Bagging, Boosting & Stacking in Financial Machine Learning

In artificial intelligence (AI) and machine learning (ML), bagging, boosting, and stacking are techniques used to improve prediction accuracy by combining multiple models.

They’re part of a class known as ensemble methods (i.e., multiple methodologies used to solve a problem).

Given machine learning’s rapidly increasing importance in various forms of finance, these concepts are important for algorithmic traders and financial engineers.


Key Takeaways – Bagging, Boosting & Stacking in Financial Machine Learning

  • Bagging – Enhances trading strategies by diversifying across multiple models, which can help reduce risk and smooth returns.
    • Designed to reduce variance.
  • Boosting – Improves predictive accuracy by iteratively correcting errors. Helps adapt to changes effectively.
    • Designed to reduce bias and variance.
  • Stacking – Leverages strengths of diverse models through a meta-learner.
    • May reduce both bias and variance, but depends on the meta-learner.


Each has its unique approach and application scenarios:

1. Bagging (Bootstrap Aggregating)

Bagging involves creating multiple versions of a predictor and using these to get an aggregated predictor.

Each version is trained on a random subset of the training data, selected with replacement, which is known as bootstrapping.

The aggregation of predictions is typically done by voting for classification and averaging for regression.

Use Case

It’s effective for reducing variance and avoiding overfitting.

This makes it suitable for high-variance models like decision trees.

A classic example is the Random Forest algorithm, which consists of a collection of decision trees whose results are aggregated into a single consensus outcome.

Bagging in Trading

Example: Portfolio Diversification

Traders can use bagging to create a diversified portfolio by generating multiple trading strategies based on bootstrap samples of historical market data.

Each strategy operates independently and focuses on different segments of the market or asset classes (or just simply has independent approaches from the others in whatever form).


A trader might, for instance, develop several currency trading models, each trained on a random subset of historical data with replacement.

The final trading decision could be made by aggregating predictions (e.g., majority vote for direction of trade or averaging for position sizing) from all models to reduce risk and smooth out a trader’s equity curve.


2. Boosting

Boosting is an iterative technique that adjusts the weight of observations based on the previous classification.

If an observation was classified incorrectly, it tries to increase the weight of this observation and decrease it for those that were classified correctly.

Successive models are thus focused more on difficult-to-classify observations.

It’s a way to create a strong classifier from a number of weak classifiers.

Use Case

Boosting is used to reduce bias and variance in supervised learning.

It’s useful for decision trees, although it can be applied to any type of algorithm.

Examples include AdaBoost (Adaptive Boosting) and Gradient Boosting Machines (GBMs), like XGBoost, LightGBM, and CatBoost.

Boosting in Trading

Example: Adaptive Strategy Enhancement

Boosting can be used to incrementally improve a trading strategy by focusing on trades or market conditions where the current strategy performs poorly.

Successive models are trained to correct the mistakes of the previous ones.

This enhances the strategy’s ability to adapt to changing economic/market conditions.


A trader might start with a basic algorithmic trading strategy and analyze its weaknesses (e.g., environments with poor performance (like rising interest rates or during periods of weak growth and high inflation), specific market conditions leading to losses).

Then, additional models are trained to perform well in these conditions, with each model focusing on the residuals or errors of the previous ensemble of models.

The final decision could be a weighted sum of the predictions from all models.

Weights are generally determined by each model’s accuracy.


3. Stacking (Stacked Generalization)

Stacking involves training a new model to combine the predictions of several other models.

The original models are trained on the full dataset and then make predictions.

A new model is then trained on these predictions as input features to make a final prediction.

This model is often called a meta-learner or blender.

Use Case

Stacking can be used to blend the predictions of models of different types (e.g., combining tree-based models with linear models).

This makes it effective at capturing a wide variety of patterns in the data.

It’s often used in machine learning competitions for achieving high performance.

Stacking in Trading

Example: Meta-Strategy Development

Stacking involves combining predictions from multiple diverse trading models using another model (meta-learner) that decides how to best combine these predictions to make a final trading decision.

This allows traders to triangulate and leverage the strengths of different approaches.


A trader might develop a variety of trading models based on different methodologies – e.g., technical factors (like volume, market microstructure), fundamental factors (economic indicators), sentiment analysis (NLP to understand social media sentiment) – and use their predictions as inputs to a meta-model.

The meta-model, possibly a machine learning algorithm, learns how to best combine these inputs to make more accurate final predictions about market movements or asset prices.


Comparison: Bagging vs. Boosting vs. Stacking


All three methods can improve model performance compared to a single model.

The effectiveness depends on the problem, the underlying data, and the choice of base models.

Bias-Variance Tradeoff

  • Bagging is mainly used to reduce variance
  • Boosting is used to reduce both bias and variance, and
  • Stacking can potentially reduce both but depends heavily on the choice of meta-learner.

Complexity and Speed

Boosting and stacking are generally more computationally intensive than bagging.

Boosting, due to its sequential nature, can be slower and harder to parallelize compared to bagging and stacking.



Bagging, boosting, and stacking are ensemble techniques in machine learning that can materially improve model performance.

The choice between them depends on the:

  • specific requirements of the task, including the need to reduce bias or variance
  • computational constraints, and
  • types of models being combined

In each of our examples, the key advantage is the reduction of risk (variance) through diversification (bagging), improvement of strategy adaptiveness – i.e., bias reduction (boosting), and leveraging the strengths of multiple strategies (stacking).

It’s important for traders to thoroughly backtest and validate these ensemble methods in simulated environments before applying them to live trading due to the complexities and risks involved.