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faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)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/
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Instance Constructors
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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
- type Fac_QR = Fac_QR_H[MatrixD]
Value Members
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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final
def
asInstanceOf[T0]: T0
- Definition Classes
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val
b: VectoD
- Attributes
- protected
- Definition Classes
- Predictor
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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.
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def
clone(): AnyRef
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- protected[java.lang]
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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
- RidgeRegression → PredictorMat
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def
crossValidate(algor: (MatriD, VectoD) ⇒ PredictorMat, k: Int = 10, rando: Boolean = true): Array[Statistic]
- Definition Classes
- PredictorMat
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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
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val
e: VectoD
- Attributes
- protected
- Definition Classes
- Predictor
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
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def
equals(arg0: Any): Boolean
- Definition Classes
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def
eval(): Unit
Compute the error and useful diagnostics.
Compute the error and useful diagnostics.
- Definition Classes
- RidgeRegression → PredictorMat → 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
- Definition Classes
- PredictorMat → Predictor
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def
finalize(): Unit
- Attributes
- protected[java.lang]
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- @throws( classOf[java.lang.Throwable] )
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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
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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
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def
fitMap: Map[String, String]
Build a map of quality of fit measures (use of
LinedHashMapmakes it ordered).Build a map of quality of fit measures (use of
LinedHashMapmakes it ordered). Override to add more quality of fit measures.- Definition Classes
- Fit
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final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
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var
fname: Strings
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- protected
- Definition Classes
- PredictorMat
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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- @native()
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def
hparameter: HyperParameter
Return the hyper-parameters.
Return the hyper-parameters.
- Definition Classes
- PredictorMat
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val
index_rSq: Int
- Definition Classes
- Fit
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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val
k: Int
- Attributes
- protected
- Definition Classes
- PredictorMat
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val
m: Int
- Attributes
- protected
- Definition Classes
- PredictorMat
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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
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
parameter: VectoD
Return the vector of parameter/coefficient values.
Return the vector of parameter/coefficient values.
- Definition Classes
- Predictor
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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
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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
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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
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
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- Predictor
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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
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def
summary(): String
Compute and return summary diagostics for the regression model.
Compute and return summary diagostics for the regression model.
- Definition Classes
- PredictorMat
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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
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
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def
toString(): String
- Definition Classes
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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
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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
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def
train2(yy: VectoD = y): PredictorMat
- Definition Classes
- PredictorMat
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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.
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
- Definition Classes
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val
x: MatriD
- Attributes
- protected
- Definition Classes
- PredictorMat
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def
xtx: MatrixD
Compute x.t * x and add lambda to the diagonal
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val
y: VectoD
- Attributes
- protected
- Definition Classes
- PredictorMat