[python-package] `init_score` causes the predictions different about lightgbm HOT 6 CLOSED

import pandas as pd
import lightgbm as lgb
from sklearn import datasets
from sklearn.linear_model import LinearRegression

diabetes = datasets.load_diabetes()
n, p = diabetes["data"].shape


def lgb_model(init_score):
    train_set = lgb.Dataset(
        data=diabetes["data"],
        label=diabetes["target"],
        feature_name=diabetes["feature_names"],
        init_score=init_score,
    )
    params = {
        "objective": "tweedie",  # change to tweedie
        "verbosity": -1,
        "seed": 0,
    }
    model = lgb.train(params, train_set)
    predictions = model.predict(diabetes["data"])
    if init_score is not None:
        predictions += init_score. # add init_score
    return predictions


init_model = LinearRegression().fit(diabetes["data"], diabetes["target"])
results = pd.DataFrame(
    {
        "target": diabetes["target"],
        "init - None": lgb_model(None),
        "init - mean": lgb_model([diabetes["target"].mean()] * n),
        "init - linear": lgb_model(init_model.predict(diabetes["data"])),
    }
)

print(results.head())

def lgb_model(init_score):
    train_set = lgb.Dataset(
        data=diabetes["data"],
        label=diabetes["target"],
        feature_name=diabetes["feature_names"],
    )
    if init_score is not None:
        train_set.set_init_score(np.log(init_score))
    params = {
        "objective": "tweedie",
        "verbosity": -1,
        "seed": 0,
    }
    model = lgb.train(params, train_set)
    predictions = model.predict(diabetes["data"])
    if init_score is not None:
        # transform back to log scale and add init_score
        predictions = np.exp(np.log(predictions) + train_set.init_score)
    return predictions

    convert_output = np.exp  # for tweedie and poisson
    predictions = model.predict(diabetes["data"], raw_score=True)
    if init_score is not None:
        predictions += init_score
    return convert_output(predictions)