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MultitargetRidgeRegressor

MultitargetRidgeRegressor

A model type for constructing a multitarget ridge regressor, based on MultivariateStats.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

MultitargetRidgeRegressor = @load MultitargetRidgeRegressor pkg=MultivariateStats

Do model = MultitargetRidgeRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in MultitargetRidgeRegressor(lambda=...).

Multi-target ridge regression adds a quadratic penalty term to multi-target least squares regression, for regularization. Ridge regression is particularly useful in the case of multicollinearity. In this case, the output represents a response vector. Options exist to specify a bias term, and to adjust the strength of the penalty term.

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X, y)

Here:

  • X is any table of input features (eg, a DataFrame) whose columns are of scitype Continuous; check column scitypes with schema(X).
  • y is the target, which can be any table of responses whose element scitype is Continuous; check the scitype with scitype(y).

Train the machine using fit!(mach, rows=...).

Hyper-parameters

  • lambda=1.0: Is the non-negative parameter for the regularization strength. If lambda is 0, ridge regression is equivalent to linear least squares regression, and as lambda approaches infinity, all the linear coefficients approach 0.
  • bias=true: Include the bias term if true, otherwise fit without bias term.

Operations

  • predict(mach, Xnew): Return predictions of the target given new features Xnew, which should have the same scitype as X above.

Fitted parameters

The fields of fitted_params(mach) are:

  • coefficients: The linear coefficients determined by the model.
  • intercept: The intercept determined by the model.

Examples

using MLJ
using DataFrames

RidgeRegressor = @load MultitargetRidgeRegressor pkg=MultivariateStats

X, y = make_regression(100, 6; n_targets = 2)  ## a table and a table (synthetic data)

ridge_regressor = RidgeRegressor(lambda=1.5)
mach = machine(ridge_regressor, X, y) |> fit!

Xnew, _ = make_regression(3, 6)
yhat = predict(mach, Xnew) ## new predictions

See also LinearRegressor, MultitargetLinearRegressor, RidgeRegressor