torus-ml/docs/advanced_examples/ExperimentPrivacyTreePaper.ipynb

Experimentation with Privacy Tree: Reproducing Results from the Paper

This notebook provides a way to reproduce the experiment described in the paper Privacy-Preserving Tree-Based Inference with Fully Homomorphic Encryption. By following the instructions in this notebook, users can run the experiment themselves and verify the results reported in the paper.

In [1]:

# Importing necessary libraries and modules

import time

import numpy as np
from IPython.display import display
from onnx import numpy_helper
from sklearn.datasets import fetch_openml
from sklearn.metrics import (
    accuracy_score,
    average_precision_score,
    f1_score,
    precision_score,
    recall_score,
)
from sklearn.model_selection import RepeatedKFold
from sklearn.preprocessing import LabelBinarizer, OrdinalEncoder

from torus.ml.sklearn import DecisionTreeClassifier, RandomForestClassifier, XGBClassifier


def basic_preprocessing(df, target_column):
    """
    Convert categorical columns to their corresponding code values
    and binarize the target column.

    Parameters:
        df (pandas.DataFrame): Input dataframe to preprocess.
        target_column (str): Name of the target column to be binarized.

    Returns:
        pandas.DataFrame: Preprocessed dataframe.
    """

    for col in df.columns:
        if df[col].dtype == "object":
            df[col] = df[col].astype("category")
            df[col] = df[col].cat.codes
        elif df[col].dtype == "category":
            df[col] = df[col].cat.codes
    df[target_column] = LabelBinarizer().fit_transform(df[target_column])

    return df

In [2]:

# Set up dataset names and their respective IDs for fetching from OpenML
dataset_names = {
    "spambase": 44,
    "wine": None,
    "heart-h": 1565,
    "wdbc": 1510,
    "adult": None,
    "steel": 1504,
}

datasets = {}


def load_dataset(name, data_id=None):
    """Load dataset from OpenML by name or by ID.

    Args:
        name (str): Name of the dataset.
        data_id (int, optional): The ID of the dataset on OpenML.
            If provided, the dataset is loaded by ID.

    Returns:
        X (np.array): Features of the dataset.
        y (np.array): Target labels of the dataset.
    """
    if data_id is not None:
        X, y = fetch_openml(data_id=data_id, as_frame=True, cache=True, return_X_y=True)
    else:
        X, y = fetch_openml(name=name, as_frame=True, cache=True, return_X_y=True)
    return X, y


def preprocess_features(X):
    """Convert categorical columns to numerical."""
    X_processed = X.copy()

    for column in X_processed.columns:
        if X_processed[column].dtype == "object" or X_processed[column].dtype.name == "category":
            # Convert categorical columns to numeric using label encoding
            X_processed[column] = X_processed[column].astype("category").cat.codes

    return X_processed.astype(np.float32)


for ds_name, ds_id in dataset_names.items():
    print(f"Loading {ds_name}")

    X, y = load_dataset(ds_name, ds_id)

    # Preprocess features (handle categorical data)
    X = preprocess_features(X)

    # Remove rows with NaN values
    not_nan_mask = ~np.isnan(X).any(axis=1)
    X = X[not_nan_mask]
    y = y[not_nan_mask]

    # Convert non-integer target labels to integers
    if not y.dtype == np.int64:
        encoder = OrdinalEncoder()
        # Convert pandas Series to numpy array before reshaping
        y = encoder.fit_transform(np.array(y).reshape(-1, 1)).astype(np.int32).squeeze()

    # Ensure both X and y are numpy arrays before storing
    datasets[ds_name] = {"X": np.array(X), "y": np.array(y)}

Loading spambase
Loading wine

Loading heart-h

Loading wdbc

Loading adult

Loading steel

In [3]:

# Setting a random seed for reproducibility across all models and operations
random_seed = 42

# Models with their hyper-parameters
model_hyperparameters = {
    DecisionTreeClassifier: {"max_depth": 5, "random_state": random_seed},
    XGBClassifier: {"max_depth": 3, "n_estimators": 50, "random_state": random_seed},
    RandomForestClassifier: {"n_estimators": 50, "random_state": random_seed},
}

decision_tree_comparison_params = {
    "spam": {"max_leaf_nodes": 58, "max_depth": 17},
    "heart-h": {"max_leaf_nodes": 5, "max_depth": 3},
    "steel": {"max_leaf_nodes": None, "max_depth": 5},
    "wdbc": {"max_leaf_nodes": None, "max_depth": 10},
}

# List of bit-width used for quantization
n_bits_list = list(range(1, 10))

In [4]:

def analyze_gemm_computation(torus_classifier):
    """Analyze the GEMM (General Matrix Multiply) operations in the given ONNX model.

