It seems if lightgbm.train is used with an initial score (init_score) it cannot boost this score.
Here is a simple example:
params = {"learning_rate": 0.1,"metric": "binary_logloss","objective": "binary",
"boosting_type": "gbdt","num_iterations": 5, "num_leaves": 2 ** 2,
"max_depth": 2, "num_threads": 1, "verbose": 0, "min_data_in_leaf": 1}
x = pd.DataFrame([[1, 0.1, 0.3], [1, 0.1, 0.3], [1, 0.1, 0.3],
[0, 0.9, 0.3], [0, 0.9, 0.3], [0, 0.9, 0.3]], columns=["a", "b", "prob"])
y = pd.Series([0, 1, 0, 0, 1, 0])
d_train = lgb.Dataset(x, label=y)
model = lgb.train(params, d_train)
y_pred_default = model.predict(x, raw_score=False)
In the case above, no init_score is used. The predictions are correct: y_pred_default = [0.33333333, ... ,0.33333333]
d_train = lgb.Dataset(x, label=y, init_score=scipy.special.logit(x["prob"]))
model = lgb.train(params, d_train)
y_pred_raw = model.predict(x, raw_score=True)
In this part, we assume column "prob" from x to be our initial guess (maybe by some other model). We apply logit and use it as initial score. However, the model cannot improve and the boosting will always return 0: y_pred_raw = [0, 0, 0, 0, 0, 0]
y_pred_raw_with_init = scipy.special.logit(x["prob"]) + y_pred_raw
y_pred = scipy.special.expit(y_pred_raw_with_init)
This part above shows the way I suppose is correct to translate the initial scores together with the boosting back to probabilities. Since the boosting is zero y_pred yields [0.3, ..., 0.3] which is our initial probability.
