Packages

class Regression extends PredictorMat

The Regression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_0 + 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faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)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

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Linear Supertypes
PredictorMat, Error, Predictor, Fit, AnyRef, Any
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  1. Regression
  2. PredictorMat
  3. Error
  4. Predictor
  5. Fit
  6. AnyRef
  7. Any
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Instance Constructors

  1. new Regression(x: MatrixD, y: VectorD, technique: RegTechnique = QR)

    x

    the input/design m-by-n matrix augmented with a first column of ones

    y

    the response vector

    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 crossVal(k: Int = 10, rando: Boolean = true): Unit

    Perform 'k'-fold cross-validation.

    Perform 'k'-fold cross-validation.

    k

    the number of folds

    rando

    whether to use randomized cross-validation.

    Definition Classes
    Regression → PredictorMat
  9. def crossValidate(algor: (MatriD, VectoD) ⇒ PredictorMat, k: Int = 10, rando: Boolean = true): Array[Statistic]
    Definition Classes
    PredictorMat
  10. def diagnose(e: VectoD, w: VectoD = null, yp: VectoD = null, y_: VectoD = y): 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
  11. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  12. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  13. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  14. def eval(): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    Definition Classes
    Regression → PredictorMat → Predictor
  15. 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
  16. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  17. def fit: VectoD

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

    Return the quality of fit including 'rSq', 'sst', 'sse', 'mse0', rmse', 'mae', '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
  18. 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
  19. 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
  20. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  21. var fname: Strings
    Attributes
    protected
    Definition Classes
    PredictorMat
  22. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  23. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  24. def hparameter: HyperParameter

    Return the hyper-parameters.

    Return the hyper-parameters.

    Definition Classes
    PredictorMat
  25. val index_rSq: Int
    Definition Classes
    Fit
  26. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  27. val k: Int
    Attributes
    protected
    Definition Classes
    PredictorMat
  28. val m: Int
    Attributes
    protected
    Definition Classes
    PredictorMat
  29. 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
  30. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  31. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  32. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  33. def parameter: VectoD

    Return the vector of parameter/coefficient values.

    Return the vector of parameter/coefficient values.

    Definition Classes
    Predictor
  34. def predict(z: VectoD): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    z

    the new vector to predict

    Definition Classes
    Regression → PredictorMat → Predictor
  35. def predict(z: MatriD = x): 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 resetDF(df_update: (Double, Double)): Unit

    Reset the degrees of freedom to the new updated values.

    Reset the degrees of freedom to the new updated values. For some models, the degrees of freedom is not known until after the model is built.

    df_update

    the updated degrees of freedom

    Definition Classes
    Fit
  38. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  39. 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
  40. def summary(): String

    Compute and return summary diagostics for the regression model.

    Compute and return summary diagostics for the regression model.

    Definition Classes
    PredictorMat
  41. def summary(b: VectoD, stdErr: VectoD = null, show: Boolean = false): 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

    show

    flag indicating whether to print the summary

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

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ...

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ... b_k] dot [1, x_1 , ... x_k] + e using the least squares method.

    yy

    the new response vector

    Definition Classes
    Regression → PredictorMat → Predictor
  45. def train(): Regression

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation y = b dot x + e = [b_0, ...

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation y = b dot x + e = [b_0, ... b_k] dot [1, x_1 , ... x_k] + e using the least squares method. FIX - needs to be updated

    Definition Classes
    Regression → PredictorMat
  46. def train2(yy: VectoD = y): PredictorMat
    Definition Classes
    PredictorMat
  47. 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.

  48. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  49. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  50. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  51. val x: MatriD
    Attributes
    protected
    Definition Classes
    PredictorMat
  52. 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

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