    Args:
        torus_classifier (object): Classifier that contains an ONNX model representation.
        x_train (np.array): Training dataset.

    Returns:
        tuple: Shapes of the matrices involved in GEMM operations.
    """

    # Extract weights and biases from the ONNX model graph
    quant_params = {
        onnx_init.name: numpy_helper.to_array(onnx_init)
        for onnx_init in torus_classifier.onnx_model.graph.initializer
        if "weight" in onnx_init.name or "bias" in onnx_init.name
    }

    # Extract the shapes of matrices used in GEMM operations
    matrix_shapes = []
    for i in range(1, 4):
        key = [key for key in quant_params.keys() if f"_{i}" in key and "weight" in key][0]
        matrix_shapes.append(quant_params[key].shape)

    return tuple(matrix_shapes)

Experiments for table 1

In [5]:

def benchmark_model(X, y, model, model_params, n_bits, rkf):
    """Benchmark a given model and return its evaluation scores."""
    scores = {
        "precision": [],
        "recall": [],
        "accuracy": [],
        "f1": [],
        "average_precision": [],
        "nodes": None,
    }
    scores_fp32 = {"precision": [], "recall": [], "accuracy": [], "f1": [], "average_precision": []}

    metric_func_to_key = {
        "precision_score": "precision",
        "recall_score": "recall",
        "f1_score": "f1",
        "average_precision_score": "average_precision",
    }

    for train_index, test_index in rkf.split(X):
        X_train, X_test = X[train_index], X[test_index]
        y_train, y_test = y[train_index], y[test_index]

        torus_model, sklearn_model = model(n_bits=n_bits, **model_params).fit_benchmark(
            X_train, y_train
        )

        y_pred = torus_model.predict(X_test)
        if len(set(y_test)) == 2:
            for metric_func in [precision_score, recall_score, average_precision_score, f1_score]:
                scores_key = metric_func_to_key[metric_func.__name__]
                scores[scores_key].append(metric_func(y_test, y_pred))
        scores["accuracy"].append(accuracy_score(y_test, y_pred))

        y_pred_fp32 = sklearn_model.predict(X_test)
        if len(set(y_test)) == 2:
            for metric_func in [precision_score, recall_score, average_precision_score, f1_score]:
                scores_key = metric_func_to_key[metric_func.__name__]
                scores_fp32[scores_key].append(metric_func(y_test, y_pred_fp32))
        scores_fp32["accuracy"].append(accuracy_score(y_test, y_pred_fp32))

        shapes = analyze_gemm_computation(torus_model)
        scores["nodes"] = shapes[0][0]

    # Calculate inference time
    torus_model.compile(X_train)
    torus_model.fhe_circuit.keygen(force=False)

    start = time.time()
    torus_model.predict(X_test[:1], fhe="execute")
    end = time.time()
    scores["inference_time"] = end - start

    start = time.time()
    torus_model.predict(X_test[:1])
    end = time.time()
    scores_fp32["inference_time"] = end - start

    return scores, scores_fp32


n_bits = 6
scores_global = {}

rkf = RepeatedKFold(n_splits=5, n_repeats=3, random_state=0)

for dataset_name, dataset_data in datasets.items():
    X, y = dataset_data["X"].astype(np.float32), dataset_data["y"]
    assert len(set(y)) >= 2
    if y.dtype not in [np.int32, bool]:
        print(f"Unexpected datatype for y in dataset {dataset_name}: {y.dtype}")

    key_dataset = f"{dataset_name} (#features: {X.shape[1]})"
    scores_global[key_dataset] = {}

    for cls, model_params in model_hyperparameters.items():
        scores, scores_fp32 = benchmark_model(X, y, cls, model_params, n_bits, rkf)

        scores_global[key_dataset][cls.__name__ + "_torus"] = scores
        scores_global[key_dataset][cls.__name__ + "_fp32"] = scores_fp32

        print(
            f"{cls.__name__} on {key_dataset} -> Acc: {np.mean(scores['accuracy']):.4f}, "
            f"Acc (fp32): {np.mean(scores_fp32['accuracy']):.4f}, "
            f"FHE inference time: {scores['inference_time']:.2f}s"
        )

DecisionTreeClassifier on spambase (#features: 57) -> Acc: 0.9103, Acc (fp32): 0.9035, FHE inference time: 1.28s

XGBClassifier on spambase (#features: 57) -> Acc: 0.9448, Acc (fp32): 0.9497, FHE inference time: 1.01s

