Post by Robin on Jul 28, 2017 11:45:10 GMT 8
It has become clear to me that using quasi-Newton (hill climbing optimisation) will cause the optimisation to almost always get stuck in local minima. This should be compared with methods using Bayesian inference such as a Markov Chain Monte Carlo (MCMC) approach which attempts to collect a large number of samples of the parameter space and finds the global maximum of likelihood within the posterior distributions.
As an example, I show the outcomes of an optimisation of a galaxy for which I have chosen to feed in differing initial conditions for the effective radii of the bulge and disk. First, here are the results of running a 'BFGS' downhill gradient method:
Note that there are three distinct solutions for which initial conditions appear to converge upon.
Now compare this to the results from the MCMC optimisation with the same initial conditions:
Not only do the majority of solutions converge, they appear to be finding the global minimum of the full parameter space that the BFGS routine could not.
*Note that there is one solution in the MCMC optimisations that has diverged. Upon inspection, this is due to constraints which unfortunately caused the effective radius of the bulge and disk to be fixed. Without constraints, the solutions are almost always robust to the provision of the initial conditions.
As an example, I show the outcomes of an optimisation of a galaxy for which I have chosen to feed in differing initial conditions for the effective radii of the bulge and disk. First, here are the results of running a 'BFGS' downhill gradient method:
Note that there are three distinct solutions for which initial conditions appear to converge upon.
Now compare this to the results from the MCMC optimisation with the same initial conditions:
Not only do the majority of solutions converge, they appear to be finding the global minimum of the full parameter space that the BFGS routine could not.
*Note that there is one solution in the MCMC optimisations that has diverged. Upon inspection, this is due to constraints which unfortunately caused the effective radius of the bulge and disk to be fixed. Without constraints, the solutions are almost always robust to the provision of the initial conditions.
