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Each iteration sees an update of the weight by the computed gradient.
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Here's an update on the weight of that evidence.
A gradient based update of the weights is performed at discrete time instants over a moving measurement window in order to reduce the model output – real output mismatch.
This assumption leads to a recursive update of the weights as (2).
If we sample from the Markov kernels of X [ t 0, ∞ ) directly, then ϱ τ d ∗ | τ d - 1 x τ d ∗ i | x τ d - 1 i ≡ 1 and the update of the weights does not depend on the new states x τ d ∗ i. Hence we only need to compute the weight update and the corresponding ESS estimate until we find an adequate stepsize.
Note that if one chooses X ~ [ t 0, ∞ ) = X [ t 0, ∞ ) (in law), then ϱ t k | t k - 1 (x t k i | x t k - 1 i ) ≡ 1 and the update of the weights simplifies to w t k i = g k y k | x t k i, t k w t k - 1 i.
This divergence problem can be resolved by proposing a leak term during the update process of the weight vector.
e(n) is the error sequence in Equation (2), which equals the difference between the expected response d(n) and the output of the filter y(n) as Equation (6), and u is the update step of the weight coefficient.
To investigate the performance of the adaptive updating of the weights for this algorithm, we have used the optimal weights as initial weights.
When early stopping is used, 20% of the data will be selected by stratified random sampling to constitute a validation set, which is left outside of the updating of the weights.
Using Eq. (4) in (6) we get begin{aligned} d(i -z_{b} (i -z_{b}^{pri =f_{b}^{prime}^{l}cdot Delta u^{l}(i)+Delta w_{b}^{l}cdotb}^{l} (i) enDeltagned} (7)All qu^{lities in Eq. (7) are based on former network values, apart from the updates of the weights (Delta w^{l}) and of the outputs (Delta u^{l}).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com