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UnivariateBoxCoxTransformer

UnivariateBoxCoxTransformer

A model type for constructing a single variable Box-Cox transformer, based on MLJModels.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

UnivariateBoxCoxTransformer = @load UnivariateBoxCoxTransformer pkg=MLJModels

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

Box-Cox transformations attempt to make data look more normally distributed. This can improve performance and assist in the interpretation of models which suppose that data is generated by a normal distribution.

A Box-Cox transformation (with shift) is of the form

x -> ((x + c)^λ - 1)/λ

for some constant c and real λ, unless λ = 0, in which case the above is replaced with

x -> log(x + c)

Given user-specified hyper-parameters n::Integer and shift::Bool, the present implementation learns the parameters c and λ from the training data as follows: If shift=true and zeros are encountered in the data, then c is set to 0.2 times the data mean. If there are no zeros, then no shift is applied. Finally, n different values of λ between -0.4 and 3 are considered, with λ fixed to the value maximizing normality of the transformed data.

Reference: Wikipedia entry for power transform.

Training data

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

mach = machine(model, x)

where

  • x: any abstract vector with element scitype Continuous; check the scitype with scitype(x)

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

Hyper-parameters

  • n=171: number of values of the exponent λ to try
  • shift=false: whether to include a preliminary constant translation in transformations, in the presence of zeros

Operations

  • transform(mach, xnew): apply the Box-Cox transformation learned when fitting mach
  • inverse_transform(mach, z): reconstruct the vector z whose transformation learned by mach is z

Fitted parameters

The fields of fitted_params(mach) are:

  • λ: the learned Box-Cox exponent
  • c: the learned shift

Examples

using MLJ
using UnicodePlots
using Random
Random.seed!(123)

transf = UnivariateBoxCoxTransformer()

x = randn(1000).^2

mach = machine(transf, x)
fit!(mach)

z = transform(mach, x)

julia> histogram(x)
                ┌                                        ┐
   [ 0.0,  2.0) ┤███████████████████████████████████  848
   [ 2.0,  4.0) ┤████▌ 109
   [ 4.0,  6.0) ┤█▍ 33
   [ 6.0,  8.0) ┤▍ 7
   [ 8.0, 10.0) ┤▏ 2
   [10.0, 12.0) ┤  0
   [12.0, 14.0) ┤▏ 1
                └                                        ┘
                                 Frequency

julia> histogram(z)
                ┌                                        ┐
   [-5.0, -4.0) ┤█▎ 8
   [-4.0, -3.0) ┤████████▊ 64
   [-3.0, -2.0) ┤█████████████████████▊ 159
   [-2.0, -1.0) ┤█████████████████████████████▊ 216
   [-1.0,  0.0) ┤███████████████████████████████████  254
   [ 0.0,  1.0) ┤█████████████████████████▊ 188
   [ 1.0,  2.0) ┤████████████▍ 90
   [ 2.0,  3.0) ┤██▊ 20
   [ 3.0,  4.0) ┤▎ 1
                └                                        ┘
                                 Frequency