DiffPrivLib设ε=∞时决策树/随机森林与Sklearn结果不符求助

IBM专门设计了差分隐私库DiffPrivLib，使其使用方式与Scikit-learn完全一致以提升易用性。其官方教程指出，当设置epsilon=∞且使用相同random_state时，DiffPrivLib模型应与Scikit-learn的非私有模型完全一致。我已验证该特性在Gaussian Naive Bayes上有效，但使用几乎相同的代码框架运行Decision Tree Classifier时，得到的结果却截然不同；后续扩展到随机森林模型测试，也发现了同样的问题，求排查代码问题。

1. Scikit-learn非私有决策树代码及结果 #

# Import necessary packages
import pandas as pd
import numpy as np
from sklearn.tree import DecisionTreeClassifier
from sklearn.metrics import confusion_matrix, matthews_corrcoef
from sklearn import datasets
from sklearn.model_selection import train_test_split
import diffprivlib as dp

# Load breast cancer dataset into a dataframe
dataset = datasets.load_breast_cancer()
data = pd.DataFrame(data=dataset.data, columns=dataset.feature_names)
data['target'] = dataset.target
    
# Split into test and training sets
X = data.drop(['target'], axis=1)
y = data['target']
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# Build a Decision Tree Classifier
dt = DecisionTreeClassifier(random_state=42)

# Model training
dt.fit(X_train, y_train)

# Predict Output
y_pred_dt = dt.predict(X_test)

# Output metrics
print(matthews_corrcoef(y_test, y_pred_dt))
print(confusion_matrix(y_test, y_pred_dt))

运行结果：

0.8170347321131809
[[40  4]
 [ 4 66]]

2. DiffPrivLib决策树（epsilon=∞）代码及结果 #

# Calculate the bounds to prevent a privacy warning with DP-RF
min_values = data.min().tolist()[:-1]
max_values = data.max().tolist()[:-1]
bounds = (min_values, max_values)

# Define the classes to prevent a privacy warning with DP-RF
classes = np.array([0, 1])

# Build a Decision Tree Classifier
DPdt = dp.models.DecisionTreeClassifier(random_state=42, epsilon=np.inf, bounds=bounds, classes=classes)

# Model training
DPdt.fit(X_train, y_train)

# Predict Output
y_pred_DPdt = DPdt.predict(X_test)

# Output metrics
print(matthews_corrcoef(y_test, y_pred_DPdt))
print(confusion_matrix(y_test, y_pred_DPdt))

运行结果：

0.2813017973520981
[[13 33]
 [ 5 63]]

3. 扩展测试：随机森林模型的问题 #

我用DiffPrivLib的Random Forest和sklearn乳腺癌数据集重新测试，发现存在同样问题：

# Load the required packages
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import confusion_matrix
from sklearn.metrics import matthews_corrcoef
from sklearn.ensemble import RandomForestClassifier
from sklearn import datasets
from sklearn.model_selection import train_test_split
import diffprivlib as dp
    
# Load breast cancer dataset into a dataframe
dataset = datasets.load_breast_cancer()
data = pd.DataFrame(data=dataset.data, columns=dataset.feature_names)
data['target'] = dataset.target

# Calculate the bounds to prevent a privacy warning with DP-RF
min_values = data.min().tolist()[:-1]
max_values = data.max().tolist()[:-1]
bounds = (min_values, max_values)

# Calculate the classes to prevent a privacy warning with DP-RF
classes = np.array([0, 1])
    
# Split into test and training sets
X = data.drop(['target'], axis=1)
y = data['target']
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
    
# Calculate the MCC for the non-DP version of RF
rf = RandomForestClassifier(random_state=42)
rf.fit(X_train, y_train)
y_pred_rf = rf.predict(X_test)
rf_MCC = matthews_corrcoef(y_test, y_pred_rf)
print(confusion_matrix(y_test, y_pred_rf))
print("MCC: ", rf_MCC)
    
# Build a Differentially Private Random Forest Classifier
epsilon = np.inf  # Example epsilon value for differential privacy
    
DPrf = dp.models.RandomForestClassifier(epsilon=epsilon, random_state=42, bounds=bounds, classes=classes)
DPrf.fit(X_train, y_train)
y_pred_DPrf = DPrf.predict(X_test)
y_pred_DPrf = y_pred_DPrf.astype(int)
DPinf_MCC = matthews_corrcoef(y_test, y_pred_DPrf)
    
# Output metrics
print(confusion_matrix(y_test, y_pred_DPrf))
print("MCC: ", DPinf_MCC)

将测试在一系列epsilon值上重复30次并取平均值，得到如下结果：

可以看到DP版本的Random Forest收敛到的准确率远低于标准Scikit-learn版本。

请问我哪里出错了？

内容的提问来源于stack exchange，提问作者Alison Krauskopf