Packages

c

scalation.analytics.par

PolyRegression

class PolyRegression extends PredictorVec

The PolyRegression class supports polynomial regression. In this case, 't' is expanded to [1, t, t2 ... tk]. Fit the parameter vector 'b' in the regression equation

y = b dot x + e = b_0 + b_1 * t + b_2 * t2 ... b_k * tk + 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

where 'x_pinv' is the pseudo-inverse.

See also

www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx

Linear Supertypes
PredictorVec, Predictor, Model, Error, AnyRef, Any
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Inherited
  1. PolyRegression
  2. PredictorVec
  3. Predictor
  4. Model
  5. Error
  6. AnyRef
  7. Any
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new PolyRegression(t: VectorD, y: VectorD, ord: Int, technique: RegTechnique.RegTechnique = QR, raw: Boolean = true)

    t

    the input vector: t_i expands to x_i = [1, t_i, t_i2, ... t_ik]

    y

    the response vector

    ord

    the order of the polynomial

    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. def analyze(x_r: MatriD = null, y_r: VectoD = y, x_e: MatriD = null, y_e: VectoD = y): PredictorVec

    Analyze a dataset using this model using ordinary training with the 'train' method.

    Analyze a dataset using this model using ordinary training with the 'train' method.

    x_r

    the training/full data/input matrix

    y_r

    the training/full response/output vector

    x_e

    the test/full data/input matrix

    y_e

    the test/full response/output vector

    Definition Classes
    PredictorVec → Predictor
  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. def backwardElim(cols: Set[Int], index_q: Int = index_rSqBar, first: Int = 1): (Int, PredictorMat)

    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.

    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.

    cols

    the columns of matrix x included in the existing model

    index_q

    index of Quality of Fit (QoF) to use for comparing quality

    first

    first variable to consider for elimination (default (1) assume intercept x_0 will be in any model)

    Definition Classes
    PolyRegression → PredictorVec
  7. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native() @HotSpotIntrinsicCandidate()
  8. def corrMatrix(xx: MatriD): MatriD

    Return the correlation matrix for the columns in data matrix 'xx'.

    Return the correlation matrix for the columns in data matrix 'xx'.

    xx

    the data matrix shose correlation matrix is sought

    Definition Classes
    Predictor
  9. def crossVal(ord: Int, k: Int = 10, rando: Boolean = true): Unit

    Perform 'k'-fold cross-validation.

    Perform 'k'-fold cross-validation.

    ord

    the order of the expansion (e.g., max degree in PolyRegression)

    k

    the number of folds

    rando

    whether to use randomized cross-validation

    Definition Classes
    PolyRegression → PredictorVec
  10. def crossValidate(algor: (VectoD, VectoD, Int) ⇒ PredictorVec, k: Int = 10, rando: Boolean = true): Array[Statistic]
    Attributes
    protected
    Definition Classes
    PredictorVec
  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. def eval(xx: MatriD = x, yy: VectoD = y): Regression

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    xx

    the test data/input matrix

    yy

    the test response/output vector

    Definition Classes
    PolyRegression → PredictorVec → Model
  14. def eval(yy: VectoD): Regression

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    yy

    the test response vector

    Definition Classes
    PredictorVec
  15. def eval(tt: VectoD, yy: VectoD): Regression

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    tt

    the test data vector (unexpanded)

    yy

    the test response vector

    Definition Classes
    PredictorVec
  16. def expand(t: Double): VectorD

    Expand the scalar 't' into a vector of powers of 't': [1, t, t2 ... tk].

    Expand the scalar 't' into a vector of powers of 't': [1, t, t2 ... tk].

    t

    the scalar to expand into the vector

    Definition Classes
    PolyRegression → PredictorVec
  17. def expand(t: VectoD): MatriD

    Expand the vector 't' into a matrix.

    Expand the vector 't' into a matrix.

    t

    the vector to expand into the matrix

    Definition Classes
    PredictorVec
  18. def fit: VectoD

    Return the quality of fit including 'rSquared'.

