Packages

c

scalation.analytics

LassoRegression

class LassoRegression[MatT <: MatriD, VecT <: VectoD] extends Predictor with Error

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). 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:

'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Linear Supertypes
Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new LassoRegression(x: MatT, y: VecT, λ0: Double = 0.01, technique: RegTechnique = QR)

    x

    the input/design m-by-n matrix augmented with a first column of ones

    y

    the response vector

    λ0

    the initial vale for the regularization weight

    technique

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

Value Members

  1. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  2. def diagnose(yy: VectoD): Unit

    Compute diagostics for the regression model.

    Compute diagostics for the regression model.

    yy

    the response vector

    Definition Classes
    LassoRegression → Predictor
  3. def f(yy: VectoD)(b: VectorD): 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

  4. def fit: VectorD

    Return the quality of fit.

    Return the quality of fit.

    Definition Classes
    LassoRegression → Predictor
  5. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    LassoRegression → Predictor
  6. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  7. def predict(z: MatT): 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

  8. 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
    LassoRegression → Predictor
  9. 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
  10. def report(): Unit

    Print results and diagnostics for each predictor 'x_j' and the overall quality of fit.

  11. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  12. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation for the response passed into the class 'y'.

    Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation for the response passed into the class 'y'.

    Definition Classes
    LassoRegression → Predictor
  13. def train(yy: VectoD): Unit

    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 → Predictor
    See also

    scalation.minima.LassoAdmm

    pdfs.semanticscholar.org/969f/077a3a56105a926a3b0c67077a57f3da3ddf.pdf