Modeling toolkit
Different models, one stronger signal.
Dakota combines probabilistic and tree-based methods to capture uncertainty, nonlinear relationships, and complementary patterns in financial data.
Bayesian Regression
Bayesian Regression models the relationship between financial features and future stock returns while explicitly quantifying prediction uncertainty. Rather than estimating a single coefficient for each feature, Bayesian inference estimates a posterior probability distribution, allowing the model to produce both an expected return and a credible interval.
Objective
P(θ | D) = P(D | θ)P(θ) / P(D)
- P(θ) = Prior distribution
- P(D | θ) = Likelihood
- P(θ | D) = Posterior distribution
Role in Dakota
- Probabilistic forecasting
- Prediction uncertainty estimation
- Robust inference under noisy financial data
XGBoost
XGBoost is a gradient-boosted decision tree algorithm designed to capture complex nonlinear relationships between financial variables. Trees are added sequentially, with each new tree learning from the residual errors of the previous ensemble.
Prediction function
ŷ = ∑m=1M fm(x)
Each fm(x) represents an individual regression tree.
Objective function
L = ∑i l(yi, ŷi) + ∑m Ω(fm)
- l(·) measures prediction error
- Ω(f) penalizes model complexity
Role in Dakota
- Nonlinear feature interaction learning
- High predictive accuracy
- Automatic handling of complex financial relationships
LightGBM
LightGBM is a gradient boosting framework optimized for computational efficiency. Unlike traditional level-wise tree growth, LightGBM expands the leaf that produces the greatest reduction in prediction error, allowing faster training while maintaining strong predictive performance.
Objective function
L = ∑i l(yi, ŷi) + Ω(f)
LightGBM differs from XGBoost primarily in its leaf-wise tree growth strategy, enabling faster learning on large financial datasets.
Role in Dakota
- Efficient large-scale learning
- Complementary nonlinear modeling
- Ensemble diversification
Why multiple models?
Dakota combines multiple machine learning algorithms because no single model captures every aspect of financial markets.
| Model |
Primary contribution |
| Bayesian Regression |
Probabilistic forecasting and uncertainty estimation |
| XGBoost |
Nonlinear pattern recognition |
| LightGBM |
Efficient gradient boosting and complementary predictions |
By combining independent forecasting models, Dakota reduces model-specific bias and produces more robust estimates of future quarterly stock returns.