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From |
"Glenn Goldsmith" <glenn.goldsmith@gmail.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Combining analytical and numerical derivatives in mata -optmize()- |

Date |
Sun, 22 Feb 2009 15:24:17 -0000 |

Hello again list, On the off chance that anybody else is at all interested, I've managed to solve the problem I outlined below, and now have something that allows -optimize()- to combine analytical and numerical derivatives. I'm not convinced that the solution I have is the most elegant way of proceeding, but it appears to work. Outline below: /* Begin Code */ function my_optimizer() { transmorphic scalar R, S ... // define handle for v0 evaluator, and validate as if called by optimize() S = optimize_init() optimize_init_evaluator(S,&v0evaluator()) optimize_init_evaluatortype(S,"v0") optimize_init_params(S,lambda) optimize_init_argument(S,1,beta) (void) opt__validate(S) // define handle for v1 evaluator, passing R and S as arguments R = optimize_init() optimize_init_params(R,theta) optimize_init_evaluator(R,&v1evaluator()) optimize_init_evaluatortype(R,"v1") optimize_init_argument(R,1,R) optimize_init_argument(R,2,S) (void) optimize(main) ... } void v1evaluator(todo, param, transmorphic scalar R, struct__optstruct scalar S, lli, si, H) { real scalar hi real rowvector beta, lambda, g0, h real colvector fp, fm real matrix H0 // partition the param vector into beta and lambda beta = param[1..p] lambda = param[q..r] // use a v0 evaluator to obtain lli (passing beta as a separate argument) v0evaluator(0,lambda,beta,lli,si,H) if (todo>0) { si = J(N,r,.) h = J(1,cols(lambda),.) // obtain the scores for beta analytically si[.,1..p] = [analytical expression for beta scores] // obtain the scores for lambda numerically // update S elements manually *S.arglist[1] = beta S.params = lambda S.iter = optimize_result_iterations(R) S.value = quadcolsum(lli) // calculate scores (copied from internal -optimize()- code) for (i=q; i<=r; i++) { (void) opt__v0_h(S,i,hi,fp,fm,g0,H0) h[i] = hi si[,i] = (fp - fm)/(2*h[i]) } } } /* End Code */ Interestingly enough, my first attempt at this managed to fool v1debug into thinking that the v1 evaluator calculated the same numerical scores as the v0 evaluator, when actually it didn't. I guess that's what happens when you start messing around with structures that you're not supposed to. Glenn. -----Original Message----- From: Glenn Goldsmith [mailto:glenn.goldsmith@gmail.com] Sent: 21 February 2009 15:10 To: 'statalist@hsphsun2.harvard.edu' Subject: Combining analytical and numerical derivatives in mata -optmize()- Dear list, I am trying to code a maximum likelihood estimator using mata -optimize()-. For most of the model parameters (call them betas) I have analytical expressions for the gradients/scores. However, for a small subset of the parameters (call them lambdas), I do not. My hope was that instead of coding a v0 evaluator, which would use numerical derivatives for both the betas and the lambdas, I could somehow take advantage of the fact that I have analytical expressions for the beta scores (and Hessian components), and only use numerical derivatives for the small number of lambdas - potentially saving substantially on computation time. Unfortunately, while it seems like this should be possible, I can't quite get it to work. The approach I've tried to take so far is set out below. I'd be very grateful for: 1. any advice on how to salvage my approach (or on whether it is salvageable at all); or 2. any suggestions as to whether there might be another way to achieve what I trying do here. The thought was to construct a v1 evaluator (and ultimately a v2 evaluator, but the problems arise at the v1 stage already, so I'll restrict discussion to that) that uses an internal call to -optimize_evaluate()- to calculate numerical scores with respect to lambda, but calculates everything else analytically. I've used v1debug to check the analytical scores, and they're correct. However, the numerical scores generated by -optimize_evaluate()- only agree with the numerical scores that -optimize()- calculates at the 0th iteration (when they're identical). After that, they diverge. (Sometimes they're still quite close, sometimes they're not.) Is this to be expected, or does it mean I must have made a mistake somewhere? Is the problem that -optimize()- somehow modifies its gradient calculating routine at each iteration? And if that is the case, is there any way to take advantage of this in my code? A rough outline of the structure of my v1 evaluator is below (this is drastically simpler than what I am actually dealing with, but should hopefully convey the essence of what I'm trying to do). /* Begin Code */ void v1evaluator(todo, param, lli, si, H) { // partition the param vector into beta and lambda beta = param[1..p] lambda = param[q..r] // use a v0 evaluator to obtain lli (passing beta as a separate argument) v0evaluator(0,lambda,beta,lli,si,H) if (todo>0) { si = J(N,r,.) // obtain the scores for beta analytically si[.,1..p] = [analytical expression for beta scores] // obtain the scores for lambda numerically, using -optimize_evaluate()- S = optimize_init() optimize_init_evaluator(S,&v0evaluator()) optimize_init_evaluatortype(S,"v0") optimize_init_params(S,lambda) optimize_init_argument(S,1,beta) (void) optimize_evaluate(S) si[.,q..r] = optimize_result_scores(S) } } /* End Code */ Independently of the problems noted above, this is at least slightly inefficient, in that -optimize_evaluate()- automatically calculates the Hessian, which is unnecessary here. Specifying -optimize_init_technique(S,"bhhh")- prevents that. However, it may still be that the -optimize_evaluate()- call is an inefficient way of doing what I want, even if I could get it to work. Best wishes, Glenn * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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