Multi-Granularity Residual Learning with Confidence Estimation for Time Series Prediction

Hou, Min, et al. “Multi-Granularity Residual Learning with Confidence Estimation for Time Series Prediction.” Proceedings of the ACM Web Conference 2022. 2022.

\[\mathcal{L} = \sum^S_{s=1}||y^s - \hat{y}^s||^2 + \lambda_1 \sum_{s=1}^{S} \mathcal{L}_{Rec} + \frac{\lambda_{\theta}}{2}||\Theta||_F^2\] \[\mathcal{L}_{Rec} = \sum_{m=1,2,..m} ||F^m - G^{m-1}||^2_F\] \[\mathcal{L} = \sum^S_{s=1}||y^s - \hat{y}^s||^2 + \lambda_1 \sum_{s=1}^{S} \mathcal{L}_{Rec} + \lambda_2 \sum_{x=1}^S \sum_{m=1}^M \sum_{t=1}^T \mathcal{L}_N^C + \frac{\lambda_{\theta}}{2}||\Theta||_F^2\] \[\mathcal{L}_N^C = - E_{\mathcal{P}}\] \[c_m^{t} = AR(h_m^{<t})\] \[\hat{y} =\mathcal{F}_\theta(X^1, ..., X^M) \\ X^m = [x_1^m, ..., x_T^m] \in \mathit{R}^{D \times K^m \times T}\] \[\begin{align} F^m &= \mathcal{F}_{Linear}^m(X^m) \\ F^m &\in \mathit{R}^{D \times K \times T} \end{align}\] \[\hat{y}\]

dd

\[\hat{y}_1 \\ \\ \hat{y}_2 \\ \\ \hat{y}_3 \\\]