scalation.analytics.par

RidgeRegression

Related Docs: object RidgeRegression | package par

class RidgeRegression extends Predictor with Error

The RidgeRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [x_1, ... x_k]. Both the input matrix 'x' and the response vector 'y' are centered (zero mean). Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_1 * x_1 + ... b_k * x_k + e

where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

b = x_pinv * y [ alternative: b = solve (y) ]

where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

Fac_QR // QR Factorization: slower, more stable (default) Fac_Cholesky // Cholesky Factorization: faster, less stable (reasonable choice) Inverse // Inverse/Gaussian Elimination, classical textbook technique (outdated)

This version uses parallel processing to speed up execution. see http://statweb.stanford.edu/~tibs/ElemStatLearn/

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Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new RidgeRegression(x: MatrixD, y: VectorD, lambda: Double = 0.1, technique: RegTechnique = Inverse)

    x

    the centered input/design m-by-n matrix NOT augmented with a first column of ones

    y

    the centered response vector

    lambda

    the shrinkage parameter (0 => OLS) in the penalty term 'lambda * b dot b'

    technique

    the technique used to solve for b in x.t*x*b = x.t*y

Value Members

  1. final def !=(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  5. def backElim(): (Int, VectorD, Double, Double)

    Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector, the new R-squared value and the new F statistic.

  6. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
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    @throws( ... )
  7. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  8. def equals(arg0: Any): Boolean

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    AnyRef → Any
  9. def finalize(): Unit

    Attributes
    protected[java.lang]
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    Annotations
    @throws( classOf[java.lang.Throwable] )
  10. def fit: (VectorD, Double, Double, Double)

    Return the fit (parameter vector b, quality of fit including rSquared).

  11. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  12. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  13. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  14. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  15. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  16. final def notify(): Unit

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    AnyRef
  17. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  18. def predict(z: Matrix): VectorD

    Predict the value of y = f(z) by evaluating the formula y = b dot z for each row of matrix z.

    Predict the value of y = f(z) by evaluating the formula y = b dot z for each row of matrix z.

    z

    the new matrix to predict

    Definition Classes
    RidgeRegressionPredictor
  19. def predict(z: VectorD): Double

    Predict the value of y = f(z) by evaluating the formula below.

    Predict the value of y = f(z) by evaluating the formula below.

    z

    the new vector to predict

    Definition Classes
    RidgeRegressionPredictor
  20. def predict(z: VectorI): Double

    Given a new discrete data vector z, predict the y-value of f(z).

    Given a new discrete data vector z, predict the y-value of f(z).

    z

    the vector to use for prediction

    Definition Classes
    Predictor
  21. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  22. def toString(): String

    Definition Classes
    AnyRef → Any
  23. def train(yy: VectorD): Unit

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_1, ...

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_1, ... b_k] dot [x_1, ... x_k] + e using the least squares method.

    yy

    the new response vector

  24. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation y = b dot x + e = [b_1, ...

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation y = b dot x + e = [b_1, ... b_k] dot [x_1, ... x_k] + e using the least squares method.

    Definition Classes
    RidgeRegressionPredictor
  25. def vif: VectorD

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-colinearity by regressing xj against the rest of the variables.

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-colinearity by regressing xj against the rest of the variables. A VIF over 10 indicates that over 90% of the varaince of xj can be predicted from the other variables, so xj is a candidate for removal from the model.

  26. final def wait(): Unit

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    @throws( ... )
  27. final def wait(arg0: Long, arg1: Int): Unit

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    @throws( ... )
  28. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  29. def xtx: MatrixD

    Compute x.t * x and add lambda to the diagonal

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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