Can we have shap value in the log-odds for binary target? about shapviz

[actuarial-lonewolf]

I stumbled into this thread, searching for a way to display a shapviz waterfall with probabilities.
I understand the concern about the misleading element.

@madprogramer ... it would be nice if you shared your solution.

After having spent a good hour on my end, I'm sharing the completed function that was hinted last year, as it might help others in the future.

# Gross approximation to transform shap values into binary probabilities
special_transform <- function(shp) {
  b <- get_baseline(shp)
  S <- get_shap_values(shp)
  X <- get_feature_values(shp)
  
  # calculate prediction:
  p <- exp(b + rowSums(S)) / ( 1 + exp(b + rowSums(S)) )
  
  # transforming the baseline and shap values:
  b_new <- exp(b) / (1 + exp(b))
  S_new <- S / rowSums(S)*(p - b_new)
  
  shapviz(S_new, X, b_new)
}

[mayer79]

Actually, the SHAP values returned by XGBoost or LightGBM are on the logit link scale.

library(shapviz)
library(xgboost)

X <- iris[, -1]

# Binary logistic regression with XGBoost
fit <- xgb.train(
  params = list(objective = "binary:logistic"), 
  data = xgb.DMatrix(data.matrix(X), label = iris[, 1] >= 5.8), 
  nrounds = 30
)

# On logit scale
shp <- shapviz(fit, X_pred = data.matrix(X), X = X)
sv_waterfall(shp, row_id = 66)

If you rather mean to switch to probabilities, I don't think it is possible without violating at least some of the Shapley fairness axioms (linearity). Still, I think we could add a utility function that would map the "shapviz" object approximately from logit to probability space, using the approach in the blog post you provided.

[ferrenlove]

Thank you ! If you can add a link function it would be superb!
BTW, I used your script and it retuned a below pic:

For the The E(f(x)] = 0.116, f(x) = 2.7, I guess there are not probabilities and still need to convert , along with the numbers highlighted in yellow bar together.

[mayer79]

The values in the plot above are log-odds and they are on the logit scale. So I think you are interested in transforming them (somehow) via logistic functio (= inverse logit) to propabilities without badly violating SHAP properties. I will look into that in the next time!

[mayer79]

I looked into the matter. According to the proposed transformation, a jump from 0.5 to 0.59 would be as large as a jump from 0.9 to 0.99 on the probability scale. I currently don't see a situation where this makes sense. Thus I wont add this transformation to "shapviz". If you still need it, simply do the transformation based on

special_transform <- function(shp) {
  b <- get_baseline(shp)
  S <- get_shap_values(shp)
  X <- get_feature_values(shp)
  b_new <- g(b, S)
  S_new <- f(b, S)
  shapviz(S_new, X, b_new)
}

[ferrenlove]

Thank you for writing this specical transform funtion for me. However, it gives me a error "Error in g(b, S) : could not find function "g"". Can you help with this?

[mayer79]

I leave this as an exercise to you. Based on your link, it is just 2-3 lines of code. But as I said, I can't think of a situation where the proposed mapping makes much sense. On the contrary, I think it is misleading.

[ferrenlove]

Thank you! I ran the python codes to get an idea of what shap output array and baseline prediction looks like. I tried a few different codes and results turn out differntly. I will spend more time looking at it. Appreciate your help!

[madprogramer]

@mayer79 I know the issue is closed, but I made a logit to binary linking function some time ago.

I still understand that you don't want to add it in though :<

[mayer79]

As far as I remember, any non-linear transform will violate the fairness axioms of Shapley, so I'd like to keep it outside the package.

Since the "shapviz" object contains the baseline b and all SHAP values S, you could write a blogpost or similar for those interested?

[mayer79]

@actuarial-lonewolf : Thanks for this input!

Comparing with Kernel SHAP (once on link scale and once on probability scale):

library(kernelshap)
library(shapviz)

fit <- glm(Treatment ~ Type + conc + uptake, data = CO2, family = binomial)
v <- c("Type", "conc", "uptake")
(link_scale <- shapviz(kernelshap(fit, X = CO2, bg_X = CO2, feature_names = v)))
(prob_scale <- shapviz(kernelshap(fit, X = CO2, bg_X = CO2, feature_names = v, type = "response")))

transformed <- special_transform(link_scale)

get_shap_values(prob_scale[1:5, ])
#           Type        conc      uptake
# [1,] 0.1945444 -0.12989845  0.34064436
# [2,] 0.1970985 -0.15394423 -0.08552033
# [3,] 0.1711899 -0.11740017 -0.23216460
# [4,] 0.1613382 -0.06415103 -0.30143362
# [5,] 0.1884975  0.02929410 -0.22343369

get_shap_values(transformed[1:5, ])
#           Type        conc     uptake
# [1,] 0.2197120 -0.19802628  0.3731001
# [2,] 0.3076373 -0.21203252 -0.1484753
# [3,] 0.2954062 -0.14487101 -0.3394145
# [4,] 0.2910848 -0.06558863 -0.4402471
# [5,] 0.3082047  0.05310590 -0.3774572