So rather than a regression it's more like the "line simplification" problem in graphics: (https://bost.ocks.org/mike/simplify/ https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93...)
Just thought this solution seems a little overkill. Surely you can pick some error metric over the splits to optimize instead?
In my group at Arm there's a solid expectation that we'll see neural networks integrated into every part of a running application, and whether they execute on special NN processors or the general-purpose CPU will largely depend on where the data is needed.
I cut a very long comment short and wrote the rest of this up here: http://yieldthought.com/post/170830096265/when-are-neural-ne...
DP[i][j] = min over k of (DP[i][k] + (cost of splitting at k) + (linear regression error of points from kth to jth))
This should run in O(n^3) which will be fine for the author's requirement of ~100 points. But this isn't a complete solution since it's not obvious how to choose the cost of splitting (which is needed otherwise it will just split everything into 1 or 2 point segments).
I think thinking about this more and explicitly trying to design this cost function is still better than labeling a bunch of data until the machine learning algorithm can reverse engineer the cost function from your head. Then you can be confident of what your code is doing and why and know that it won't randomly output potato.
Maybe the author of the app had other uses for CNNs in mind for other features in the future.
So if you account for that, why have individual analytical solutions when you can solve a whole bunch of problems with one cognitive approach?