Timeline for Nonlinear regression model linear in some parameters
Current License: CC BY-SA 3.0
10 events
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| Sep 21 at 16:36 | comment | added | JeeyCi |
or see example for your model function y = a + b * exp(c * t) from scipy.optimize import least_squares; res_log = least_squares(fun, x0, loss='cauchy', f_scale=0.1, args=(t_train, y_train)) here... But all depends on data to be successive in convergence
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| Sep 20 at 16:22 | comment | added | JeeyCi |
in python, use scipy.optimize.curve_fit() if you already now your model_function... your link's lecture says to fix theta_3 meaning give it some/any value...
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| Jan 9, 2020 at 21:59 | comment | added | Dave | @mpiktas What would be the advantage of doing it this way instead of picking a value for $\theta_3$ and then optimizing $\theta_1$ and $\theta_2$ via OLS? | |
| Apr 13, 2012 at 21:53 | comment | added | neo123 | Improved convergence is of course desirable. Thanks for that answer! I may be wrong, but I think you may, in principle, use OLS estimates for the so called Gauss-Newton regressions which are used for computing the step size at each iteration in a Gauss-Newton method. | |
| Apr 13, 2012 at 18:54 | comment | added | mpiktas | You do not perform lots of OLS regressions if you run NLS. The point of the procedure is that it practice it might work better than straight NLS. The NLS is guaranteed to work if your starting values are close to the optimal ones. So the outlined procedure can be thought of a way to get better starting values. Theory is nice, but in practice sometimes is very hard to get convergence. Any trick then helps. | |
| Apr 13, 2012 at 14:38 | history | tweeted | twitter.com/#!/StackStats/status/190811321149816832 | ||
| Apr 13, 2012 at 14:19 | answer | added | whuber♦ | timeline score: 7 | |
| Apr 13, 2012 at 14:03 | comment | added | neo123 | Ok, thanks, but what do you gain from iterating like that compared to performing a full-blown NLS on the complete model? You essentially perform lots of OLS regressions iteratively if you run NLS using a Gauss-Newton method anyway, right? | |
| Apr 13, 2012 at 13:37 | comment | added | mpiktas | You pick values for $\theta_1$ and $\theta_2$. Then minimise with respect to $\theta_3$. You get the value $\theta_3^{(1)}$. Having it you now use OLS to estimate $\theta_1^{(1)}$ and $\theta_2^{(1)}$. You got your first iteration. Then iterate until convergence. | |
| Apr 13, 2012 at 13:04 | history | asked | neo123 | CC BY-SA 3.0 |