Packages

class RidgeRegression extends PredictorMat

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faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)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 also

statweb.stanford.edu/~tibs/ElemStatLearn/

Linear Supertypes
PredictorMat, Error, Predictor, Fit, AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. RidgeRegression
  2. PredictorMat
  3. Error
  4. Predictor
  5. Fit
  6. AnyRef
  7. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

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

Type Members

  1. type Fac_QR = Fac_QR_H[MatrixD]

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. val b: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  6. def backElim(): (Int, VectoD, VectoD)

    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.

  7. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  8. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  9. def crossVal(k: Int = 10): Unit

    Perform 'k'-fold cross-validation.

    Perform 'k'-fold cross-validation. FIX

    k

    the number of folds

    Definition Classes
    RidgeRegression → PredictorMat
  10. def crossValidate(algor: (MatriD, VectoD) ⇒ PredictorMat, k: Int = 10): Array[Statistic]
    Definition Classes
    PredictorMat
  11. val df: (Double, Double)
    Definition Classes
    Fit
  12. def diagnose(e: VectoD, w: VectoD = null, yp: VectoD = null): Unit

    Given the error/residual vector, compute the quality of fit measures.

    Given the error/residual vector, compute the quality of fit measures.

    e

    the corresponding m-dimensional error vector (y - yp)

    w

    the weights on the instances

    yp

    the predicted response vector (x * b)

    Definition Classes
    Fit
  13. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  16. def eval(): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    Definition Classes
    RidgeRegression → PredictorMat → Predictor
  17. def eval(xx: MatriD, yy: VectoD): Unit

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    xx

    the test data matrix

    yy

    the test response vector

    Definition Classes
    PredictorMat → Predictor
  18. def f_(z: Double): String

    Format a double value.

    Format a double value.

    z

    the double value to format

    Definition Classes
    Fit
  19. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  20. def fit: VectoD

    Return the quality of fit including 'sst', 'sse', 'mse0', rmse', 'mae', 'rSq', 'df._2', 'rBarSq', 'fStat', 'aic', 'bic'.

    Return the quality of fit including 'sst', 'sse', 'mse0', rmse', 'mae', 'rSq', 'df._2', 'rBarSq', 'fStat', 'aic', 'bic'. Note, if 'sse > sst', the model introduces errors and the 'rSq' may be negative, otherwise, R^2 ('rSq') ranges from 0 (weak) to 1 (strong). Note that 'rSq' is the number 5 measure. Override to add more quality of fit measures.

    Definition Classes
    Fit
  21. def fitLabel: Seq[String]

    Return the labels for the quality of fit measures.

    Return the labels for the quality of fit measures. Override to add more quality of fit measures.

    Definition Classes
    Fit
  22. def fitMap: Map[String, String]

    Build a map of quality of fit measures (use of LinedHashMap makes it ordered).

    Build a map of quality of fit measures (use of LinedHashMap makes it ordered). Override to add more quality of fit measures.

    Definition Classes
    Fit
  23. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  24. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  25. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  26. val index_rSq: Int
    Definition Classes
    Fit
  27. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  28. val k: Int
    Attributes
    protected
    Definition Classes
    PredictorMat
  29. val m: Int
    Attributes
    protected
    Definition Classes
    PredictorMat
  30. def mse_: Double

    Return the mean of squares for error (sse / df._2).

    Return the mean of squares for error (sse / df._2). Must call diagnose first.

    Definition Classes
    Fit
  31. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  33. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  34. def predict(z: VectoD): 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
    RidgeRegression → PredictorMat → Predictor
  35. def predict(z: MatriD): VectoD

    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
    PredictorMat
  36. def predict(z: VectoI): 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
  37. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  38. def sumCoeff(b: VectoD, stdErr: VectoD = null): String

    Produce the summary report portion for the cofficients.

    Produce the summary report portion for the cofficients.

    b

    the parameters/coefficients for the model

    Definition Classes
    Fit
  39. def summary(): Unit

    Compute diagostics for the regression model.

    Compute diagostics for the regression model.

    Definition Classes
    PredictorMat
  40. def summary(b: VectoD, stdErr: VectoD = null): String

    Produce a summary report with diagnostics for each predictor 'x_j' and the overall quality of fit.

    Produce a summary report with diagnostics for each predictor 'x_j' and the overall quality of fit.

    b

    the parameters/coefficients for the model

    Definition Classes
    Fit
  41. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  42. def toString(): String
    Definition Classes
    AnyRef → Any
  43. def train(yy: VectoD): RidgeRegression

    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

    Definition Classes
    RidgeRegression → PredictorMat → Predictor
  44. def train(): RidgeRegression

    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
    RidgeRegression → PredictorMat
  45. def vif: VectorD

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

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

  46. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  47. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  48. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  49. val x: MatriD
    Attributes
    protected
    Definition Classes
    PredictorMat
  50. def xtx: MatrixD

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

  51. val y: VectoD
    Attributes
    protected
    Definition Classes
    PredictorMat

Inherited from PredictorMat

Inherited from Error

Inherited from Predictor

Inherited from Fit

Inherited from AnyRef

Inherited from Any

Ungrouped