Why does lightgbm not fit my toy example but catboost does? (2 order interactions) [D]

I am trying understand how tree-based regression model handle the dependencies of the target variables on the interaction of explanatory variables. However my experiment revealed that my understanding about the fitting process of a lgbm is not correct. And I don’t know why. My experiment is quite simple: a target (for sake of simplicity only in [0, 1]) and two explanatory variables with two values such that the mean of the target is the same for each of the values of the explanatory variables. Then there is a third variable that models the interaction of the explanatory variables by a simple count. So in code: >>> import polars as pl df = pl.Dataframe( { „y“: [0, 0, 1, 1, 0, 0, 1, 1], # mean across „A“ values the same; mean across „B“ values the same „A“: [1, 1, 1, 1, 0, 0, 0, 0], „B“: [1, 1, 0, 0, 1, 1, 0, 0], „AB“ [1, 1, 2, 2, 3, 3, 4, 4] # just some IDs for the interaction } ) <<< I then fitted a lgbm just with „A“ and „B“ and got the expected constant 0.5 forecast >>> from lightgbm import LGBMRegressor lgbm = LGBMRegressor(min_child_samples=1) lgbm.fit(df[[„A“, „B“]].to_numpy(), df[„y“].to_numpy()) lgbm.predict(df[[„A“, „B“]].to_numpy()).round(0) array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]) <<< Then I did the same but with „AB“ and expected a perfect fit. But I was disappointed, it fitted to constant zero >>> lgbm = LGBMRegressor(min_child_samples=1) lgbm.fit(df[[„AB“]].to_numpy(), df[„y“].to_numpy()) lgbm.predict(df[[„AB“]].to_numpy()).round(0) array([0, 0, 0, 0, 0, 0, 0, 0,]) <<< I tried to code „AB“ as category. But still no perfect fit: >>> lgbm = LGBMRegressor(min_child_samples=1) lgbm.fit(df[[„AB“]].to_numpy(), df[„y“].to_numpy()) lgbm.predict(df[[„AB“]].to_numpy()).round(0) array([0, 0, 1, 1, 0, 0, 0, 0,]) <<< Super confusing! I then turned to catboost and found even without „AB“ it fit the data perfectly: >>> from catboost import CatBoostRegressor cbm = LGBMRegressor(min_data_in_leaf=1) cbm.fit(df[[„A“, „B“]].to_numpy(), df[„y“].to_numpy()) cbm.predic