Robustness to Learning Algorithm Noise

Diagnostics

Is the variance of the same model fit and evaluated on the same data when the random seed for the learning algorithm is varied?

Procedure

This procedure evaluates whether the model demonstrates robustness by analyzing the variance in performance metrics when trained and evaluated using different random seeds. This helps identify overfitting and sensitivity to small changes in data or model initialization.

Choose Random Seeds for Testing
- What to do: Define a set of random seeds for consistent reproducibility across experiments.
  - Select at least 5-10 random seeds to ensure a representative analysis of variance.
  - Ensure the seeds are applied consistently to all randomized operations in the learning algorithm (e.g., data shuffling, weight initialization).
Train and Evaluate the Model
- What to do: Train the model multiple times using the defined random seeds.
  - Split the data consistently into train and test sets for each run.
  - Use the chosen model configuration and keep all other hyperparameters constant.
  - Evaluate the model on the test set after each training run using the preselected performance metric (e.g., accuracy, F1-score, RMSE).
Record Performance Metrics
- What to do: Capture the performance metric for each training run.
  - Store the results in a structured format, such as a table or spreadsheet, for easy analysis.
  - Verify that each metric corresponds to the correct random seed.
Calculate Variance in Performance
- What to do: Compute the variance (or standard deviation) of the performance metrics across all random seed runs.
  - Use basic statistical tools or libraries (e.g., Pandas, NumPy) to calculate variance or standard deviation.
  - Higher variance suggests sensitivity to randomness, whereas low variance indicates robustness.
Interpret Variance Results
- What to do: Analyze the variance in the context of acceptable performance stability.
  - Low variance (e.g., close to 0) suggests that the model generalizes well and is robust to perturbations.
  - High variance may indicate sensitivity to randomness, signaling potential overfitting or instability in model training.
Report the Findings
- What to do: Summarize your results and their implications.
  - Present the computed variance or standard deviation alongside the individual performance metrics for each random seed.
  - Include visualizations such as a box plot or histogram to depict performance distribution.
  - Highlight any patterns or concerns, such as consistently high variance, and suggest next steps (e.g., tuning regularization, increasing data size, or modifying model architecture).

Code Example

This Python function evaluates whether a model demonstrates robustness by analyzing the variance in performance metrics when trained and tested with different random seeds.

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

def robustness_variance_test(X, y, model, metric=accuracy_score, n_seeds=30, test_size=0.2, random_state=42):
    """
    Test whether the model's performance is robust by evaluating variance in metrics across multiple random seeds.

    Parameters:
        X (np.ndarray): Features of the dataset.
        y (np.ndarray): Target variable of the dataset.
        model: Pre-configured machine learning model to evaluate.
        metric (callable): Performance metric function (default=accuracy_score).
        n_seeds (int): Number of random seeds to test (default=10).
        test_size (float): Proportion of the data for the test set (default=0.2).
        random_state (int): Seed for reproducibility of train/test splits (default=42).

    Returns:
        dict: Dictionary containing variance, mean performance, and interpretation.
    """
    performance_scores = []

    # Split data with different seeds
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=test_size, random_state=42)

    for seed in range(n_seeds):
        # Set the model random seed
        model.random_state = seed

        # Train and evaluate the model
        model.fit(X_train, y_train)
        y_pred = model.predict(X_test)
        score = metric(y_test, y_pred)
        performance_scores.append(score)

    # Calculate variance and mean performance
    variance = np.var(performance_scores)
    mean_performance = np.mean(performance_scores)

    # Interpret the results
    if variance < 0.01:
        interpretation = "The model demonstrates high robustness with very low variance in performance."
    elif variance < 0.05:
        interpretation = "The model shows moderate robustness with acceptable variance in performance."
    else:
        interpretation = "The model appears sensitive to randomness with high variance in performance, indicating potential instability."

    return {
        "Variance": variance,
        "Mean Performance": mean_performance,
        "Interpretation": interpretation,
    }

# Demo Usage
if __name__ == "__main__":
    from sklearn.ensemble import RandomForestClassifier
    from sklearn.datasets import make_classification

    # Generate synthetic dataset
    X, y = make_classification(
        n_samples=500, n_features=10, n_informative=5, random_state=42
    )

    # Define model
    model = RandomForestClassifier(n_estimators=10, random_state=42)

    # Perform robustness variance test
    results = robustness_variance_test(X, y, model, n_seeds=30)

    # Print results
    print("Robustness Variance Test Results:")
    for key, value in results.items():
        print(f"{key}: {value}")

Example Output

Robustness Variance Test Results:
Variance: 0.0003072222222222225
Mean Performance: 0.8983333333333334
Interpretation: The model demonstrates high robustness with very low variance in performance.

Robustness to Label Noise Robustness to Algorithm Hyperparameter Noise