Timeline for When will $\text{Variance}=\text{Bias}^2$ hold for the optimal model?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2021 at 16:43 | comment | added | markowitz | @StephanKolassa; I agree. | |
| Mar 18, 2021 at 15:46 | comment | added | Stephan Kolassa | Hm. What is "variance" and "bias" if "we have the data that we have"? What do we take expectations over? I'd say we need to consider the BVT in the context of a specific amount of data, not a specific set of observations. | |
| Mar 18, 2021 at 15:32 | comment | added | markowitz | But what situation is very common? You have some $n$ but $n=10, 100, 300, 2000, … ?$ … if the symmetry you are interested in depend, among other things, from $n$ … it seems me impossible that it is a common or relevant situation. This is my point. If it was true that this symmetry depend only about the true model … become more interesting what kind of true model imply it. But it is not so; from dimensionality problem, no kind of true model can imply the summetry you are interested in. | |
| Mar 18, 2021 at 15:13 | comment | added | Richard Hardy | Hmm, I am not sure I get the point. The relevance does not decrease if the situation is very common. And I think it is, because we usually have a fixed data sample that we want to analyze. Or at least I do. There can be occasions where one can collect more data, but that is not always possible and often costly. And the snapshot is unfortunately misleading as it implies Variance = Bias^2 which is rarely the case. It would be nice to find out how commonly it may apply, hence the question. | |
| Mar 18, 2021 at 15:04 | comment | added | markowitz | Sure. But, as said above, this fact decrease substantially the relevance of the question. Sophisticated reasonings around the true model become much less important. Agree? I think that the graph above represent only a snapshot for figured out the BVT message; not so realistic or geometrically important. | |
| Mar 18, 2021 at 14:41 | comment | added | Richard Hardy | True, BVT must be analyzed under a fixed amount of data. But that is often the case; we have the data that we have and then we are looking for a good predictive model. | |
| Mar 18, 2021 at 14:35 | history | answered | markowitz | CC BY-SA 4.0 |