0
$\begingroup$

Let's say I have a set $I$ of input parameters, a set $J$ of output parameters, and a set $N$ of experiments that relates $I$ to $J$ for each $n\in N$.

When I train the algorithm how can I ensure that there is a certain smoothness in the solution given? Let me explain what I mean by that with an example: if for $i_1,i_2 \in I$, I have the corresponding output $f(i_1)$ and $f(i_2)$, and if I join $i_1$ and $i_2$ by a straight line in my multi-dimensional domain I need the function $f(i)$ to behave smoothly or 'nicely' between these values, for instance monotonically.

What I want to avoid in my function is having a 'spiked' surface that for a certain element $j\in J$ has several $i^* \in I$ such that $f(i^*)=j$ and these $i^*$ are distributed randomly on the domain I.

I think that my options are imposing that the training algorithm takes this into account as it reads the sample data, or creating first my predictive function $f$ and then use a second algorithm to smooth it, trying to maintain its predictive capabilities.

Any opinion on how to approach or rethink this is welcomed.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.