Xkcd curve dating
Xkcd curve dating - Freelivechatxxx
This requires some actual understanding of the system being considered.If you change it by, for example, pumping lots of greenhouse gases into the atmosphere, then the training data will almost certainly not be appropriate.
In particular, by Markov’s inequality we have the conditional probabilities and thus, if is large enough, and small enough, it will be true with probability that and and simultaneously that for all natural numbers .
It will then suffice to show that (say) with probability , since the contribution of those outside of can be absorbed by the factor with probability .
As one consequence of the GUE hypothesis, we have with probability . Applying the Hardy-Littlewood maximal inequality, we see that with probability , we have which implies in particular that for all .
However, if we let 0}" title="" class="latex" / be a moderately large constant (and assume small depending on ), one can show using -point correlation functions for the Dyson sine process (and the fact that the Dyson kernel equals to second order at the origin) that for any natural number , where denotes the number of elements of the process in .
For instance, the expression can be written in terms of the three-point correlation function as which can easily be estimated to be (since in this region), and similarly for the other estimates claimed above.
This, of course, does not mean that it can’t vary, but we do mostly understand what can cause these variations.
There are internal/natural cycles that can produce variations, but there are limits as to how large these internally-driven cycles can be and how long they can last.
These are all rather complex processes and the idea that one could predict how they will change in future by fitting some sine curves to a few different temperature proxy records is rather ridiculous.
This highlights the key problem with the approach in this paper; you can’t try and understand what causes our climate to vary, or how it might vary in future, using machine learning alone.
That’s not to say that machine learning can’t play a role.
However, if you are going to use something like machine learning to make predictions about the future, you do need to be pretty confident that the data that you use to train the machine learning algorithm presents a reasonable representation of the system you’re trying to model.
An example of such a pair would be the classical pair discovered by Lehmer.