RandomForestClassifier on spambase (#features: 57) -> Acc: 0.9089, Acc (fp32): 0.9184, FHE inference time: 1.58s

DecisionTreeClassifier on wine (#features: 13) -> Acc: 0.9083, Acc (fp32): 0.9046, FHE inference time: 0.73s

XGBClassifier on wine (#features: 13) -> Acc: 0.9699, Acc (fp32): 0.9624, FHE inference time: 1.63s

RandomForestClassifier on wine (#features: 13) -> Acc: 0.9850, Acc (fp32): 0.9813, FHE inference time: 1.14s

DecisionTreeClassifier on heart-h (#features: 13) -> Acc: 0.6100, Acc (fp32): 0.5998, FHE inference time: 0.65s

XGBClassifier on heart-h (#features: 13) -> Acc: 0.6543, Acc (fp32): 0.6463, FHE inference time: 2.91s

RandomForestClassifier on heart-h (#features: 13) -> Acc: 0.6679, Acc (fp32): 0.6644, FHE inference time: 1.51s

DecisionTreeClassifier on wdbc (#features: 30) -> Acc: 0.9420, Acc (fp32): 0.9391, FHE inference time: 0.72s

XGBClassifier on wdbc (#features: 30) -> Acc: 0.9678, Acc (fp32): 0.9649, FHE inference time: 0.82s

RandomForestClassifier on wdbc (#features: 30) -> Acc: 0.9561, Acc (fp32): 0.9526, FHE inference time: 1.35s

DecisionTreeClassifier on adult (#features: 14) -> Acc: 0.8364, Acc (fp32): 0.8364, FHE inference time: 0.67s

XGBClassifier on adult (#features: 14) -> Acc: 0.8535, Acc (fp32): 0.8543, FHE inference time: 0.88s

RandomForestClassifier on adult (#features: 14) -> Acc: 0.8341, Acc (fp32): 0.8341, FHE inference time: 2.30s

DecisionTreeClassifier on steel (#features: 33) -> Acc: 0.9717, Acc (fp32): 0.9717, FHE inference time: 0.59s

XGBClassifier on steel (#features: 33) -> Acc: 1.0000, Acc (fp32): 1.0000, FHE inference time: 0.66s

RandomForestClassifier on steel (#features: 33) -> Acc: 0.9687, Acc (fp32): 0.9586, FHE inference time: 1.41s

In [6]:

import math

import pandas as pd

df = pd.DataFrame.from_dict(
    {(i, j): value for i, scores in scores_global.items() for j, value in scores.items()},
    orient="index",
)


df["FHE/Clear ratio"] = (df["inference_time"] / df["inference_time"].shift(-1)).apply(
    lambda x: "" if (x < 1) or (math.isnan(x)) else str(int(round(x, 0))) + "x"
)


def format_scores(val):
    if isinstance(val, list):
        if not val:
            return "-"
        return f"{np.mean(val) * 100:.1f}\\% ± {np.std(val) * 100:.1f}\\%"

    if pd.isna(val):
        return "-"

    if isinstance(val, (float, int)):
        # To ensure all floating point values are treated as percentages
        return f"{val:.3f}"

    if "x" in str(val):  # Ensure that val is treated as a string
        return val

    return "-"


df = df.applymap(format_scores)

# Renaming for display
model_names = {
    "DecisionTreeClassifier_torus": "FHE-DT",
    "DecisionTreeClassifier_fp32": "FP32-DT",
    "XGBClassifier_torus": "FHE-XGB",
    "XGBClassifier_fp32": "FP32-XGB",
    "RandomForestClassifier_torus": "FHE-RF",
    "RandomForestClassifier_fp32": "FP32-RF",
}

for original, renamed in model_names.items():
    df.index = df.index.set_levels(df.index.levels[1].str.replace(original, renamed), level=1)

df.columns = df.columns.str.replace("average_precision", "AP")

# Reordering Columns
columns_order = [col for col in df if col not in ["FHE/Clear ratio", "inference_time"]] + [
    "inference_time",
    "FHE/Clear ratio",
]
df = df[columns_order]

# Drop and rename columns
df.columns = df.columns.str.replace("inference_time", "Time (s)")
df.drop(columns=["precision", "recall"], inplace=True)

