The Dirichlet Mechanism

This is the official code associated with the following paper:

Donlapark Ponnoprat (2022). Dirichlet Mechanism for Differentially Private KL Divergence Minimization. Transactions on Machine Learning Research.

This is a simple implementation of differentially private Naïve Bayes classification and differentially private Bayesian network.

• Flexible options for the underlying private mechanism, namely the Gaussian mechanism, Laplace mechanism, or Dirichlet mechanism.
• Preprocessing pipeline that can take data with non-numeric features and missing values.

Installation

1. Install the latest version of numpy, scipy, pandas and sklearn.
2. Place models.py, samplers.py and utils.py in the working directory.

Usage

1. Differentially Private Naïve Bayes Algorithm

Below is an example of fitting the model and making predictions on the Adult dataset. The model is privatized via sampling from the Dirichlet mechanism, where each sampling satisfies $(1,5)$-Renyi Differential Privacy.

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from models import DPNaiveBayes
from samplers import (DirichletMechanism,
                      GaussianMechanism,
                      LaplaceMechanism,
                      MLECalculator)
from utils import prepare_labeled_data

seed = 1


# Discretize continuous attributes and split the data, missing values allowed
# The label must be in the last column of the data file.
X_train, X_test, y_train, y_test = prepare_labeled_data("experiments/data/Adult.csv",
                                                        test_size=0.3,
                                                        num_bins=10,
                                                        seed=seed)

# Create a new sampler with (epsilon, lambda)-RDP. Currently, we have:
# 1. DirichletMechanism
# 2. GaussianMechanism
# 3. LaplaceMechanism
DM_sampler = DirichletMechanism(epsilon=1.0, lambda_=5)

# Create a DP naive bayes model with the specified sampler
dpnb = DPNaiveBayes(sampler=DM_sampler, random_state=seed)

# Fit the model
dpnb.fit(X_train, y_train)

# Make predictions on the test set
y_pred = dpnb.predict(X_test)

# Make predicted probabilities on the test set
y_prob = dpnb.predict_proba(X_test)

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2. Differentially Private Bayesian Network

Below is an example of fitting the model with a specific graph on the Adult dataset. The model is privatized via sampling from the Dirichlet mechanism, where each sampling satisfies $(1,5)$-Renyi Differential Privacy.

To compute the log-likelihood on the test data, we have to fit an MLE model (no sampling) on the test set in order to obtain the count data.

---

from models import DPBayesianNetwork
from samplers import (DirichletMechanism,
                      GaussianMechanism,
                      LaplaceMechanism,
                      MLECalculator)
from utils import loglikelihood, prepare_data

seed = 1


# Define a Bayesian networks. The keys are nodes, and the values are associated parents.
adult_net = {"age": [],
             "sex": [],
             "education": ["age"],
             "occupation": ["age", "sex", "education"],
             "capital-gain": ["sex", "education", "occupation"],
             "capital-loss": ["sex", "occupation", "capital-gain"],
             "income": ["occupation", "capital-gain", "capital-loss"]}

# Discretize continuous attributes and split the data, missing values allowed
X_train, X_test = prepare_data("experiments/data/Adult.csv",
                               test_size=0.3,
                               num_bins=10,
                               seed=seed)

# Create a new sampler with (epsilon, lambda)-RDP. Currently, we have:
# 1. DirichletMechanism
# 2. GaussianMechanism
# 3. LaplaceMechanism
DM_sampler = DirichletMechanism(epsilon=1.0, lambda_=5)

# Create a DP Bayesian network with the specified sampler
dpbn = DPBayesianNetwork(bayesian_net=adult_net,
                         sampler=DM_sampler,
                         random_state=seed)

# Fit the model and obtain private parameters
dpbn.fit(X_train)

# To compute the log-likelihood on the test set,
# we need its count data, which can be obtained
# by fitting an MLE model (specifying MLE_calc 
# as the sampler)
MLE_calc = MLECalculator(prior=0.1)
mlebn = DPBayesianNetwork(bayesian_net=adult_net,
                          sampler=MLE_calc,
                          random_state=seed)

# Fit the MLE model and obtain test counts
mlebn.fit(X_test)

# Compute the log-likelihood on the test set
# using the test counts and private parameters
ll = loglikelihood(mlebn.count_dict, dpbn.param_dict)

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