Research·Model Explainability·Advanced

Feature Contribution Tracker

Track how each input feature marginal contribution to the model output evolves over calendar time as market conditions change, algorithmically detecting when the model internal decision logic is shifting and identifying specific features whose predictive importance is systematically degrading over time.

model-explainabilityquant-research

Track Feature Contributions Over Time

This notebook explores methods for understanding and tracking how the importance of different features evolves in a machine learning model over time. In dynamic environments, feature contributions can change due to various factors like data drift, concept drift, or seasonal patterns. Monitoring these changes is crucial for maintaining model performance, interpretability, and reliability.

Key Concepts

ConceptDescription
Feature ImportanceA score assigned to input features of a machine learning model, indicating how much each feature contributes to the model's predictions. Methods include Gini importance (for tree-based models), permutation importance, and SHAP values.
Permutation ImportanceA model-agnostic technique that measures the decrease in a model's score when a single feature's values are randomly shuffled. This breaks the relationship between the feature and the target, revealing how much the model relies on that feature.
SHAP (SHapley Additive exPlanations)A game-theoretic approach to explain the output of any machine learning model. It connects optimal credit allocation with local explanations using Shapley values, providing a consistent and locally accurate feature importance for individual predictions.
Rolling Window AnalysisA technique used for time-series data where a statistic or model is computed over a fixed-size 'window' of data that slides through the time series, allowing for the observation of changes in patterns or parameters over time.
Concept DriftOccurs when the relationship between the input features and the target variable changes over time, leading to a degradation in model performance if not addressed.
Data DriftRefers to changes in the distribution of the input data over time, which can impact model performance even if the underlying concept remains stable.

Dependency Installation

This section installs all necessary Python libraries required for data manipulation, machine learning, and visualization.

[1]
import sys

# Install required libraries
!{sys.executable} -m pip install pandas numpy scikit-learn matplotlib seaborn shap loguru
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Library Imports

This section imports all standard and third-party libraries used throughout the notebook.

[2]
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.ensemble import RandomForestRegressor
from sklearn.inspection import permutation_importance
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
import shap
import logging
from collections import deque
import random
import time

# Configure logging
logging.basicConfig(level=logging.INFO, format='%(asctime)s - %(levelname)s - %(message)s')
logger = logging.getLogger(__name__)

Function Name: create_initial_state

This function initializes the state dictionary, which will be used to store and manage variables across different operations in the notebook. It sets up an empty dictionary to hold data, models, and results.

Parameters: None

Returns: state (dict): An empty dictionary ready for state management.

[3]
def create_initial_state() -> dict:
    """
    Initializes an empty state dictionary.

    Returns
    -------
    dict
        An empty dictionary to manage the state of the notebook.

    Examples
    --------
    >>> state = create_initial_state()
    >>> print(state)
    {}
    """
    logger.info("Initializing new state dictionary.")
    return {}

Function Name: simulate_time_series_data

This function generates synthetic time-series data for demonstration purposes. It creates a dataset with a time index, several features (some with constant impact, others with changing impact over time), and a target variable. This simulation helps in understanding how feature contributions can evolve.

Parameters: state (dict): The current state dictionary. n_samples (int): The total number of time steps (samples) to generate. n_features (int): The number of features to generate. seed (int): Random seed for reproducibility.

Returns: state (dict): The updated state dictionary containing the generated DataFrame under the key 'data'.

[4]
def simulate_time_series_data(state: dict, n_samples: int = 1000, n_features: int = 5, seed: int = 42) -> dict:
    """
    Simulates time-series data with evolving feature contributions.

    Parameters
    ----------
    state : dict
        Current state dictionary.
    n_samples : int, optional
        Number of samples to generate, defaults to 1000.
    n_features : int, optional
        Number of features to generate, defaults to 5.
    seed : int, optional
        Random seed for reproducibility, defaults to 42.

    Returns
    -------
    dict
        Updated state with a 'data' key containing the generated DataFrame.

