Counterfactuals

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

julia

using SpeciesDistributionToolkit
using CairoMakie
using PrettyTables

We will work on the demo data:

julia

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

RawData → NaiveBayes → P(x) ≥ 0.482

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:

julia

inst = 6

And look at its outcome:

julia

outcome = predict(sdm)[inst]

true

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):

julia

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

0.4342054891497297

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

julia

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

19×5 Matrix{Float64}:
  11.7197   13.0627   11.1446   12.9848   12.7248
   3.4       3.4       3.4       3.4       3.4
  18.8      18.8      18.8      18.8      18.8
 509.6     509.6     509.6     509.6     509.6
  19.7      19.7      19.7      19.7      19.7
   1.7       1.7       1.7       1.7       1.7
  18.0      18.0      18.0      18.0      18.0
   8.7       8.7       8.7       8.7       8.7
  16.4      16.4      16.4      16.4      16.4
  17.5      17.5      17.5      17.5      17.5
   3.4       3.4       3.4       3.4       3.4
 810.759   946.152   757.566   937.084   907.891
 133.0     133.0     133.0     133.0     133.0
  15.0      15.0      15.0      15.0      15.0
  44.0      44.0      44.0      44.0      44.0
 381.0     381.0     381.0     381.0     381.0
  69.0      69.0      69.0      69.0      69.0
  85.0      85.0      85.0      85.0      85.0
 281.0     281.0     281.0     281.0     281.0

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:

julia

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

Variable	Obs.	C. 1	C. 2	C. 3	C. 4	C. 5
1	9.8	11.7	13.1	11.1	13.0	12.7248
12	947.0	810.8	946.2	757.6	937.1	907.891

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

julia

predict(sdm, cf)

5-element BitVector:
 0
 0
 0
 0
 0

Counterfactuals ​

Counterfactuals