Timeline for Bishop equation 3.67
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 6, 2021 at 16:34 | comment | added | microhaus | @DancingIceCream. [...] In that $p(\mathcal{M}_i \vert \mathcal{D}, \mathbf{x})$ may make mathematical sense, and your derivation is correct; but it may not respect standard model selection procedure to additionally condition on $\mathbf{x}$ when computing the model posterior probability $p(\mathcal{M}_i \vert \mathcal{D})$. Without having looked at whether $\mathbf{x}$ is a test-data point or validation-data point, I cannot be sure of this currently. Perhaps I will edit when I get time to revisit the chapter. | |
| Jul 6, 2021 at 16:33 | comment | added | microhaus | @DancingIceCream. Without refreshing my memory of that chapter of Bishop, I can think of two possibilities. Either the model choice $\mathcal{M}_i$ is conditionally independent of $\mathbf{x}$ given the training data set $\mathcal{D}$, meaning that $p(\mathcal{M}_i \vert \mathcal{D}, \mathbf{x}) = p(\mathcal{M}_i \vert \mathcal{D})$. In this case your derivation is correct. The other possibility is that your derivation is correct mathematically, but does not respect the semantics of the model selection procedure.[...] | |
| Jul 6, 2021 at 15:54 | comment | added | DancingIceCream | Thanks, but I don't understand the last equality. If I employ the algebra I show in my post I won't get the same answer as you. | |
| Jul 6, 2021 at 15:50 | history | answered | microhaus | CC BY-SA 4.0 |