Why not polynomial regression?
Today I tried polynomial regression on the monotone problem. It seems that the polynomial regression is not better as linear regression for detecting the monotone as following:
1) more complex to compute. I did not check the complexity yet.
2) harder to decide the segment border. The polynomial frequently has a small fluctuation at the endpoints of the segments. It may move if you let the segment overlap though. But maybe it is not worth to investigate the optimal ways.
3) it is so fit to the data that it does not remove the “waves” caused by noise.
4) difficult to choose the order for the polynomial. You may need to choose different order at different segments.
1) more complex to compute. I did not check the complexity yet.
2) harder to decide the segment border. The polynomial frequently has a small fluctuation at the endpoints of the segments. It may move if you let the segment overlap though. But maybe it is not worth to investigate the optimal ways.
3) it is so fit to the data that it does not remove the “waves” caused by noise.
4) difficult to choose the order for the polynomial. You may need to choose different order at different segments.
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