LinearRegressor.newton constructor

LinearRegressor.newton(DataFrame trainData, String targetName, { double lambda = lambdaDefaultValue, bool fitIntercept = fitInterceptDefaultValue, double interceptScale = interceptScaleDefaultValue, bool collectLearningData = collectLearningDataDefaultValue, DType dtype = dTypeDefaultValue, Matrix? initialCoefficients, })

Linear regression with Newton-Raphson optimization and L2 regularization

The application of Newton-Raphson method for Ordinary Least Squares problem isn't iterative, it converges for one iteration and it's completely equal to the Closed-Form solution (LinearOptimizerType.closedForm). The only difference is the possibility to regularize the coefficients.

Parameters:

trainData A DataFrame with observations that is used by the regressor to learn coefficients of the predicting hyperplane. Must contain targetName column.

targetName A string that serves as a name of the target column containing observation labels.

lambda L2 regularization coefficient. Uses to prevent the regressor's overfitting. The greater the value of lambda, the more regular the coefficients are. Extremely large lambda may decrease the coefficients to nothing, otherwise too small lambda may be a cause of too large absolute values of the coefficients.

fitIntercept Whether or not to fit intercept term. Default value is false. Intercept in 2-dimensional space is a bias of the line (relative to X-axis).

interceptScale A value defining a size of the intercept.

initialCoefficients Coefficients to be used during the first iteration of optimization algorithm. initialCoefficients should have length that is equal to the number of features in the trainData.

collectLearningData Whether or not to collect learning data, for instance cost function value per each iteration. Affects performance much. If collectLearningData is true, one may access costPerIteration getter in order to evaluate learning process more thoroughly.

dtype A data type for all the numeric values, used by the algorithm. Can affect performance or accuracy of the computations. Default value is DType.float32.

Implementation

factory LinearRegressor.newton(
  DataFrame trainData,
  String targetName, {
  double lambda = lambdaDefaultValue,
  bool fitIntercept = fitInterceptDefaultValue,
  double interceptScale = interceptScaleDefaultValue,
  bool collectLearningData = collectLearningDataDefaultValue,
  DType dtype = dTypeDefaultValue,
  Matrix? initialCoefficients,
}) =>
    initLinearRegressorModule().get<LinearRegressorFactory>().create(
          fittingData: trainData,
          targetName: targetName,
          optimizerType: LinearOptimizerType.newton,
          iterationsLimit: 1,
          learningRateType: learningRateTypeDefaultValue,
          initialCoefficientsType: InitialCoefficientsType.zeroes,
          initialLearningRate: initialLearningRateDefaultValue,
          decay: decayDefaultValue,
          dropRate: dropRateDefaultValue,
          minCoefficientsUpdate: minCoefficientsUpdateDefaultValue,
          lambda: lambda,
          regularizationType: RegularizationType.L2,
          fitIntercept: fitIntercept,
          interceptScale: interceptScale,
          randomSeed: 1,
          batchSize: 1,
          initialCoefficients: initialCoefficients,
          isFittingDataNormalized: false,
          collectLearningData: collectLearningData,
          dtype: dtype,
        );