This frustrates me about AI - which has become an incredibly powerful tool. I have a LightGBM algorithm that I am pleased with, but I also wanted to test whether it is possible to combine it with others to strengthen my algorithm and at the same time remove weaknesses. So I asked 6 different deep thinking models, and what do I get?! Good answers, but different answers.
Often, I end up choosing the answers from the most robust models or choosing answers that most of the models agree on.
Here are the answers I received from the various thinking models:
Detailed Schematic Overview of Each Analysis's Recommendation
| Analysis / Source | Recommended Partner | Detailed Theoretical Rationale for the Choice | Rationale for Discarding Others |
|---|---|---|---|
| My Original Answer | linear | - Maximum Structural Difference: Combines a complex, non-linear tree-based model (LightGBM) with a simple, global linear model. They operate in fundamentally different function spaces. - Optimal Bias-Variance Tradeoff: Pairs LightGBM's low bias and high variance with the linear model's high bias and low variance. This creates a highly robust ensemble model that is less prone to overfitting. - Highest Decorrelation: Because the models make fundamentally different assumptions about the data, their errors will be the least correlated, providing maximum diversification benefits. |
- XGBoost: Too similar. Both are gradient boosting models, leading to high correlation. - RandomForest: Better, but still tree-based. Partial correlation since they capture similar non-linear patterns. |
| Analysis 1 | randomforest | - Boosting vs. Bagging: LightGBM builds trees sequentially to correct errors (boosting). RandomForest builds trees independently and in parallel on random subsets (bagging). This methodological difference is a core reason for decorrelation. - Balanced Bias-Variance: LightGBM's low bias/high variance is stabilized by RandomForest's slightly higher bias/low variance. RandomForest is robust to noise, which is a weakness of boosting. - Practical Robustness: RandomForest handles non-stationary and high-dimensional financial data well, providing a stable partner to LightGBM's signal hunting. |
- XGBoost: Too similar (both are boosting). - Linear Model: Too simple, fails to capture the critical non-linear patterns in the stock market. - Neural Networks (NN): "Black box," requires a lot of data, and can also overfit to noise. |
| Analysis 2 | linear | - Structural Orthogonality: LightGBM captures local, non-linear interactions. Linear regression only captures global, linear trends. They are "orthogonal" in their approach. - Complementarity in Bias-Variance: Perfectly complementary. LightGBM is a "high alpha, high volatility" strategy, while linear is a "stable beta, low volatility" component. Together, they lower total variance. - Regime Robustness: The ensemble becomes robust across market regimes. Linear performs well in trending markets, while LightGBM can capture more complex patterns in other periods. |
- XGBoost/RandomForest: Too high correlation (ρ > 0.85 for XGBoost, ρ ≈ 0.65-0.75 for RF). - NN: Unnecessary complexity when a simpler solution (linear) provides better decorrelation. High-variance + high-variance is risky. - SVM: Scales poorly in practice for quantitative finance. |
| Analysis 3 | gam | - Complementary Non-Linearity: GAM models non-linearity as a sum of smooth functions of each individual variable (additive), whereas LightGBM specializes in finding complex interactions between variables. They thus capture different types of non-linear patterns. - Balanced Complexity: GAM is a low-variance, higher-bias model that is more sophisticated than a pure linear model but avoids the extreme complexity of LightGBM. This provides a good middle ground. - Decorrelated Errors: Because the learning mechanisms are so different (additive vs. interactive), their errors often become decorrelated. |
- XGBoost/RF: Too similar in structure and error correlation. - NN: Often high-variance and a "black box," which can increase correlation with LightGBM. - Linear Model: Too simple. Loses too much signal by assuming pure linearity. |
| Analysis 4 | deeptablesnn | - Fundamentally Different Paradigm: LightGBM is tree-based (discrete, rule-based). DeepTablesNN is a neural network (a continuous function approximator based on gradient descent). This is the largest conceptual difference among all alternatives. - Different Optimization Dynamics: Boosting focuses sequentially on residuals. Gradient descent trains the entire network simultaneously. This allows them to capture entirely different types of patterns. - Complementary Error Types: The difference in "inductive bias" (the model's inherent assumptions) leads to very low error correlation. |
- XGBoost/RF/ExtraTrees: All are tree-based and share the same basic structure, leading to moderate to high correlation. - Linear/GAM: Considered too low-capacity models (too high bias) to be a full-fledged partner capable of capturing remaining complex signals. - SVM: Scales poorly and is less practical. |
| Analysis 5 | linear | - Lowest Covariance: Argues that the empirical correlation between the predictions of a GBM and a linear model is extremely low (often ρ < 0.2), which provides the greatest reduction in the ensemble's total variance. - Portfolio Theory: Uses the formula for the Information Ratio (IR) of an ensemble to show that even a model with a lower individual IR (linear) contributes massively to the total risk-adjusted return due to the low correlation (ρ). - Robust Factor Exposure: A linear model is best suited to capture pure, stable factor premia, which complements LightGBM's hunt for more idiosyncratic alpha signals. |
- XGBoost/RF: Too high correlation (provides estimates ρ ≈ 0.7-0.9 and ρ ≈ 0.5-0.6). - NN: Also a low-bias/high-variance model that can be sensitive to the same non-linear patterns. - GAM: A step in the right direction, but the correlation is still higher (estimated at ~0.4) than for a linear model. |
| Analysis 6 | extratrees | - Maximum Randomization in Bagging: ExtraTrees is a bagging model (like RandomForest), but it introduces an extra level of randomization by choosing split-points completely at random, instead of calculating the optimal ones. - Even Lower Variance: This extra randomness reduces the model's variance even more than RandomForest, at the cost of a slight increase in bias. This makes it an even more stable partner for the high-variance LightGBM. - Higher Decorrelation than RF: Because the trees in ExtraTrees are less correlated with each other, they are also less correlated with LightGBM's trees, providing a better diversification effect than a standard RandomForest. |
- XGBoost: Too similar (both are boosting). - RandomForest: Good, but ExtraTrees is better because the extra randomization provides a greater decorrelation effect. |