    Examples
    --------
    >>> state = create_initial_state()
    >>> state = simulate_time_series_data(state, n_samples=100, n_features=3, seed=1)
    >>> print(state['data'].head())
    """
    logger.info(f"Simulating time-series data with {n_samples} samples and {n_features} features.")
    np.random.seed(seed)
    random.seed(seed)

    # Generate time index
    time_index = pd.date_range(start='2020-01-01', periods=n_samples, freq='D')

    # Generate features
    features = pd.DataFrame(np.random.randn(n_samples, n_features), columns=[f'feature_{i}' for i in range(n_features)])

    # Introduce time-varying effects for some features
    # Feature_0 might have a strong, consistent effect
    # Feature_1 might have an effect that increases over time
    # Feature_2 might have an effect that decreases over time
    # Other features have random noise contribution

    weights = np.array([1.5] + [0.5] * (n_features - 1))

    # Introduce a time-dependent weight for feature_1 and feature_2
    time_effect_feature_1 = np.linspace(0.1, 1.0, n_samples) # increasing importance
    time_effect_feature_2 = np.linspace(1.0, 0.1, n_samples) # decreasing importance

    # Calculate target based on features and time-varying weights
    # A simple linear relationship for demonstration
    target = (1.5 * features['feature_0'] + # Strong constant contributor
              0.8 * features['feature_1'] * time_effect_feature_1 + # Increasing importance
              0.6 * features['feature_2'] * time_effect_feature_2 + # Decreasing importance
              np.sum(features.iloc[:, 3:] * weights[3:], axis=1) + # Other features (if any) with constant low weights
              np.random.randn(n_samples) * 0.5) # Noise

    df = pd.DataFrame({
        'timestamp': time_index,
        **{col: features[col] for col in features.columns},
        'target': target
    }).set_index('timestamp')

    state['data'] = df
    logger.info("Time-series data generated and stored in state['data'].")
    return state

Function Name: train_model

This function trains a machine learning model, specifically a RandomForestRegressor, on the provided feature matrix X and target vector y. It allows for customization of model parameters. The trained model is stored in the state dictionary.

Parameters: state (dict): The current state dictionary. X (pd.DataFrame): The feature matrix. y (pd.Series): The target variable. model_params (dict): Optional dictionary of parameters for the RandomForestRegressor.

Returns: state (dict): The updated state dictionary with the trained model stored under the key 'model'.

[5]
def train_model(state: dict, X: pd.DataFrame, y: pd.Series, model_params: dict = None) -> dict:
    """
    Trains a RandomForestRegressor model.

    Parameters
    ----------
    state : dict
        Current state dictionary.
    X : pd.DataFrame
        Feature matrix for training.
    y : pd.Series
        Target variable for training.
    model_params : dict, optional
        Parameters for the RandomForestRegressor, defaults to {'random_state': 42}.

    Returns
    -------
    dict
        Updated state with the trained model under the 'model' key.

    Examples
    --------
    >>> state = create_initial_state()
    >>> state = simulate_time_series_data(state)
    >>> X = state['data'].drop('target', axis=1)
    >>> y = state['data']['target']
    >>> state = train_model(state, X, y)
    >>> print(state['model'])
    RandomForestRegressor(random_state=42)
    """
    if model_params is None:
        model_params = {'random_state': 42}

    logger.info(f"Training RandomForestRegressor with parameters: {model_params}")
    model = RandomForestRegressor(**model_params)
    model.fit(X, y)
    state['model'] = model
    logger.info("Model trained and stored in state['model'].")
    return state

Function Name: calculate_permutation_importance

This function calculates the permutation importance for a trained model on a given dataset. Permutation importance is a model-agnostic technique that quantifies the importance of a feature by measuring how much the model's performance decreases when that feature's values are randomly shuffled. It provides a reliable way to assess feature contribution.

Parameters: state (dict): The current state dictionary, expected to contain a 'model'. model: The trained machine learning model. X (pd.DataFrame): The feature matrix. y (pd.Series): The true target values. n_repeats (int): The number of times to permute a feature. Higher values increase reliability but also computation time.

Returns: state (dict): The updated state dictionary, optionally storing the calculated permutation importance or simply passing through if the result is directly consumed.

[6]
def calculate_permutation_importance(state: dict, model, X: pd.DataFrame, y: pd.Series, n_repeats: int = 10) -> dict:
    """
    Calculates permutation importance for a given model and dataset.

    Parameters
    ----------
    state : dict
        Current state dictionary (model expected in state['model'] if not passed directly).
    model : estimator
        Trained machine learning model.
    X : pd.DataFrame
        Feature matrix.
    y : pd.Series
        True target values.
    n_repeats : int, optional
        Number of times to permute a feature, defaults to 10.

    Returns
    -------
    dict
        Updated state dictionary. This function directly returns the importance scores, not modifying state for generality.

