more details about the decomposition of Eq. (3)

[fikry102]

By Eq. (3), the probability density $p(f)$ can be decomposed into the form of a factor which does not depend on the distribution parameters $μ$, $σ$ multiplied by the other factor depending on $μ$, $σ$ and statistics ...

Could you please give a more specific formulation of the two factors mentioned? Thank you!

[youthhoo]

please refer to the Fisher-neyman factorization theorem [9,35] mentioned in our paper.

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By Eq. (3), the probability density $p(f)$ can be decomposed into the form of a factor which does not depend on the distribution parameters $μ$, $σ$ multiplied by the other factor depending on $μ$, $σ$ and statistics ...

Could you please give a more specific formulation of the two factors mentioned? Thank you!

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[fikry102]

please refer to the Fisher-neyman factorization theorem [9,35] mentioned in our paper. … ---- Replied Message ---- | From | @.> | | Date | 10/17/2022 22:22 | | To | @.> | | Cc | @.> | | Subject | [youthhoo/AFA_For_Few_shot_learning] more details about the decomposition of Eq. (3) (Issue #1) | By Eq. (3), the probability density $p(f)$ can be decomposed into the form of a factor which does not depend on the distribution parameters $μ$, $σ$ multiplied by the other factor depending on $μ$, $σ$ and statistics ... Could you please give a more specific formulation of the two factors mentioned? Thank you! — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you are subscribed to this thread.Message ID: @.>

Thanks for your quick reply! Sorry for my possibly unclear expression. I am not asking the theorem. I just want to know the specific decomposition of the right side of the Eq. (3). Does the paper mean $(2 \pi)^{-\frac{N}{2}}$ is the factor which does not depend on the distribution parameters?

As the Fisher-neyman factorization theorem says: If the probability density function is $f\theta(x)$, then $T$ is sufficient for $\theta$ if and only if nonnegative functions $g$ and $h$ can be found such that $f{\theta}(x)=h(x) g_{\theta}(T(x))$, i.e. the density $f$ can be factored into a product such that one factor, h, does not depend on $\theta$ and the other factor, which does depend on $\theta$, depends on $x$ only through $T(x)$.