# Adjust LaTeX output
latex_code = df.to_latex(multirow=True, escape=False, column_format="l|l|l|l|l|l|l|l")

latex_code = latex_code.replace("#", "\\#")
display(df)

		accuracy	f1	AP	nodes	Time (s)	FHE/Clear ratio
spambase (#features: 57)	FHE-DT	91.0\% ± 1.0\%	88.0\% ± 1.3\%	84.3\% ± 1.7\%	23.000	1.283	610x
	FP32-DT	90.3\% ± 1.0\%	87.4\% ± 1.2\%	82.4\% ± 1.8\%	-	0.002	-
	FHE-XGB	94.5\% ± 0.8\%	92.9\% ± 1.1\%	89.6\% ± 1.4\%	350.000	1.014	474x
	FP32-XGB	95.0\% ± 0.7\%	93.6\% ± 0.9\%	90.5\% ± 1.1\%	-	0.002	-
	FHE-RF	90.9\% ± 1.1\%	87.5\% ± 1.5\%	84.6\% ± 1.7\%	750.000	1.582	664x
	FP32-RF	91.8\% ± 1.1\%	89.0\% ± 1.4\%	86.0\% ± 1.6\%	-	0.002	-
wine (#features: 13)	FHE-DT	90.8\% ± 5.2\%	-	-	7.000	0.731	649x
	FP32-DT	90.5\% ± 5.0\%	-	-	-	0.001	-
	FHE-XGB	97.0\% ± 2.4\%	-	-	900.000	1.634	1321x
	FP32-XGB	96.2\% ± 2.9\%	-	-	-	0.001	-
	FHE-RF	98.5\% ± 1.4\%	-	-	500.000	1.139	804x
	FP32-RF	98.1\% ± 2.0\%	-	-	-	0.001	-
heart-h (#features: 13)	FHE-DT	61.0\% ± 5.4\%	-	-	21.000	0.647	596x
	FP32-DT	60.0\% ± 5.5\%	-	-	-	0.001	-
	FHE-XGB	65.4\% ± 7.8\%	-	-	1750.000	2.908	1732x
	FP32-XGB	64.6\% ± 7.5\%	-	-	-	0.002	-
	FHE-RF	66.8\% ± 6.4\%	-	-	750.000	1.508	1362x
	FP32-RF	66.4\% ± 5.3\%	-	-	-	0.001	-
wdbc (#features: 30)	FHE-DT	94.2\% ± 1.9\%	92.0\% ± 2.8\%	88.4\% ± 4.1\%	15.000	0.717	401x
	FP32-DT	93.9\% ± 1.9\%	91.7\% ± 3.0\%	87.3\% ± 4.8\%	-	0.002	-
	FHE-XGB	96.8\% ± 1.1\%	95.5\% ± 1.8\%	93.4\% ± 2.5\%	350.000	0.825	555x
	FP32-XGB	96.5\% ± 1.6\%	95.2\% ± 2.4\%	92.9\% ± 3.4\%	-	0.001	-
	FHE-RF	95.6\% ± 1.7\%	93.9\% ± 2.6\%	91.2\% ± 3.6\%	700.000	1.350	883x
	FP32-RF	95.3\% ± 1.8\%	93.4\% ± 2.9\%	90.4\% ± 4.1\%	-	0.002	-
adult (#features: 14)	FHE-DT	83.6\% ± 0.4\%	60.4\% ± 0.7\%	50.3\% ± 0.8\%	30.000	0.666	548x
	FP32-DT	83.6\% ± 0.4\%	60.4\% ± 0.7\%	50.3\% ± 0.7\%	-	0.001	-
	FHE-XGB	85.3\% ± 0.2\%	67.3\% ± 0.7\%	55.5\% ± 0.7\%	350.000	0.880	673x
	FP32-XGB	85.4\% ± 0.2\%	67.8\% ± 0.4\%	55.8\% ± 0.6\%	-	0.001	-
	FHE-RF	83.4\% ± 0.4\%	57.6\% ± 1.1\%	49.2\% ± 0.8\%	750.000	2.295	2073x
	FP32-RF	83.4\% ± 0.4\%	57.6\% ± 1.2\%	49.2\% ± 0.9\%	-	0.001	-
steel (#features: 33)	FHE-DT	97.2\% ± 0.7\%	96.1\% ± 0.9\%	92.5\% ± 1.7\%	5.000	0.587	346x
	FP32-DT	97.2\% ± 0.7\%	96.1\% ± 0.9\%	92.5\% ± 1.7\%	-	0.002	-
	FHE-XGB	100.0\% ± 0.0\%	100.0\% ± 0.0\%	100.0\% ± 0.0\%	200.000	0.662	423x
	FP32-XGB	100.0\% ± 0.0\%	100.0\% ± 0.0\%	100.0\% ± 0.0\%	-	0.002	-
	FHE-RF	96.9\% ± 1.2\%	95.4\% ± 1.8\%	93.6\% ± 2.2\%	700.000	1.413	899x
	FP32-RF	95.9\% ± 1.1\%	93.9\% ± 1.5\%	91.4\% ± 2.3\%	-	0.002	-