    Examples
    --------
    >>> state = create_initial_state()
    >>> state = simulate_time_series_data(state, n_samples=100)
    >>> X = state['data'].drop('target', axis=1)
    >>> y = state['data']['target']
    >>> state = train_model(state, X, y)
    >>> model = state['model']
    >>> importance_results = calculate_permutation_importance(state, model, X, y)
    >>> print(importance_results['importances_mean'])
    """
    logger.info(f"Calculating permutation importance with {n_repeats} repeats.")
    result = permutation_importance(model, X, y, n_repeats=n_repeats, random_state=state.get('seed', 42), scoring='neg_mean_squared_error')

    # Store results for easier access
    state['permutation_importance_mean'] = pd.Series(result.importances_mean, index=X.columns)
    state['permutation_importance_std'] = pd.Series(result.importances_std, index=X.columns)

    logger.info("Permutation importance calculated.")
    return state

Function Name: track_rolling_feature_contributions

This function performs a rolling window analysis to track how feature contributions change over time. It iterates through the time-series data, trains a model on each window, and calculates the permutation importance for that window. This process allows for observing the evolution of feature relevance.

Parameters: state (dict): The current state dictionary, expected to contain 'data'. data (pd.DataFrame): The time-series DataFrame with features and a target. window_size (int): The number of samples in each rolling window. step_size (int): The number of samples to advance the window in each iteration. Defaults to 1. n_repeats (int): The number of repeats for permutation importance calculation.

Returns: state (dict): The updated state dictionary with 'rolling_contributions' which is a DataFrame of feature importances over time, and 'rolling_metrics' which is a DataFrame of model evaluation metrics (e.g., RMSE) over time.

[7]
def track_rolling_feature_contributions(state: dict, data: pd.DataFrame, window_size: int = 200, step_size: int = 10, n_repeats: int = 5) -> dict:
    """
    Tracks feature contributions over time using a rolling window approach.

    Parameters
    ----------
    state : dict
        Current state dictionary.
    data : pd.DataFrame
        Time-series data with features and target.
    window_size : int, optional
        Size of the rolling window, defaults to 200.
    step_size : int, optional
        Step size to advance the window, defaults to 10.
    n_repeats : int, optional
        Number of repeats for permutation importance, defaults to 5.

    Returns
    -------
    dict
        Updated state with 'rolling_contributions' (DataFrame of feature importances over time)
        and 'rolling_metrics' (DataFrame of model evaluation metrics over time).

    Examples
    --------
    >>> state = create_initial_state()
    >>> state = simulate_time_series_data(state, n_samples=500)
    >>> state = track_rolling_feature_contributions(state, state['data'], window_size=100, step_size=20)
    >>> print(state['rolling_contributions'].head())
    >>> print(state['rolling_metrics'].head())
    """
    logger.info(f"Starting rolling window analysis with window_size={window_size} and step_size={step_size}.")

    feature_columns = [col for col in data.columns if col.startswith('feature_')]
    target_column = 'target'

    all_importances = []
    all_metrics = []
    window_timestamps = []

    # Use deque for an efficient rolling window
    # For this example, we'll manually slice the dataframe, but deque is good for streaming data.

    for i in range(0, len(data) - window_size + 1, step_size):
        window_data = data.iloc[i : i + window_size]

        if len(window_data) < window_size:
            continue # Skip incomplete windows at the end

        X_window = window_data[feature_columns]
        y_window = window_data[target_column]
        window_end_time = window_data.index[-1]
        window_timestamps.append(window_end_time)

        # Train model for the current window
        current_state = create_initial_state() # Create a temporary state for the model
        current_state = train_model(current_state, X_window, y_window)
        model = current_state['model']

        # Calculate permutation importance
        importance_state = create_initial_state()
        importance_state = calculate_permutation_importance(importance_state, model, X_window, y_window, n_repeats=n_repeats)
        importance_series = importance_state['permutation_importance_mean']
        all_importances.append(importance_series)

        # Evaluate model performance
        predictions = model.predict(X_window)
        rmse = np.sqrt(mean_squared_error(y_window, predictions))
        all_metrics.append({'rmse': rmse})

        # Add a small random jitter for demonstration of 'timing/backoff' mechanism concept
        time.sleep(random.uniform(0.01, 0.05))
        logger.debug(f"Processed window ending at {window_end_time}. RMSE: {rmse:.3f}")

    if not all_importances:
        logger.warning("No windows were processed. Check window_size and step_size.")
        state['rolling_contributions'] = pd.DataFrame()
        state['rolling_metrics'] = pd.DataFrame()
        return state

    rolling_contributions_df = pd.DataFrame(all_importances, index=window_timestamps)
    rolling_metrics_df = pd.DataFrame(all_metrics, index=window_timestamps)

    state['rolling_contributions'] = rolling_contributions_df
    state['rolling_metrics'] = rolling_metrics_df
    logger.info("Rolling feature contributions and metrics calculated and stored.")
    return state

Demonstration and Visualization

This section demonstrates the use of the core functions by simulating data, training a model, and tracking feature contributions over time. Visualizations will be used to illustrate key insights.

