Simulated data, real problem
Simulated data
Let’s consider a following problem, the model is defined as
y = x1 * x2 + x2
But x1 and x2 are correlated. How XAI methods work for such model?
Explainer for the models
In fact this model is defined by the predict function
the_model_predict. So it does not matter what is in the
first argument of the explain function.
#> Preparation of a new explainer is initiated
#> -> model label : numeric ( default )
#> -> data : 50 rows 2 cols
#> -> target variable : not specified! ( WARNING )
#> -> predict function : the_model_predict
#> -> predicted values : No value for predict function target column. ( default )
#> -> model_info : package Model of class: numeric package unrecognized , ver. Unknown , task regression ( default )
#> -> model_info : Model info detected regression task but 'y' is a NULL . ( WARNING )
#> -> model_info : By deafult regressions tasks supports only numercical 'y' parameter.
#> -> model_info : Consider changing to numerical vector.
#> -> model_info : Otherwise I will not be able to calculate residuals or loss function.
#> -> predicted values : numerical, min = -0.1726853 , mean = 7.70239 , max = 29.16158
#> -> residual function : difference between y and yhat ( default )
#> A new explainer has been created!Ceteris paribus
Use the ceteris_paribus() function to see Ceteris
Paribus profiles. Clearly it’s not an additive model, as the effect of
x1 depends on x2.
library("ingredients")
library("ggplot2")
sample_rows <- data.frame(x1 = -5:5,
x2 = -5:5)
cp_model <- ceteris_paribus(explain_the_model, sample_rows)
plot(cp_model) +
show_observations(cp_model) +
ggtitle("Ceteris Paribus profiles")
Dependence profiles
Lets try Partial Dependence profiles, Conditional Dependence profiles and Accumulated Local profiles. For the last two we can try different smoothing factors
pd_model <- partial_dependence(explain_the_model, variables = c("x1", "x2"))
pd_model$`_label_` = "PDP"
cd_model <- conditional_dependence(explain_the_model, variables = c("x1", "x2"))
cd_model$`_label_` = "CDP 0.25"
ad_model <- accumulated_dependence(explain_the_model, variables = c("x1", "x2"))
ad_model$`_label_` = "ALE 0.25"
plot(ad_model, cd_model, pd_model) +
ggtitle("Feature effects - PDP, CDP, ALE")
cd_model_1 <- conditional_dependence(explain_the_model, variables = c("x1", "x2"), span = 0.1)
cd_model_1$`_label_` = "CDP 0.1"
cd_model_5 <- conditional_dependence(explain_the_model, variables = c("x1", "x2"), span = 0.5)
cd_model_5$`_label_` = "CDP 0.5"
ad_model_1 <- accumulated_dependence(explain_the_model, variables = c("x1", "x2"), span = 0.5)
ad_model_1$`_label_` = "ALE 0.1"
ad_model_5 <- accumulated_dependence(explain_the_model, variables = c("x1", "x2"), span = 0.5)
ad_model_5$`_label_` = "ALE 0.5"
plot(ad_model, cd_model, pd_model, cd_model_1, cd_model_5, ad_model_1, ad_model_5) +
ggtitle("Feature effects - PDP, CDP, ALE")
Dependence profiles in groups
And now, let’s see how the grouping factor works
# add grouping variable
df$x3 <- factor(sign(df$x2))
# update the data argument
explain_the_model$data = df
# PDP in groups
pd_model_groups <- partial_dependence(explain_the_model,
variables = c("x1", "x2"),
groups = "x3")
plot(pd_model_groups) +
ggtitle("Partial Dependence")
# ALE in groups
ad_model_groups <- accumulated_dependence(explain_the_model,
variables = c("x1", "x2"),
groups = "x3")
plot(ad_model_groups) +
ggtitle("Accumulated Local")
# CDP in groups
cd_model_groups <- conditional_dependence(explain_the_model,
variables = c("x1", "x2"),
groups = "x3")
plot(cd_model_groups) +
ggtitle("Conditional Dependence")
Session info
#> R version 4.4.1 (2024-06-14)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.1 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] ggplot2_3.5.1 ranger_0.16.0 ingredients_2.3.1 DALEX_2.5.1
#> [5] rmarkdown_2.28
#>
#> loaded via a namespace (and not attached):
#> [1] Matrix_1.7-1 gtable_0.3.6 jsonlite_1.8.9 highr_0.11
#> [5] compiler_4.4.1 Rcpp_1.0.13 jquerylib_0.1.4 scales_1.3.0
#> [9] yaml_2.3.10 fastmap_1.2.0 lattice_0.22-6 R6_2.5.1
#> [13] labeling_0.4.3 knitr_1.48 tibble_3.2.1 maketools_1.3.1
#> [17] munsell_0.5.1 bslib_0.8.0 pillar_1.9.0 rlang_1.1.4
#> [21] utf8_1.2.4 cachem_1.1.0 xfun_0.48 sass_0.4.9
#> [25] sys_3.4.3 cli_3.6.3 withr_3.0.2 magrittr_2.0.3
#> [29] digest_0.6.37 grid_4.4.1 lifecycle_1.0.4 vctrs_0.6.5
#> [33] evaluate_1.0.1 glue_1.8.0 farver_2.1.2 buildtools_1.0.0
#> [37] fansi_1.0.6 colorspace_2.1-1 tools_4.4.1 pkgconfig_2.0.3
#> [41] htmltools_0.5.8.1