Experiments Figure 2. - Impact of the precision

In [7]:

def evaluate_model(X, y, model, rkf):
    """Evaluate a given model and return its scores."""
    scores = {"precision": [], "recall": [], "accuracy": [], "f1": [], "average_precision": []}
    scores_fp32 = {"precision": [], "recall": [], "accuracy": [], "f1": [], "average_precision": []}

    metric_func_to_key = {
        "precision_score": "precision",
        "recall_score": "recall",
        "f1_score": "f1",
        "average_precision_score": "average_precision",
    }

    for train_index, test_index in rkf.split(X):
        X_train, X_test = X[train_index], X[test_index]
        y_train, y_test = y[train_index], y[test_index]

        torus_model, sklearn_model = model.fit_benchmark(X_train, y_train)

        for model_instance, score_dict in [(torus_model, scores), (sklearn_model, scores_fp32)]:
            y_pred = model_instance.predict(X_test)
            for metric_func in [precision_score, recall_score, average_precision_score, f1_score]:
                score_key = metric_func_to_key[metric_func.__name__]
                score_dict[score_key].append(metric_func(y_test, y_pred))
            score_dict["accuracy"].append(accuracy_score(y_test, y_pred))

    return scores, scores_fp32


rkf = RepeatedKFold(n_splits=5, n_repeats=3, random_state=0)
X, y = datasets["spambase"]["X"].astype(np.float32), datasets["spambase"]["y"]
assert len(set(y)) == 2
if y.dtype not in [np.int32, bool]:
    print(f"Unexpected datatype for y in dataset spambase: {y.dtype}")

scores_global = {}

for n_bits in n_bits_list:
    scores_global[n_bits] = {}

    for model_cls, params in model_hyperparameters.items():
        model_instance = model_cls(n_bits=n_bits, **params)
        scores, scores_fp32 = evaluate_model(X, y, model_instance, rkf)

        model_name = model_cls.__name__
        scores_global[n_bits][model_name + "_torus"] = scores
        scores_global[n_bits][model_name + "_fp32"] = scores_fp32

        print(f"{model_name} with {n_bits}-bits:")
        print("Average precision:", np.mean(scores["average_precision"]))
        print("Average precision (fp32):", np.mean(scores_fp32["average_precision"]))

DecisionTreeClassifier with 1-bits:
Average precision: 0.408932530057913
Average precision (fp32): 0.8240131348716936

XGBClassifier with 1-bits:
Average precision: 0.39404467418842154
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 1-bits:
Average precision: 0.39404467418842154
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 2-bits:
Average precision: 0.5783561241072402
Average precision (fp32): 0.8240131348716936

XGBClassifier with 2-bits:
Average precision: 0.6247177037498485
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 2-bits:
Average precision: 0.5692185974635017
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 3-bits:
Average precision: 0.6809716709773868
Average precision (fp32): 0.8240131348716936

XGBClassifier with 3-bits:
Average precision: 0.7950698031111193
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 3-bits:
Average precision: 0.7371651377079289
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 4-bits:
Average precision: 0.733924323832143
Average precision (fp32): 0.8240131348716936

XGBClassifier with 4-bits:
Average precision: 0.8521287716294133
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 4-bits:
Average precision: 0.8056925848877744
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 5-bits:
Average precision: 0.8101306169806723
Average precision (fp32): 0.8240131348716936

XGBClassifier with 5-bits:
Average precision: 0.878407427344724
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 5-bits:
Average precision: 0.8304046578932958
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 6-bits:
Average precision: 0.8426735780163795
Average precision (fp32): 0.8240131348716936

XGBClassifier with 6-bits:
Average precision: 0.8964789946563898
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 6-bits:
Average precision: 0.8459941433803378
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 7-bits:
Average precision: 0.8440934158260279
Average precision (fp32): 0.8240131348716936

XGBClassifier with 7-bits:
Average precision: 0.8987745041709022
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 7-bits:
Average precision: 0.8523380007137836
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 8-bits:
Average precision: 0.8329951951056004
Average precision (fp32): 0.8240131348716936

XGBClassifier with 8-bits:
Average precision: 0.9012936586221614
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 8-bits:
Average precision: 0.8527017103592347
Average precision (fp32): 0.8601540794231147

DecisionTreeClassifier with 9-bits:
Average precision: 0.8344647983632885
Average precision (fp32): 0.8240131348716936