[8]
# 1. Initialize State
state = create_initial_state()
state['seed'] = 42 # Set seed for reproducibility
logger.info("Initial state created.")
[9]
# 2. Simulate Time-Series Data
n_samples_sim = 1000
n_features_sim = 5
state = simulate_time_series_data(state, n_samples=n_samples_sim, n_features=n_features_sim, seed=state['seed'])
df = state['data']

print("\nSimulated Data Head:")
display(df.head())
print("\nSimulated Data Info:")
df.info()

Simulated Data Head:
feature_0 feature_1 feature_2 feature_3 feature_4 target
timestamp
2020-01-01 0.496714 -0.138264 0.647689 1.523030 -0.234153 1.555182
2020-01-02 -0.234137 1.579213 0.767435 -0.469474 0.542560 0.046152
2020-01-03 -0.463418 -0.465730 0.241962 -1.913280 -1.724918 -3.305061
2020-01-04 -0.562288 -1.012831 0.314247 -0.908024 -1.412304 -2.063818
2020-01-05 1.465649 -0.225776 0.067528 -1.424748 -0.544383 1.601980

Simulated Data Info:
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 1000 entries, 2020-01-01 to 2022-09-26
Data columns (total 6 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   feature_0  1000 non-null   float64
 1   feature_1  1000 non-null   float64
 2   feature_2  1000 non-null   float64
 3   feature_3  1000 non-null   float64
 4   feature_4  1000 non-null   float64
 5   target     1000 non-null   float64
dtypes: float64(6)
memory usage: 54.7 KB

Initial Model Training and Feature Importance

Let's train a model on the entire simulated dataset first to get a baseline understanding of feature importance.

[10]
X_full = df.drop('target', axis=1)
y_full = df['target']

# Train model on full data
state = train_model(state, X_full, y_full)
full_data_model = state['model']

# Calculate permutation importance on full data
state = calculate_permutation_importance(state, full_data_model, X_full, y_full)
initial_importance = state['permutation_importance_mean']

# Plot initial feature importance
plt.figure(figsize=(10, 6))
sns.barplot(x=initial_importance.index, y=initial_importance.values, palette='viridis')
plt.title('Initial Feature Importance (Full Dataset)')
plt.xlabel('Features')
plt.ylabel('Permutation Importance Mean')
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()

print("\nInitial Feature Importance:")
display(initial_importance.sort_values(ascending=False).to_frame(name='Importance Mean'))
/tmp/ipykernel_12557/3148268169.py:14: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  sns.barplot(x=initial_importance.index, y=initial_importance.values, palette='viridis')
cell output

Initial Feature Importance:
Importance Mean
feature_0 4.697306
feature_4 0.556423
feature_3 0.511143
feature_1 0.449220
feature_2 0.177466

Rolling Window Feature Contribution Tracking

Now, we apply the track_rolling_feature_contributions function to see how feature importances and model performance change over time using a sliding window. We'll set a window_size and step_size to control the granularity of our analysis.

[11]
window_s = 200 # Size of the training window
step_s = 20  # How many steps to advance the window
n_repeats_pi = 3 # Fewer repeats for faster demo

state = track_rolling_feature_contributions(state, df, window_size=window_s, step_size=step_s, n_repeats=n_repeats_pi)

rolling_contributions = state['rolling_contributions']
rolling_metrics = state['rolling_metrics']

print("\nRolling Feature Contributions Head:")
display(rolling_contributions.head())
print("\nRolling Metrics Head:")
display(rolling_metrics.head())

Rolling Feature Contributions Head:
feature_0 feature_1 feature_2 feature_3 feature_4
2020-07-18 4.044176 0.068102 0.436704 0.292965 0.459574
2020-08-07 4.071721 0.062664 0.453749 0.317969 0.341818
2020-08-27 4.074874 0.061985 0.369094 0.373197 0.371008
2020-09-16 4.643767 0.053068 0.379498 0.354399 0.363214
2020-10-06 4.441076 0.060653 0.381378 0.335361 0.285928

Rolling Metrics Head:
rmse
2020-07-18 0.286340
2020-08-07 0.273208
2020-08-27 0.268787
2020-09-16 0.273362
2020-10-06 0.261029

Visualization of Evolving Feature Contributions

We can visualize the permutation importance of each feature over the rolling windows. This allows us to observe which features become more or less influential over time.

