class LassoRegression extends PredictorMat
The LassoRegression 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 equation
y = 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).
- See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
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Instance Constructors
-
new
LassoRegression(x: MatriD, y: VectoD, λ0: Double = 0.01)
- x
the input/design m-by-n matrix
- y
the response vector
- λ0
the initial value for the regularization weight
Value Members
-
def
coefficient: VectoD
Return the vector of coefficient/parameter values.
Return the vector of coefficient/parameter values.
- Definition Classes
- Predictor
-
def
crossVal(k: Int = 10): Unit
Perform 'k'-fold cross-validation.
Perform 'k'-fold cross-validation.
- k
the number of folds
- Definition Classes
- LassoRegression → PredictorMat
-
def
crossValidate(algor: (MatriD, VectoD) ⇒ PredictorMat, k: Int = 10): Array[Statistic]
- Definition Classes
- PredictorMat
-
val
df: (Double, Double)
- Definition Classes
- Fit
-
def
diagnose(e: VectoD, w: VectoD = null, yp: VectoD = null): 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
-
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
-
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
- PredictorMat → Predictor
-
def
f(yy: VectoD)(b: VectoD): Double
Compute the sum of squares error + λ * sum of the magnitude of coefficients.
Compute the sum of squares error + λ * sum of the magnitude of coefficients. This is the objective function to be minimized.
- yy
the response vector
- b
the vector of coefficients/parameters
-
def
f_(z: Double): String
Format a double value.
-
def
fit: VectoD
Return the quality of fit including 'sst', 'sse', 'mse0', rmse', 'mae', 'rSq', 'df._2', 'rBarSq', 'fStat', 'aic', 'bic'.
Return the quality of fit including 'sst', 'sse', 'mse0', rmse', 'mae', 'rSq', '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
-
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
-
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
-
final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
-
val
index_rSq: Int
- Definition Classes
- Fit
-
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
-
def
predict(z: MatriD): 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
-
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
- PredictorMat → Predictor
-
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
-
def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- Predictor
-
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
-
def
summary(): Unit
Compute diagostics for the regression model.
Compute diagostics for the regression model.
- Definition Classes
- PredictorMat
-
def
summary(b: VectoD, stdErr: VectoD = null): 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
- Definition Classes
- Fit
-
def
train(yy: VectoD = y): LassoRegression
Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation
Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation
y = b dot x + e = [b_0, ... b_k] dot [1, x_1 , ... x_k] + e
regularized by the sum of magnitudes of the coefficients.
- yy
the response vector
- Definition Classes
- LassoRegression → PredictorMat → Predictor
- See also
scalation.minima.LassoAdmmpdfs.semanticscholar.org/969f/077a3a56105a926a3b0c67077a57f3da3ddf.pdf
-
def
train(): PredictorMat
Given a set of data vectors 'x's and their corresponding responses 'y's, passed into the implementing class, train the prediction function 'y = f(x)' by fitting its parameters.
Given a set of data vectors 'x's and their corresponding responses 'y's, passed into the implementing class, train the prediction function 'y = f(x)' by fitting its parameters.
- Definition Classes
- PredictorMat