Packages

c

scalation.analytics

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 solve for the parameter vector 'b' using the Normal Equations:

x.t * x * b = x.t * y b = fac.solve (.)

See also

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

Linear Supertypes
PredictorVec, Error, Predictor, AnyRef, Any
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Inherited
  1. PolyRegression
  2. PredictorVec
  3. Error
  4. Predictor
  5. AnyRef
  6. Any
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Visibility
  1. Public
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Instance Constructors

  1. new PolyRegression(t: VectoD, y: VectoD, ord: Int, technique: RegTechnique = Cholesky, 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 (k) of the polynomial (max degree)

    technique

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

    raw

    whether the polynomials are raw or orthogonal

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 backwardElim(cols: Set[Int]): (Int, VectoD, VectoD)

    Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit.

    Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, 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

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

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    PredictorVec → Predictor
  9. def corrMatrix: MatriD

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

  10. def crossVal(ord: Int, k: Int = 10): 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

    Definition Classes
    PolyRegression → PredictorVec
  11. def crossValidate(algor: (VectoD, VectoD, Int) ⇒ PredictorVec, ord: Int, k: Int = 10): Array[Statistic]
    Definition Classes
    PredictorVec
  12. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  13. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  14. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  15. def eval(tt: VectoD, yy: VectoD): Unit

    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
  16. def eval(): Unit

    Compute the error and useful diagnostics for the entire dataset.

    Compute the error and useful diagnostics for the entire dataset.

    Definition Classes
    PredictorVec → 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 FIX - implement in classes

    Definition Classes
    Predictor
  18. def expand(t: Double): VectoD

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

    Return the quality of fit measures including 'rSq'.

    Return the quality of fit measures including 'rSq'.

    Definition Classes
    PredictorVec
  22. def fitLabel: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

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

    Build a map of quality of fit measures.

    Build a map of quality of fit measures.

    Definition Classes
    PredictorVec
  24. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  25. def forwardSel(cols: Set[Int]): (Int, VectoD, VectoD)

    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

    Definition Classes
    PredictorVec
  26. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  27. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  28. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  29. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  30. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  32. def orthoVector(v: VectoD): VectoD

    Follow the same transformations used to orthogonalize the data/design matrix 'x', on vector 'v', so its elements are correctly mapped.

    Follow the same transformations used to orthogonalize the data/design matrix 'x', on vector 'v', so its elements are correctly mapped.

    v

    the vector to be transformed based the orthogonalize procedure

  33. def orthogonalize(x: MatriD): (MatriD, MatriD)

    Orthogonalize the data/design matrix 'x' using Gram-Schmidt Orthogonalization, returning the a new orthogonal matrix 'z' and the orthogonalization multipliers 'a'.

    Orthogonalize the data/design matrix 'x' using Gram-Schmidt Orthogonalization, returning the a new orthogonal matrix 'z' and the orthogonalization multipliers 'a'. This will eliminate the multi-collinearity problem.

    x

    the matrix to orthogonalize

  34. 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
  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 expanded/orhogonalized vector to predict

    Definition Classes
    PredictorVec → Predictor
  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
    PredictorVec → Predictor
  38. var rg: Regression
    Attributes
    protected
    Definition Classes
    PredictorVec
  39. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  40. def toString(): String
    Definition Classes
    AnyRef → Any
  41. def train(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.

    yy

    the response vector

    Definition Classes
    PredictorVec → Predictor
  42. def vif: VectoD

    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.

    Definition Classes
    PredictorVec
  43. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  44. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  45. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )

Inherited from PredictorVec

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

Ungrouped