... rule¹

The subscripts of all pdf's are assumed to be the same as their arguments, and are omitted for keeping the notation simpler.

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... probability²

More accurately, one could show the dependence on the chosen model ${\cal H}$ by conditioning all the pdf's in (1) by ${\cal H}$: $p(\boldsymbol{\theta}\vert \boldsymbol{X},{\cal H} )$, $p(\boldsymbol{X}\vert {\cal H} )$, etc. We have here dropped also the dependence on ${\cal H}$ out for notational simplicity. See Valpola02NC for a somewhat more complete discussion of Bayesian methods and ensemble learning.

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... form³

Note that constants are dropped out since they do not depend on $\overline{s}$ or $\widetilde{s}$.

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... dimensions⁴

Higher dimensional SOMs become quickly intractable due to exponential number of parameters.

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... nodes.⁵

Note that delay node only rewires connections so it does not affect the formulas.

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