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
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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
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final
def
!=(arg0: Any): Boolean
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final
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final
def
asInstanceOf[T0]: T0
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val
b: VectoD
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- Predictor
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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
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def
clone(): AnyRef
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def
corrMatrix: MatriD
Return the correlation matrix for the columns in data matrix 'x'.
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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
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def
crossValidate(algor: (VectoD, VectoD, Int) ⇒ PredictorVec, k: Int = 10, rando: Boolean = true): Array[Statistic]
- Definition Classes
- PredictorVec
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val
e: VectoD
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- Predictor
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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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
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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
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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
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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
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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
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def
finalize(): Unit
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def
fit: VectoD
Return the quality of fit measures including 'rSq'.
Return the quality of fit measures including 'rSq'.
- Definition Classes
- PredictorVec
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def
fitLabel: Seq[String]
Return the labels for the fit.
Return the labels for the fit.
- Definition Classes
- PredictorVec
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def
fitMap: Map[String, String]
Build a map of quality of fit measures.
Build a map of quality of fit measures.
- Definition Classes
- PredictorVec
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final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
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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
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final
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getClass(): Class[_]
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hashCode(): Int
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final
def
notifyAll(): Unit
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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
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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
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def
parameter: VectoD
Return the vector of parameters/coefficients.
Return the vector of parameters/coefficients.
- Definition Classes
- PredictorVec → Predictor
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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
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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
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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
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- PredictorVec → Predictor
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var
rg: Regression
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- PredictorVec
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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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
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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
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final
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wait(arg0: Long, arg1: Int): Unit
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