented)
Returns:
(undocumented)
• #### copy

public LinearRegression copy(ParamMap extra)
Description copied from interface: 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().
Specified by:
copy in interface Params
Specified by:
copy in class Predictor<Vector,LinearRegression,LinearRegressionModel>
Parameters:
extra - (undocumented)
Returns:
(undocumented)