Generating counterfactuals

The purpose of this vignette is to show how to generate counterfactual explanations from SDeMo models.

using SpeciesDistributionToolkit
using PrettyTables

We will work on the demo data:

X, y, C = SDeMo.__demodata()
sdm = SDM(RawData, NaiveBayes, X, y)
variables!(sdm, [1, 12])
train!(sdm)

☑️  RawData → NaiveBayes → P(x) ≥ 0.416

We will focus on generating a counterfactual input, i.e. a set of hypothetical inputs that lead the model to predicting the other outcome. Internally, candidate points are generated using the Nelder-Mead algorithm, which works well enough but is not compatible with categorical data.

We will pick one prediction to flip:

inst = 6

6

And look at its outcome:

outcome = predict(sdm)[inst]

false

Our target is expressed in terms of the score we want the counterfactual to reach (and not in terms of true/false, this is very important):

target = outcome ? 0.9threshold(sdm) : 1.1threshold(sdm)

0.45776404958196787

The actual counterfactual is generated as (we only account for the relevant variables):

cf = [
    counterfactual(
        sdm,
        instance(sdm, inst; strict = false),
        target,
        200.0;
        threshold = false,
    ) for _ in 1:5
]
cf = hcat(cf...)

19×5 Matrix{Float64}:
   13.473    13.5045    13.513    13.6084    13.5036
    5.1       5.1        5.1       5.1        5.1
    0.251     0.251      0.251     0.251      0.251
  537.3     537.3      537.3     537.3      537.3
   25.85     25.85      25.85     25.85      25.85
    5.65      5.65       5.65      5.65       5.65
   20.2      20.2       20.2      20.2       20.2
   13.05     13.05      13.05     13.05      13.05
   22.25     22.25      22.25     22.25      22.25
   22.25     22.25      22.25     22.25      22.25
    8.85      8.85       8.85      8.85       8.85
 1301.85   1312.55    1318.8    1361.57    1298.73
  209.3     209.3      209.3     209.3      209.3
   16.1      16.1       16.1      16.1       16.1
   51.1      51.1       51.1      51.1       51.1
  560.1     560.1      560.1     560.1      560.1
  101.7     101.7      101.7     101.7      101.7
  101.7     101.7      101.7     101.7      101.7
  418.2     418.2      418.2     418.2      418.2

The last value (set to 200.0 here) is the learning rate, which usually needs to be tuned. The input for the observation we are interested in is, as well as five possible counterfactuals, are given in the following table:

pretty_table(
    hcat(variables(sdm), instance(sdm, inst), cf[variables(sdm), :]);
    alignment = [:l, :c, :c, :c, :c, :c, :c],
    backend = :markdown,
    column_labels = ["Variable", "Obs.", "C. 1", "C. 2", "C. 3", "C. 4", "C. 5"],
    formatters = [fmt__printf("%4.1f", [2, 3, 4, 5, 6]), fmt__printf("%d", [1])],
)

Variable	Obs.	C. 1	C. 2	C. 3	C. 4	C. 5
1	15.2	13.5	13.5	13.5	13.6	13.5036
12	1318.0	1301.9	1312.6	1318.8	1361.6	1298.73

We can check the prediction that would be made on all the counterfactuals:

predict(sdm, cf)

5-element BitVector:
 1
 1
 1
 1
 1

Related documentation

SDeMo.counterfactual Function

counterfactual(model::AbstractSDM, x::Vector{T}, yhat, λ; maxiter=100, minvar=5e-5, kwargs...) where {T <: Number}

Generates one counterfactual explanation given an input vector x, and a target rule to reach yhat. The learning rate is λ. The maximum number of iterations used in the Nelder-Mead algorithm is maxiter, and the variance improvement under which the model will stop is minvar. Other keywords are passed to predict.

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