Timeline for Statistical learning when observations are not iid
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9, 2022 at 8:55 | vote | accept | riccardo-df | ||
| Feb 9, 2022 at 8:54 | comment | added | riccardo-df | I am accepting this answer according to vox populi. | |
| Feb 7, 2022 at 18:21 | comment | added | J. Delaney | It depends on what you want your model to predict - assuming that the prices change over time. Do you want it to predict the average price over the period, the price at a given year (when you supply it as a feature) or the price in the future? | |
| Feb 7, 2022 at 14:54 | comment | added | riccardo-df | @J.Delaney that is exactly my concern. Going back to my example, say I want to fit a random forest (which does not impose any parametric distribution). Is there a way to take into account the repeated measurements characteristic? Clearly, I cannot just fit a random forest as it is provided in many statistical packages. I have a guess for a simplified case where, for some reason, we can believe that there is not auto-correlation: including the time variable (e.g., year) in the set of explanatory variable. Still, this would treat the same units at different time istances as different units. | |
| Feb 7, 2022 at 14:46 | comment | added | Frank Harrell | Assuming iid when it's not satisfied is still a problem for ML. For example if there are non-completely-random dropouts, analyzing the data as if each row comes from a different subject will lead to prediction bias. | |
| Feb 7, 2022 at 14:34 | comment | added | J. Delaney | 1) Yes you could estimate both $\mu$ and $\Sigma$, but note that I just gave this model for illustration, what is best for you will depend on the details of your data 2) This is a big question by itself, but every ML model is driven by some assumptions, either explicit or implicit (for example: the choice of a loss function). Just as you pointed out, if a certain model assumes that samples are i.i.d, it will not work well for data that is not. There is no "universal" ML model, so you always have to think about which underlying assumptions holds for your data | |
| Feb 7, 2022 at 14:04 | comment | added | riccardo-df | I see, this is a good answer. I need two clarifications, though. 1) You mean that I could estimate the parameter $\mu$? 2) Your solution works if I am willing to assume a (bivariate) parametric distribution for my data. As far as I understood, ML is all about avoiding such assumptions, and learning the best function from empirical evidence (as discussed in Breiman, 2001). | |
| Feb 7, 2022 at 13:58 | history | answered | J. Delaney | CC BY-SA 4.0 |