[12]
plt.figure(figsize=(15, 8))

# Plot each feature's importance over time
for feature in rolling_contributions.columns:
    plt.plot(rolling_contributions.index, rolling_contributions[feature], label=feature)

plt.title('Evolving Feature Contributions Over Time (Permutation Importance)')
plt.xlabel('Window End Timestamp')
plt.ylabel('Permutation Importance Mean')
plt.grid(True, linestyle='--', alpha=0.7)
plt.legend(title='Features', bbox_to_anchor=(1.05, 1), loc='upper left')
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()
cell output

Heatmap of Rolling Feature Contributions

A heatmap can provide a condensed view of how feature contributions change across all features and time windows.

[13]
plt.figure(figsize=(16, 8))
sns.heatmap(rolling_contributions.T, cmap='viridis', annot=False, fmt=".2f", cbar_kws={'label': 'Permutation Importance Mean'})
plt.title('Heatmap of Rolling Feature Contributions')
plt.xlabel('Window End Timestamp')
plt.ylabel('Features')
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()
cell output

Model Performance Over Time

It's also important to track model performance alongside feature contributions. A drop in performance might correlate with changes in feature importance, indicating potential concept or data drift.

[14]
plt.figure(figsize=(15, 6))
sns.lineplot(x=rolling_metrics.index, y=rolling_metrics['rmse'])
plt.title('Model RMSE Over Time (Rolling Window)')
plt.xlabel('Window End Timestamp')
plt.ylabel('RMSE')
plt.grid(True, linestyle='--', alpha=0.7)
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()
cell output

Production Considerations

Implementing feature contribution tracking in a production environment requires careful planning to ensure robustness, efficiency, and interpretability. Here are some key considerations:

ConsiderationBest Practice
Retraining FrequencyDetermine an optimal schedule for model retraining based on observed drift in feature contributions and model performance. This could be daily, weekly, or triggered by specific thresholds.
Feature Drift DetectionImplement automated monitoring for changes in feature distributions (data drift) and changes in the relationship between features and target (concept drift). Tools like Evidently AI or Deepchecks can assist here.
Computational CostCalculating feature importance, especially permutation importance or SHAP, can be computationally expensive. Optimize by using smaller window sizes for monitoring, sampling data, or using approximations where appropriate.
Interpretability vs. PerformanceSometimes, the most performant models (e.g., deep learning) are less interpretable. Balance the need for high performance with the ability to explain predictions and track feature contributions. Tree-based models often offer a good balance.
Monitoring & AlertingSet up dashboards to visualize evolving feature contributions and model performance. Configure alerts to notify stakeholders when significant changes or anomalies are detected, prompting investigation and potential model retraining.
Robustness (Jitter/Backoff)When interacting with external APIs or databases for data fetching or model deployment, incorporate retry mechanisms with exponential backoff and random jitter to handle transient failures gracefully and avoid overwhelming services.
ScalabilityEnsure your infrastructure can handle the demands of retraining models and calculating importances on potentially large datasets within reasonable timeframes. Consider distributed computing frameworks like Spark for large-scale operations.
Version ControlKeep track of model versions, training data, and feature importance profiles. This helps in debugging and understanding why model behavior or feature contributions changed over time.
DocumentationClearly document the methods used for feature contribution tracking, the expected behavior of features, and the actions to take when drift is detected.

Conclusion

This notebook demonstrated a practical approach to tracking feature contributions over time in a machine learning pipeline. We covered:

  • Data Simulation: Creating synthetic time-series data with evolving feature influences.
  • Model Training: Using RandomForestRegressor to build predictive models.
  • Permutation Importance: Quantifying feature relevance in a model-agnostic manner.
  • Rolling Window Analysis: Implementing a sliding window strategy to observe changes in feature importance and model performance over different time periods.
  • Visualization: Using line plots and heatmaps to effectively communicate the evolution of feature contributions.
  • Production Considerations: Discussing best practices for deploying and maintaining such a system in a real-world scenario.

By continuously monitoring feature contributions, data scientists and ML engineers can gain deeper insights into model behavior, detect data and concept drift, and make informed decisions about model retraining and maintenance, ultimately leading to more robust and reliable machine learning systems.

Feature Contribution Tracker · BitPredict