Models that infer "high-level rules"

Question

Are there any models that infer "high-level" rules?

Consider for example the plot

that represents data from a table with 3 entries: A $x$ and $y$ column of real-valued data and a label column with data *yellow",blue,magenta.

Are there any models that, if I give them such data, will automatically infer things like

data is concentrated in 3 disc-like regions and a line of points
if there is a yellow dot, there will be a blue dot nearby and vice-versa
one of the disc-like regions is separated by a line of data from the others

and output these rules not implicitly, by outputting some classification or regression lines, but outputting some formal language that state these rules?

So far my guess is that for each such question I have to think deeply which model could answer - and then convert a classification/regression line into a rule by hand.
For example, an SVM would be able to answer out of the box only the first two questions (for the third one we would already need to to additional work), like so

(you can generate yourself such pics here, thx to F. Werner for pointing the website out!) and then we would have to interpret the regions the SVM detected to manually infer such rules. (I guess what I have in mind maybe comes a bit close to https://automaticstatistician.com/index/?)

I think you may be looking for [artificial general intelligence](https://en.wikipedia.org/wiki/Artificial_general_intelligence). — Stephan Kolassa, Jul 06 '18 at 10:51
@StephanKolassa No; I was more looking for something like this https://www.nature.com/articles/srep36812 (like logic regression, but much more advanced) — l7ll7, Jul 06 '18 at 20:25

Tim · Answer 1 · 2020-06-27T07:59:41.290

“Disc”, “line”, “above”, “below” are abstract categories, making rules of them needs logical reasoning, so creating such abstract rules would be a task that is too hard for a human child up to some age, so it seems like artificial general intelligence problem, as noticed by Stephen Kolassa.

It is possible to have question-answering algorithm that would be able to answer simple questions about the image, like “is there a circle”, but not being able to make any logical conclusions about it. Traditional machine learning would be able to fit patterns like the example that was shown in the question. Moreover, notice that apparently the data didn’t have “no points” class, so classifier didn’t consider it, otherwise image partitioning algorithm should manage to mark background as well.

Models that infer "high-level rules"

1 Answers1