Timeline for Is it possible to apply a monotonicity constraint on a Gaussian process regression fit?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 7 at 23:07 | comment | added | Sextus Empiricus | Is the underlying process truly a Gaussian process with a continuous kernel? This jump around 0.950 seems more like a change in the trend. If you are after a non-stationary process then you might try to model the process by $y(x) = f(x) + \epsilon(x)$ where $f(x)$ is some decreasing function (the non-stationary part), and $\epsilon(x)$ is a noise term based on a Gaussian process. | |
| Jan 7 at 21:55 | comment | added | Ben Bolker | Don't know if it's Python code or not, but see: Riihimäki, Jaakko, and Aki Vehtari. 2010. “Gaussian Processes with Monotonicity Information.” In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 645–52. JMLR Workshop and Conference Proceedings. proceedings.mlr.press/v9/riihimaki10a.html. | |
| Jan 7 at 21:09 | answer | added | marnix | timeline score: -1 | |
| Mar 4, 2019 at 3:56 | vote | accept | Mathews24 | ||
| Mar 3, 2019 at 4:11 | answer | added | j__ | timeline score: 8 | |
| Mar 1, 2019 at 19:33 | comment | added | Mathews24 | @Yves That is certainly the idea I'm trying to capture. Although perhaps this is where an example Python code applied on the above would help as I'm a bit unclear on specifics (e.g. application of knots in GPR, actual implementation of linear inequality constraints in code). | |
| Mar 1, 2019 at 19:08 | comment | added | Mathews24 | @kjetilbhalvorsen The primary reason for applying GPR is obtain accurate uncertainty estimates which are critical to my work. GPR does have a well-defined analytic derivative, although it is based upon the chosen kernel. | |
| Mar 1, 2019 at 16:41 | comment | added | Yves | This may help. | |
| Mar 1, 2019 at 16:04 | comment | added | Mathews24 | @Yves Ideally both. I would like to understand how, in both theory and code, to enforce monotonicity for the above example. | |
| Mar 1, 2019 at 14:30 | comment | added | kjetil b halvorsen♦ | Is there some specific reason you need to use gaussian processes? If not, consider using monotone splines, see. As far as I remember, most gaussian processes do not even have derivatives, so to enforce monotonicity, I guess you at least wil need a kernel giving derivatives, and then restrict those to be positive. But I beleive that gaussian processes with derivatives are very smooth, maybe too smooth! | |
| Mar 1, 2019 at 7:51 | comment | added | Yves | Are you looking for some theoretical elements on this (rather complex) problem or simply for an existing code in Python? | |
| Mar 1, 2019 at 6:21 | history | edited | Mathews24 | CC BY-SA 4.0 |
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| Mar 1, 2019 at 6:15 | history | asked | Mathews24 | CC BY-SA 4.0 |