Hierarchical¶
- Bottom-up
- Top-Down
- Middle-out
Types¶
- Hierarchical non-additive: Price of Make, model, trim
- Hierarchical additive: Revenue of Make, model, trim
Hierarchical non-additive¶
If there are multiple independent levels of features, then run a model for each levels - simple model for each level is better than one complex model for all group - especially useful for imbalanced hierarchies
Advantages: 1. Better loss definition: Predict accurately on average → Predict each subset accurately on average 2. Simpler and easier to debug 3. Faster (than requiring a single model to produce splits)
Complexity of atomic model for each hierarchy should be based on the amount of data available for that hierarchy - create a meta-estimator to conditionally apply a model
Hierarchical Additive¶
Required for coherent forecasts
| \(\hat y_\text{top}\) | \(\hat y_\text{bot}\) | \(\hat p_l\) | ||
|---|---|---|---|---|
| Bottom-up | \(\sum\limits_l \hat y_{\text{bot}, l}\) | \(\hat f\) | ||
| Top-down | \(\hat f\) | \(\sum\limits_l \hat p_l \cdot \hat y_\text{top}\) | ||
| Historical proportion | \(\dfrac{y_{\text{bot}, l}}{y_\text{top}}\) | |||
| Predicted proportion | \(\dfrac{\hat y_{\text{bot}, l}}{\hat y_\text{top}}\) | |||
| Middle-out |
2026-03-15