XGBClassifier with 9-bits:
Average precision: 0.904057847352071
Average precision (fp32): 0.9046696576909921

RandomForestClassifier with 9-bits:
Average precision: 0.8579231686644472
Average precision (fp32): 0.8601540794231147

P-Error search

In [8]:

import matplotlib.pyplot as plt
from tqdm import tqdm


def evaluate_model_on_error_rates(X_train, X_test, y_test, torus_model, p_error_list):
    """Evaluate the torus model on different error rates and return accuracy and time taken."""
    acc_scores = []
    time_scores = []
    real_p_error_list = []

    for p_error in tqdm(p_error_list):
        torus_model.compile(X_train, p_error=p_error)
        real_p_error_list.append(torus_model.fhe_circuit.p_error)
        torus_model.fhe_circuit.keygen(force=False)

        start_time = time.time()
        y_pred = torus_model.predict(X_test, fhe="execute")
        end_time = time.time()

        acc_scores.append(accuracy_score(y_pred, y_test))
        time_scores.append(end_time - start_time)

    return acc_scores, time_scores, real_p_error_list


plt.rcParams.update({"font.size": 16})
n_bits = 6
p_error_list = [2e-40, 1e-6, 1e-5, 1e-4, 0.001, 0.005, 0.01, 0.05, 0.1, 0.3, 0.5, 0.7, 0.9, 0.95]
X, y = datasets["spambase"]["X"].astype(np.float32), datasets["spambase"]["y"]

clf = DecisionTreeClassifier(n_bits=n_bits, **model_hyperparameters[DecisionTreeClassifier])
rkf = RepeatedKFold(n_splits=20, n_repeats=3, random_state=0)

for train_index, test_index in rkf.split(X):
    X_train, X_test = X[train_index], X[test_index]
    y_train, y_test = y[train_index], y[test_index]

    torus_model, _ = clf.fit_benchmark(X_train, y_train)

    # Calculating num_nodes using analyze_gemm_computation function
    shapes = analyze_gemm_computation(torus_model)
    num_nodes = shapes[0][0]

    acc_scores, time_p_error, real_p_error_list = evaluate_model_on_error_rates(
        X_train, X_test, y_test, torus_model, p_error_list
    )
    break

  0%|          | 0/14 [00:00<?, ?it/s]

  7%|▋         | 1/14 [02:02<26:31, 122.43s/it]

 14%|█▍        | 2/14 [03:31<20:32, 102.74s/it]

 21%|██▏       | 3/14 [04:53<17:07, 93.40s/it] 

 29%|██▊       | 4/14 [06:14<14:43, 88.30s/it]

 36%|███▌      | 5/14 [07:33<12:45, 85.06s/it]

 43%|████▎     | 6/14 [08:44<10:43, 80.43s/it]

 50%|█████     | 7/14 [10:13<09:42, 83.26s/it]

 57%|█████▋    | 8/14 [11:31<08:08, 81.41s/it]

 64%|██████▍   | 9/14 [12:43<06:32, 78.45s/it]

 71%|███████▏  | 10/14 [13:57<05:08, 77.04s/it]

 79%|███████▊  | 11/14 [14:54<03:32, 70.95s/it]

 86%|████████▌ | 12/14 [15:50<02:12, 66.45s/it]

 93%|█████████▎| 13/14 [16:29<00:58, 58.22s/it]

100%|██████████| 14/14 [17:14<00:00, 54.10s/it]

100%|██████████| 14/14 [17:14<00:00, 73.89s/it]

In [9]:

def plot_metrics_vs_error_rates(
    metric_values, model_name, num_nodes, xlabel, ylabel, filename, red_line_value
):
    """Plot the metrics against error rates."""
    _, ax = plt.subplots(figsize=(10, 6))

    plt.plot(
        [real_p_error_list[0], real_p_error_list[-1]],
        [red_line_value, red_line_value],
        color="red",
        linewidth=2,
        label="p_error=2E-40",
    )
    plt.plot(real_p_error_list, metric_values, color="blue", linewidth=2, marker="x")
    plt.grid(True)
    plt.legend()
    plt.title(f"{model_name} {num_nodes} nodes")
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.semilogx()
    plt.xticks(10.0 ** np.arange(-6, 1))
    ax.set_rasterized(True)
    plt.savefig(filename, bbox_inches="tight", dpi=300)
    plt.show()


# Plotting accuracy vs error rates
plot_metrics_vs_error_rates(
    acc_scores,
    "DecisionTreeClassifier",
    num_nodes,
    "$p_{error}$",
    "Metric",
    "DecisionTreeClassifier" + "acc_p_error.eps",
    0.91,
)

# Plotting execution time per data point vs error rates
plot_metrics_vs_error_rates(
    np.asarray(time_p_error) / X_test.shape[0],
    "DecisionTreeClassifier",
    num_nodes,
    "$p_{error}$",
    "Execution time",
    "DecisionTreeClassifier" + "speed_p_error.eps",
    1.807,
)

The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.