    Return the quality of fit including 'rSquared'.

    Definition Classes
    PolyRegression → PredictorVec
  19. def fitLabel: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    PredictorVec
  20. def fitMap: Map[String, String]

    Build a map of quality of fit measures.

    Build a map of quality of fit measures.

    Definition Classes
    PredictorVec
  21. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  22. def forwardSel(cols: Set[Int], index_q: Int = index_rSqBar): (Int, PredictorMat)

    Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit.

    Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit. May be called repeatedly.

    cols

    the columns of matrix x included in the existing model

    index_q

    index of Quality of Fit (QoF) to use for comparing quality

    Definition Classes
    PolyRegression → PredictorVec → Predictor
  23. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. def getX: MatriD

    Return the 'used' data matrix 'x'.

    Return the 'used' data matrix 'x'. Mainly for derived classes where 'x' is expanded from the given columns in 'x_', e.g., QuadRegression add squared columns.

    Definition Classes
    PredictorVec → Predictor
  25. def getY: VectoD

    Return the 'used' response vector 'y'.

    Return the 'used' response vector 'y'. Mainly for derived classes where 'y' is transformed, e.g., TranRegression, Regression4TS.

    Definition Classes
    PredictorVec → Predictor
  26. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  27. def hparameter: HyperParameter

    Return the hyper-parameters.

    Return the hyper-parameters.

    Definition Classes
    PredictorVec → Model
  28. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  29. val modelConcept: URI

    An optional reference to an ontological concept

    An optional reference to an ontological concept

    Definition Classes
    Model
  30. def modelName: String

    An optional name for the model (or modeling technique)

    An optional name for the model (or modeling technique)

    Definition Classes
    Model
  31. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  33. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  34. def parameter: VectoD

    Return the vector of parameters/coefficients.

    Return the vector of parameters/coefficients.

    Definition Classes
    PredictorVec → Model
  35. 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
    PolyRegression → PredictorVec → Predictor
  36. def predict(z: Double): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.g., (b_0, b_1, b_2) dot (1, z, z^2).

    Predict the value of y = f(z) by evaluating the formula y = b dot expand (z), e.g., (b_0, b_1, b_2) dot (1, z, z^2).

    z

    the new scalar to predict

    Definition Classes
    PolyRegression → PredictorVec
  37. def predict(z: MatriD = rg.getX): 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
    PredictorVec → Predictor
  38. def predict(z: VectoI): Double

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

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

    z

    the vector to use for prediction

    Definition Classes
    Predictor
  39. def report: String

    Return a basic report on the trained model.

    Return a basic report on the trained model.

    Definition Classes
    PredictorVec → Model
    See also

    'summary' method for more details

  40. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    PredictorVec → Predictor
  41. var rg: Regression
    Attributes
    protected
    Definition Classes
    PredictorVec
  42. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  43. def test(modelName: String, doPlot: Boolean = true): Unit

    Test the model on the full dataset (i.e., train and evaluate on full dataset).

    Test the model on the full dataset (i.e., train and evaluate on full dataset).

    modelName

    the name of the model being tested

    doPlot

    whether to plot the actual vs. predicted response

    Definition Classes
    Predictor
  44. def toString(): String
    Definition Classes
    AnyRef → Any
  45. def train(xx: MatriD = MatrixD (Seq (t)), yy: VectoD = y): Regression

    Train the predictor by fitting the parameter vector 'b' in the multiple regression equation using the least squares method.

    Train the predictor by fitting the parameter vector 'b' in the multiple regression equation using the least squares method.

    xx

    the data/input single column matrix (unexpanded)

    yy

    the response/output vector

    Definition Classes
    PredictorVec → Model
  46. def vif(skip: Int = 1): VectoD

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

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

    skip

    the number of columns of x at the beginning to skip in computing VIF

    Definition Classes
    PredictorVec
  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
    @throws( ... ) @native()
  49. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  50. val x: MatrixD

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] ) @Deprecated
    Deprecated

Inherited from PredictorVec

Inherited from Predictor

Inherited from Model

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped