Serializable, org.apache.spark.internal.Logging, Params, HasAggregationDepth, HasElasticNetParam, HasFeaturesCol, HasFitIntercept, HasLabelCol, HasLoss, HasMaxBlockSizeInMB, HasMaxIter, HasPredictionCol, HasRegParam, HasSolver, HasStandardization, HasTol, HasWeightCol, PredictorParams, LinearRegressionParams, DefaultParamsWritable, Identifiable, MLWritable
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.
org.apache.spark.internal.Logging.LogStringContext, org.apache.spark.internal.Logging.SparkShellLoggingFilter
Constructors
Param for suggested depth for treeAggregate (>= 2).
Creates a copy of this instance with the same UID and some extra params.
Param for the ElasticNet mixing parameter, in range [0, 1].
The shape parameter to control the amount of robustness.
Param for whether to fit an intercept term.
The loss function to be optimized.
static int
When using LinearRegression.solver == "normal", the solver must limit the number of features to at most this number.
Param for Maximum memory in MB for stacking input data into blocks.
Param for maximum number of iterations (>= 0).
Param for regularization parameter (>= 0).
Suggested depth for treeAggregate (greater than or equal to 2).
Set the ElasticNet mixing parameter.
Set if we should fit the intercept.
Sets the value of param
loss()
.
Set the maximum number of iterations.
Set the regularization parameter.
Set the solver algorithm used for optimization.
Whether to standardize the training features before fitting the model.
Set the convergence tolerance of iterations.
Whether to over-/under-sample training instances according to the given weights in weightCol.
The solver algorithm for optimization.
Param for whether to standardize the training features before fitting the model.
Param for the convergence tolerance for iterative algorithms (>= 0).
An immutable unique ID for the object and its derivatives.
Param for weight column name.
Methods inherited from interface org.apache.spark.internal.LogginginitializeForcefully, initializeLogIfNecessary, initializeLogIfNecessary, initializeLogIfNecessary$default$2, isTraceEnabled, log, logDebug, logDebug, logDebug, logDebug, logError, logError, logError, logError, logInfo, logInfo, logInfo, logInfo, logName, LogStringContext, logTrace, logTrace, logTrace, logTrace, logWarning, logWarning, logWarning, logWarning, org$apache$spark$internal$Logging$$log_, org$apache$spark$internal$Logging$$log__$eq, withLogContext
Methods inherited from interface org.apache.spark.ml.util.MLWritablesave Methods inherited from interface org.apache.spark.ml.param.Paramsclear, copyValues, defaultCopy, defaultParamMap, explainParam, explainParams, extractParamMap, extractParamMap, get, getDefault, getOrDefault, getParam, hasDefault, hasParam, isDefined, isSet, onParamChange, paramMap, params, set, set, set, setDefault, setDefault, shouldOwnpublic LinearRegression()
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.
solver in interface HasSolver
solver in interface LinearRegressionParams
loss in interface HasLoss
loss in interface LinearRegressionParams
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".
epsilon in interface LinearRegressionParams
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..
maxBlockSizeInMB in interface HasMaxBlockSizeInMB
()
Param for suggested depth for treeAggregate (>= 2).
aggregationDepth in interface HasAggregationDepth
Param for weight column name. If this is not set or empty, we treat all instance weights as 1.0.
weightCol in interface HasWeightCol
Param for whether to standardize the training features before fitting the model.
standardization in interface HasStandardization
Param for whether to fit an intercept term.
fitIntercept in interface HasFitIntercept
HasTol
Param for the convergence tolerance for iterative algorithms (>= 0).
Param for maximum number of iterations (>= 0).
maxIter in interface HasMaxIter
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.
elasticNetParam in interface HasElasticNetParam
Param for regularization parameter (>= 0).
regParam in interface HasRegParam
An immutable unique ID for the object and its derivatives.
uid in interface Identifiable
value - (undocumented)
value - (undocumented)
value - (undocumented)
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.
value - (undocumented)
value - (undocumented)
value - (undocumented)
value - (undocumented)
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".
value - (undocumented)
value - (undocumented)
Sets the value of param
loss()
. Default is "squaredError".
value - (undocumented)
Sets the value of param
epsilon()
. Default is 1.35.
value - (undocumented)
value - (undocumented)
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().
copy in interface Params
copy in class Predictor<Vector,LinearRegression,LinearRegressionModel>
extra - (undocumented)
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