Alignment

ns_sdn.typing.Alignment = Alignment

Alias of Literal['filtered', 'predicted'].

What the emission at step \(t\) conditions on, and therefore what it is.

"filtered" is the IEEE-ORSS run: the transition at \(t\) consumes \(y_t\) and the emission is scored against \(y_t\),

\[h_t = F_\psi(h_{t-1}, y_t), \qquad \hat y_{t \mid t} = \hat y(h_t), \qquad \mathcal{L} \ni \bigl(\hat y_{t \mid t} - y_t\bigr)^2,\]

so the decomposition at \(t\) is a filtered reading of the observed series given information through \(t\) (the sense in which an empirical mode decomposition or a Kalman filtered state is “of” the data). The one-step forecast of \(y_{t+1}\) under this alignment is the emission at \(t\), which is the published holdout protocol, and the paths have \(n\) rows.

"predicted" shifts the input: the transition at \(t\) consumes \(y_{t-1}\) and the emission is scored against \(y_t\),

\[h_t = F_\psi(h_{t-1}, y_{t-1}), \qquad \hat y_{t \mid t-1} = \hat y(h_t), \qquad \mathcal{L} \ni \bigl(\hat y_{t \mid t-1} - y_t\bigr)^2,\]

so every path is a one-step-ahead prediction, the network is trained as a forecaster, and the paths have \(n - 1\) rows.