package par
The par
package contains classes, traits and objects for parallel
analytics including clustering and prediction.
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Type Members
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class
ANCOVA extends Regression
The
ANCOVA
class supports ANalysis of COVAriance 'ANCOVA'.The
ANCOVA
class supports ANalysis of COVAriance 'ANCOVA'. It allows the addition of a categorical treatment variable 't' into a multiple linear regression. This is done by introducing dummy variables 'dj' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the augmented regression equationy = b dot x + e = b0 + b_1 * x_1 + b_2 * x_2 + ... b_k * x_k + b_k+1 * d_1 + b_k+2 * d_2 + ... b_k+l * d_l + 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 (.)
't' has categorical values/levels, e.g., treatment levels (0, ... 't.max ()')
- See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
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class
PolyRegression extends PredictorVec
The
PolyRegression
class supports polynomial regression.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 equationy = 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
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abstract
class
PredictorVec extends Predictor with Error
The
PredictorVec
class supports term expanded regression (work is delegated to theRegression
class).The
PredictorVec
class supports term expanded regression (work is delegated to theRegression
class). Fit the parameter vector 'b' in the regression equation. 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 (.)
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class
Regression extends PredictorMat
The
Regression
class supports multiple linear regression.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 equationy = 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
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class
RidgeRegression extends PredictorMat
The
RidgeRegression
class supports multiple linear regression.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 equationy = 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/
Value Members
-
val
BASE_DIR: String
The relative path for base directory
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object
ANCOVA extends Error
The
ANCOVA
companion object provides helper functions. -
object
ANCOVATest extends App
The
ANCOVATest
object tests theANCOVA
class using the following regression equation.The
ANCOVATest
object tests theANCOVA
class using the following regression equation.y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*d_1 + b_4*d_2
> runMain scalation.analytics.ANCOVATest
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object
ANCOVATest2 extends App
The
ANCOVATest2
object tests theANCOVA
object related to related to encoding a column 'x1' of strings.The
ANCOVATest2
object tests theANCOVA
object related to related to encoding a column 'x1' of strings. > runMain scalation.analytics.ANCOVATest2 -
object
PolyRegressionTest extends App
The
PolyRegressionTest
object testsPolyRegression
class using the following regression equation.The
PolyRegressionTest
object testsPolyRegression
class using the following regression equation.y = b dot x = b_0 + b_1*t + b_2*t^2.
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object
PredictorMatO
The
PredictorMat
companion object provides a meythod for splitting a combined data matrix in predictor matrix and a response vector. -
object
RegressionTest extends App
The
RegressionTest
object testsRegression
class using the following regression equation.The
RegressionTest
object testsRegression
class using the following regression equation.y = b dot x = b_0 + b_1*x_1 + b_2*x_2.
Test regression and backward elimination.
- See also
http://statmaster.sdu.dk/courses/st111/module03/index.html
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object
RegressionTest2 extends App
The
RegressionTest2
object testsRegression
class using the following regression equation.The
RegressionTest2
object testsRegression
class using the following regression equation.y = b dot x = b_0 + b_1*x1 + b_2*x_2.
Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse.
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object
RegressionTest3 extends App
The
RegressionTest3
object tests the multi-collinearity method in theRegression
class using the following regression equation.The
RegressionTest3
object tests the multi-collinearity method in theRegression
class using the following regression equation.y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4
- See also
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
online.stat.psu.edu/online/development/stat501/data/bloodpress.txt
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object
RidgeRegression
The
RidgeRegression
companion object is used to center the input matrix 'x'.The
RidgeRegression
companion object is used to center the input matrix 'x'. This is done by subtracting the column means from each value. -
object
RidgeRegressionTest extends App
The
RidgeRegressionTest
object testsRidgeRegression
class using the following regression equation.The
RidgeRegressionTest
object testsRidgeRegression
class using the following regression equation.y = b dot x = b_1*x_1 + b_2*x_2.
Test regression and backward elimination.
- See also
http://statmaster.sdu.dk/courses/st111/module03/index.html
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object
RidgeRegressionTest2 extends App
The
RidgeRegressionTest2
object testsRidgeRegression
class using the following regression equation.The
RidgeRegressionTest2
object testsRidgeRegression
class using the following regression equation.y = b dot x = b_1*x1 + b_2*x_2.
Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse.
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object
RidgeRegressionTest3 extends App
The
RidgeRegressionTest3
object tests the multi-collinearity method in theRidgeRegression
class using the following regression equation.The
RidgeRegressionTest3
object tests the multi-collinearity method in theRidgeRegression
class using the following regression equation.y = b dot x = b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4
- See also
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
online.stat.psu.edu/online/development/stat501/data/bloodpress.txt