The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.

Speed vs bitwidth

In [10]:

# Plot the metrics vs n_bits for each model
plt.rcParams.update({"font.size": 16})
for cls in model_hyperparameters:
    fig, ax = plt.subplots(figsize=(10, 6))

    f1_scores = []
    f1_scores_fp32 = []

    average_precision_scores = []
    average_precision_scores_fp32 = []

    for n_bits in n_bits_list:
        average_precision_scores.append(
            np.mean(scores_global[n_bits][cls.__name__ + "_torus"]["average_precision"])
        )
        average_precision_scores_fp32.append(
            np.mean(scores_global[n_bits][cls.__name__ + "_fp32"]["average_precision"])
        )

        f1_scores.append(np.mean(scores_global[n_bits][cls.__name__ + "_torus"]["f1"]))
        f1_scores_fp32.append(np.mean(scores_global[n_bits][cls.__name__ + "_fp32"]["f1"]))

    # plt.legend()
    ap_relative = np.array(average_precision_scores) / average_precision_scores_fp32
    f1_relative = np.array(f1_scores) / f1_scores_fp32
    print(f"ap relative: {ap_relative}, f1_relative: {f1_relative}")
    plt.plot(
        n_bits_list,
        average_precision_scores,
        label="torus_average_precision",
        color="blue",
        linewidth=2,
    )
    plt.plot(
        n_bits_list,
        average_precision_scores_fp32,
        label="fp32_average_precision",
        color="blue",
        linewidth=2,
        linestyle="dashed",
    )

    plt.plot(n_bits_list, f1_scores, label="torus_f1", linewidth=2, color="red")
    plt.plot(
        n_bits_list, f1_scores_fp32, label="fp32_f1", color="red", linewidth=2, linestyle="dashed"
    )

    plt.grid(True)
    plt.xlim([1, 9])
    plt.ylim([0, 1])
    plt.xticks(np.arange(1, 10))
    plt.legend()

    plt.title(cls.__name__)
    plt.xlabel("Bitwidth")
    plt.ylabel("Metric")
    # Save the figure

    # Rasterize the axes to handle transparency
    ax.set_rasterized(True)
    plt.savefig(cls.__name__ + ".eps", bbox_inches="tight", dpi=300)

    plt.show()

The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.

ap relative: [0.49626943 0.70187731 0.82640876 0.89067066 0.98315255 1.02264581
 1.02436888 1.01090038 1.01268386], f1_relative: [0.06488922 0.65490682 0.87590196 0.90861806 0.97920588 1.00604989
 1.00914511 1.00274636 1.00389957]

The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.

ap relative: [0.43556747 0.69054787 0.87885097 0.94192257 0.97097036 0.99094624
 0.99348364 0.99626825 0.99932372], f1_relative: [0.         0.65970362 0.91404942 0.95773723 0.97789164 0.99281277
 0.99447789 0.99697611 0.99969255]

The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.

ap relative: [0.45810941 0.66176353 0.85701522 0.93668402 0.96541385 0.98353791
 0.99091316 0.99133601 0.99740638], f1_relative: [0.         0.57332946 0.87035559 0.9402579  0.96505021 0.983713
 0.99082334 0.99224022 0.99758998]

In [11]:

def predict_with_fhe(clf, X_sample):
    """Predict using FHE and return elapsed time."""
    print("Compiling and keygen...")
    clf.compile(X_sample[:100])
    clf.fhe_circuit.keygen(force=False)

    print("Predict in FHE")
    start_time = time.time()
    _ = clf.predict(X_sample[:1], fhe="execute")
    end_time = time.time()

    return end_time - start_time


def analyze_and_store(clf, X_sample, nodes_dict, scores_dict):
    """Analyze the model and store results."""
    elapsed_time = predict_with_fhe(clf, X_sample)

    model_name = clf.__class__.__name__
    if model_name not in nodes_dict:
        nodes_dict[model_name] = []
        scores_dict[model_name] = []

    scores_dict[model_name].append(elapsed_time)

    shapes = analyze_gemm_computation(clf)
    nodes_dict[model_name].append(shapes[0][0])

    print(clf.n_bits)
    print(scores_dict[model_name][-1])
    print(nodes_dict[model_name][-1])


X, y = datasets["spambase"]["X"], datasets["spambase"]["y"]
nodes_dict = {}
scores_dict = {}

for model_name, hyperparameters in model_hyperparameters.items():
    for n_bits in n_bits_list:
        clf = model_name(n_bits=n_bits, **hyperparameters)
        clf.fit(X, y)

        if n_bits < 9:
            analyze_and_store(clf, X, nodes_dict, scores_dict)

Compiling and keygen...

