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LADRegressor

LADRegressor

A model type for constructing a lad regressor, based on MLJLinearModels.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

LADRegressor = @load LADRegressor pkg=MLJLinearModels

Do model = LADRegressor() to construct an instance with default hyper-parameters.

Least absolute deviation regression is a linear model with objective function

$

∑ρ(Xθ - y) + n⋅λ|θ|₂² + n⋅γ|θ|₁ $

where $ρ$ is the absolute loss and $n$ is the number of observations.

If scale_penalty_with_samples = false the objective function is instead

$

∑ρ(Xθ - y) + λ|θ|₂² + γ|θ|₁ $

.

Different solver options exist, as indicated under "Hyperparameters" below.

Training data

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

mach = machine(model, X, y)

where:

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

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

Hyperparameters

See also RobustRegressor.

Parameters

  • lambda::Real: strength of the regularizer if penalty is :l2 or :l1. Strength of the L2 regularizer if penalty is :en. Default: 1.0

  • gamma::Real: strength of the L1 regularizer if penalty is :en. Default: 0.0

  • penalty::Union{String, Symbol}: the penalty to use, either :l2, :l1, :en (elastic net) or :none. Default: :l2

  • fit_intercept::Bool: whether to fit the intercept or not. Default: true

  • penalize_intercept::Bool: whether to penalize the intercept. Default: false

  • scale_penalty_with_samples::Bool: whether to scale the penalty with the number of observations. Default: true

  • solver::Union{Nothing, MLJLinearModels.Solver}: some instance of MLJLinearModels.S where S is one of: LBFGS, IWLSCG, if penalty = :l2, and ProxGrad otherwise.

    If solver = nothing (default) then LBFGS() is used, if penalty = :l2, and otherwise ProxGrad(accel=true) (FISTA) is used.

    Solver aliases: FISTA(; kwargs...) = ProxGrad(accel=true, kwargs...), ISTA(; kwargs...) = ProxGrad(accel=false, kwargs...) Default: nothing

Example

using MLJ
X, y = make_regression()
mach = fit!(machine(LADRegressor(), X, y))
predict(mach, X)
fitted_params(mach)