Hi,
I understand that you want to calculate the Akaike Information Criterion (AIC) for Support Vector Regression (SVR), Random Forest (RF), and Gradient Boosting (GB) models. Further, you're particularly interested in determining the number of parameters ((p)) for these models.
I assume you have already trained these models and have access to their Mean Squared Error (MSE) and the number of training samples ((n)). The challenge lies in accurately determining the number of parameters ((p)) for each model type, which is not always straightforward due to the complexity of these models.Determining the Number of Parameters ((p)):
- Support Vector Regression (SVR): For SVR, (p) typically includes the number of support vectors plus the number of features (dimensions) they operate on. In SVR, each support vector contributes to the model's decision function.
- Random Forest (RF): In RF, (p) is more challenging to define due to its ensemble nature. A simplistic approach could count the total number of nodes across all trees as parameters, but this overlooks the model's inherent correlations and structure. A more nuanced approach might consider the number of trees and the depth or complexity of each tree.
- Gradient Boosting (GB): For GB, similar to RF, (p) could be approximated by considering the number of trees, their depth, and perhaps the number of features each split uses. However, this simplification may not fully capture the model's complexity, especially with feature interactions and learning rates.
Calculating AIC:
Given the number of training samples ((n)) and the MSE, AIC can be calculated as:
AIC = n * log(MSE) + 2 * p
References:
- For understanding SVR, RF, and GB models, and how their parameters might be counted, refer to the documentation of the respective libraries or functions you're using to train these models.
- For a general understanding of AIC and its applications, refer: https://www.mathworks.com/help/ident/ref/idmodel.aic.html
Hope this helps!