Predict in FHE

{'op_inputs': 1, 'op_leaves': 1}
0.2823374271392822
8
Compiling and keygen...

Predict in FHE

{'op_inputs': 2, 'op_leaves': 2}
0.4151124954223633
20
Compiling and keygen...

Predict in FHE

{'op_inputs': 3, 'op_leaves': 3}
0.37416601181030273
20
Compiling and keygen...

Predict in FHE

{'op_inputs': 4, 'op_leaves': 4}
0.5053842067718506
21
Compiling and keygen...

Predict in FHE

{'op_inputs': 5, 'op_leaves': 5}
0.6664347648620605
25
Compiling and keygen...

Predict in FHE

{'op_inputs': 6, 'op_leaves': 6}
0.6958138942718506
23
Compiling and keygen...

Predict in FHE

{'op_inputs': 7, 'op_leaves': 7}
0.7767293453216553
24
Compiling and keygen...

Predict in FHE

{'op_inputs': 8, 'op_leaves': 8}
0.7453229427337646
22

Compiling and keygen...
Predict in FHE
{'op_inputs': 1, 'op_leaves': 1}
0.008694171905517578
200

Compiling and keygen...

Predict in FHE

{'op_inputs': 2, 'op_leaves': 2}
0.26419830322265625
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 3, 'op_leaves': 3}
0.27142930030822754
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 4, 'op_leaves': 4}
0.5824518203735352
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 5, 'op_leaves': 5}
0.8332271575927734
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 6, 'op_leaves': 6}
1.0524301528930664
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 7, 'op_leaves': 7}
0.9568302631378174
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 8, 'op_leaves': 8}
1.0244622230529785
350

Compiling and keygen...

Predict in FHE

{'op_inputs': 1, 'op_leaves': 1}
0.3596482276916504
400

Compiling and keygen...

Predict in FHE

{'op_inputs': 2, 'op_leaves': 2}
0.40879082679748535
650

Compiling and keygen...

Predict in FHE

{'op_inputs': 3, 'op_leaves': 3}
0.6357009410858154
700

Compiling and keygen...

Predict in FHE

{'op_inputs': 4, 'op_leaves': 4}
1.4530513286590576
750

Compiling and keygen...

Predict in FHE

{'op_inputs': 5, 'op_leaves': 5}
1.9984874725341797
750

Compiling and keygen...

Predict in FHE

{'op_inputs': 6, 'op_leaves': 6}
2.2012531757354736
750

Compiling and keygen...

Predict in FHE

{'op_inputs': 7, 'op_leaves': 7}
1.7295961380004883
750

Compiling and keygen...

Predict in FHE

{'op_inputs': 8, 'op_leaves': 8}
2.6791625022888184
750

In [12]:

def plot_fhe_inference_time(n_bits_list, scores, model_hyperparameters):
    """Plot the FHE inference time against bitwidth for each model."""

    # Calculate average inference time per node for each bitwidth
    n_bits_timings = np.zeros((8,))
    for model in model_hyperparameters:
        for idx, n_bits in enumerate(n_bits_list):
            if n_bits < 9:
                n_bits_timings[idx] += (
                    scores[model.__name__][idx] / nodes_dict[model.__name__][idx] * 1000
                )
    n_bits_timings /= len(model_hyperparameters)

    # Plot setup
    plt.figure(figsize=(10, 6))
    plt.rcParams.update({"font.size": 16})

    plt.plot(
        range(1, 9),
        n_bits_timings,
        label="FHE Inference Time",
        color="blue",
        linewidth=2,
        marker="o",
    )

    plt.xlabel("Bitwidth")
    plt.ylabel("Time (ms)")
    plt.grid(True, which="both")
    plt.semilogy()
    plt.ylim([0, 1000])
    plt.xlim([0.5, 8.5])
    plt.xticks(np.arange(1, 9))
    plt.title("FHE Execution vs Precision", pad=10)

    plt.savefig("fhe_inference_time.eps", bbox_inches="tight", dpi=300)
    plt.show()


plot_fhe_inference_time(n_bits_list, scores_dict, model_hyperparameters)