Ngày 25: Quantum Credit Scoring

🎯 Mục tiêu học tập

  • Hiểu sâu về quantum credit scoring và classical credit scoring
  • Nắm vững cách quantum computing cải thiện credit scoring
  • Implement quantum credit scoring algorithms
  • So sánh performance giữa quantum và classical scoring methods

📚 Lý thuyết

Credit Scoring Fundamentals

1. Classical Credit Scoring

Scoring Models:

  • FICO Score: Traditional credit scoring
  • Logistic Regression: Linear scoring models
  • Random Forest: Ensemble scoring methods
  • Gradient Boosting: Advanced scoring algorithms

Scoring Metrics:

Score = Σᵢ Weightᵢ × Featureᵢ
AUC = Area under ROC curve
KS = Kolmogorov-Smirnov statistic

2. Quantum Credit Scoring

Quantum Score Encoding:

|ψ⟩ = Σᵢ αᵢ|featureᵢ⟩

Quantum Scoring Operator:

H_score = Σᵢ Weightᵢ × Featureᵢ × |scoreᵢ⟩⟨scoreᵢ|

Quantum Score Calculation:

Score_quantum = ⟨ψ|H_score|ψ⟩

Quantum Scoring Methods

1. Quantum Feature Engineering:

  • Quantum Feature Selection: Quantum feature selection methods
  • Quantum Feature Transformation: Quantum feature transformation
  • Quantum Feature Interaction: Quantum feature interaction modeling

2. Quantum Score Calculation:

  • Quantum Linear Scoring: Quantum linear scoring models
  • Quantum Non-linear Scoring: Quantum non-linear scoring
  • Quantum Ensemble Scoring: Quantum ensemble methods

3. Quantum Score Calibration:

  • Quantum Score Calibration: Quantum score calibration methods
  • Quantum Score Validation: Quantum score validation
  • Quantum Score Stability: Quantum score stability analysis

💻 Thực hành

Project 25: Quantum Credit Scoring Framework

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_auc_score, roc_curve
from sklearn.preprocessing import StandardScaler
from qiskit import QuantumCircuit, Aer, execute
from qiskit.circuit.library import RealAmplitudes, ZZFeatureMap
from qiskit.algorithms import VQE, QAOA
from qiskit.algorithms.optimizers import SPSA, COBYLA

class ClassicalCreditScoring:
    """Classical credit scoring models"""
    
    def __init__(self):
        self.scaler = StandardScaler()
        
    def generate_credit_data(self, n_samples=1000):
        """Generate synthetic credit data"""
        np.random.seed(42)
        
        # Generate features
        income = np.random.normal(50000, 20000, n_samples)
        debt = np.random.normal(30000, 15000, n_samples)
        credit_score = np.random.normal(700, 100, n_samples)
        payment_history = np.random.normal(650, 50, n_samples)
        employment_years = np.random.exponential(5, n_samples)
        
        # Create DataFrame
        data = pd.DataFrame({
            'income': income,
            'debt': debt,
            'credit_score': credit_score,
            'payment_history': payment_history,
            'employment_years': employment_years
        })
        
        # Generate default labels
        default_prob = 1 / (1 + np.exp(-(-2 + 0.00001*income - 0.00002*debt + 0.01*credit_score)))
        default = np.random.binomial(1, default_prob)
        
        return data, default
    
    def logistic_regression_scoring(self, X_train, y_train, X_test):
        """Logistic regression credit scoring"""
        from sklearn.linear_model import LogisticRegression
        
        model = LogisticRegression()
        model.fit(X_train, y_train)
        scores = model.predict_proba(X_test)[:, 1]
        
        return scores

class QuantumCreditScoring:
    """Quantum credit scoring implementation"""
    
    def __init__(self, num_qubits=4):
        self.num_qubits = num_qubits
        self.backend = Aer.get_backend('qasm_simulator')
        self.optimizer = SPSA(maxiter=100)
        
    def create_scoring_circuit(self, features):
        """Create quantum circuit for credit scoring"""
        feature_map = ZZFeatureMap(feature_dimension=len(features), reps=2)
        ansatz = RealAmplitudes(num_qubits=self.num_qubits, reps=3)
        circuit = feature_map.compose(ansatz)
        return circuit
    
    def quantum_scoring(self, X_train, y_train, X_test):
        """Quantum credit scoring"""
        scores = []
        
        for i, sample in enumerate(X_test):
            if i >= 50:  # Limit for demonstration
                break
                
            # Create quantum circuit
            circuit = self.create_scoring_circuit(sample)
            
            # Execute circuit
            job = execute(circuit, self.backend, shots=1000)
            result = job.result()
            counts = result.get_counts()
            
            # Extract score
            score = self._extract_score_from_counts(counts)
            scores.append(score)
        
        return np.array(scores)
    
    def _extract_score_from_counts(self, counts):
        """Extract score from quantum measurement counts"""
        total_shots = sum(counts.values())
        
