Table 1 Description of the individual adapted models and aggregation methods considered in the case study. \(C_1\) and \(C_2\) correspond to the computational costs of GAM and Kalman variances estimation, respectively. \(m_T\) is the number of targets in the transfer learning context, and \(n_i\) is the number of experts in the three aggregation methods. To give an order of magnitude, in our application, parameters \(n_i\) are inferior to 10 while \(m_T = 1344\).
From: Frugal day-ahead forecasting of multiple local electricity loads by aggregating adaptive models
Characteristics of adapted GAM | GAM + Kalman Static | GAM + Kalman Dynamic | AGG GAM TL | AGG GAM-Kalman TL | AGG Kalman TL |
|---|---|---|---|---|---|
Transfer of GAM | No | No | Yes | Yes | No |
Cost | \(C_1 \times m_T\) | \(C_1 \times m_T\) | \(C_1 \times n_1<< C_1 \times m_T\) | \(C_1 \times n_2<< C_1 \times m_T\) | \(C_1 \times m_T\) |
Transfer of Kalman variances | – | No | – | Yes | Yes |
Cost | – | \(C_2 \times m_T\) | – | \(C_2 \times n_2<< C_2 \times m_T\) | \(C_2 \times n_3<< C_2 \times m_T\) |
Model type | \({\mathscr {M}}_{k,0,k}\) | \({\mathscr {M}}_{k,k,k}\) | \({\mathscr {M}}_{i,\emptyset ,k}\) | \({\mathscr {M}}_{i,i,k}\) | \({\mathscr {M}}_{k,j,k}\) |
Total cost | \(C_1 \times m_T\) | \((C_1 + C_2) \times m_T\) | \(C_1 \times n_1\) | \((C_1 + C_2) \times n_2\) | \(C_1 \times m_T + C_2 \times n_3\) |