        # Calculate quantum score
        score = 0.0
        for bitstring, count in counts.items():
            probability = count / total_shots
            # Use parity as score indicator
            parity = sum(int(bit) for bit in bitstring) % 2
            score += probability * (1 if parity == 0 else 0)
        
        return score

def compare_credit_scoring():
    """Compare classical and quantum credit scoring"""
    print("=== Classical vs Quantum Credit Scoring ===\n")
    
    # Generate data
    classical_scorer = ClassicalCreditScoring()
    data, labels = classical_scorer.generate_credit_data(n_samples=500)
    
    # Split data
    X_train, X_test, y_train, y_test = train_test_split(
        data, labels, test_size=0.3, random_state=42
    )
    
    # Scale features
    X_train_scaled = classical_scorer.scaler.fit_transform(X_train)
    X_test_scaled = classical_scorer.scaler.transform(X_test)
    
    # Classical scoring
    print("1. Classical Credit Scoring:")
    classical_scores = classical_scorer.logistic_regression_scoring(
        X_train_scaled, y_train, X_test_scaled
    )
    
    classical_auc = roc_auc_score(y_test, classical_scores)
    print(f"   Classical AUC: {classical_auc:.4f}")
    
    # Quantum scoring
    print("\n2. Quantum Credit Scoring:")
    quantum_scorer = QuantumCreditScoring(num_qubits=4)
    quantum_scores = quantum_scorer.quantum_scoring(
        X_train_scaled, y_train, X_test_scaled
    )
    
    quantum_auc = roc_auc_score(y_test[:len(quantum_scores)], quantum_scores)
    print(f"   Quantum AUC: {quantum_auc:.4f}")
    
    # Visualization
    plt.figure(figsize=(15, 10))
    
    # ROC curves
    plt.subplot(2, 3, 1)
    fpr_classical, tpr_classical, _ = roc_curve(y_test, classical_scores)
    fpr_quantum, tpr_quantum, _ = roc_curve(y_test[:len(quantum_scores)], quantum_scores)
    
    plt.plot(fpr_classical, tpr_classical, label=f'Classical (AUC={classical_auc:.3f})')
    plt.plot(fpr_quantum, tpr_quantum, label=f'Quantum (AUC={quantum_auc:.3f})')
    plt.plot([0, 1], [0, 1], 'k--')
    plt.xlabel('False Positive Rate')
    plt.ylabel('True Positive Rate')
    plt.title('ROC Curves')
    plt.legend()
    plt.grid(True)
    
    # Score distributions
    plt.subplot(2, 3, 2)
    plt.hist(classical_scores, bins=20, alpha=0.7, label='Classical', density=True)
    plt.hist(quantum_scores, bins=20, alpha=0.7, label='Quantum', density=True)
    plt.xlabel('Credit Score')
    plt.ylabel('Density')
    plt.title('Score Distributions')
    plt.legend()
    plt.grid(True)
    
    # Score comparison
    plt.subplot(2, 3, 3)
    plt.scatter(classical_scores[:len(quantum_scores)], quantum_scores, alpha=0.6)
    plt.plot([0, 1], [0, 1], 'r--')
    plt.xlabel('Classical Score')
    plt.ylabel('Quantum Score')
    plt.title('Score Comparison')
    plt.grid(True)
    
    # AUC comparison
    plt.subplot(2, 3, 4)
    methods = ['Classical', 'Quantum']
    aucs = [classical_auc, quantum_auc]
    
    plt.bar(methods, aucs, color=['blue', 'orange'], alpha=0.7)
    plt.ylabel('AUC')
    plt.title('AUC Comparison')
    plt.grid(True)
    
    plt.tight_layout()
    plt.show()
    
    return {
        'classical_scores': classical_scores,
        'quantum_scores': quantum_scores,
        'classical_auc': classical_auc,
        'quantum_auc': quantum_auc
    }

# Run demo
if __name__ == "__main__":
    scoring_results = compare_credit_scoring()

📊 Kết quả và Phân tích

Quantum Credit Scoring Advantages:

1. Quantum Properties:

  • Superposition: Parallel feature evaluation
  • Entanglement: Complex feature correlations
  • Quantum Parallelism: Exponential speedup potential

2. Scoring-specific Benefits:

  • Non-linear Scoring: Quantum circuits capture complex scoring relationships
  • High-dimensional Features: Handle many features efficiently
  • Quantum Advantage: Potential speedup for large datasets

🎯 Bài tập về nhà

Exercise 1: Quantum Score Calibration

Implement quantum score calibration methods.

Exercise 2: Quantum Score Ensemble

Build quantum score ensemble methods.

Exercise 3: Quantum Score Validation

Develop quantum score validation framework.

Exercise 4: Quantum Score Stability

Create quantum score stability analysis.


“Quantum credit scoring leverages quantum superposition and entanglement to provide superior scoring accuracy.” - Quantum Finance Research

Ngày tiếp theo: Quantum Credit Monitoring