[R] How to improve the "OPTIM" results
Dear R users,
I used to "OPTIM" to minimize the obj. function below. Even though I used
the true parameter values as initial values, the results are not very good.
How could I improve my results? Any suggestion will be greatly appreciated.
Regards,
Kathryn Lord
#--
x = c(0.35938587, 0.34889725, 0.20577608, 0.1529, -4.24741146,
-1.32943326,
0.29082527, -2.38156942, -6.62584473, -0.22596237, 6.97893687,
0.22001081,
-1.39729222, -5.17860124, 0.52456484, 0.46791660, 0.03065136,
0.32155177,
-1.12530013, 0.02608057, -0.22323154, 3.30955460, 0.54653982,
0.29403011,
0.47769874, 2.42216260, 3.93518355, 0.23237890, 0.09647044,
-0.48768933,
0.37736377, 0.43739341, -0.02416010, 4.02788119, 0.07320802,
-0.29393054,
0.25184609, 0.7608, -3.34121918, 1.16028677, -0.60352008,
-2.86454069,
-0.84411691, 0.24841071, -0.11764954, 5.92662106, 1.03932953,
-6.21987657,
-0.54763352, 0.20263192) # data
theta0= c(log(2),0,c(0,-.3,.3),log(c(10,.05,.05))) # initial value(In fact,
true parameter value)
n = length(x)
fr2 = function(theta)
{
a1 = theta[1]; a2 = theta[2]
mu1 = theta[3]; mu2 = theta[4]; mu3 = theta[5]
g1 = theta[6]; g2 = theta[7]; g3 = theta[8]
w1=exp(a1)/(1+exp(a1)+exp(a2))
w2=exp(a2)/(1+exp(a1)+exp(a2))
w3=1-w1-w2
obj =((w1^2)/(2*sqrt(exp(g1)*pi))
+ (w2^2)/(2*sqrt(exp(g2)*pi))
+ (w3^2)/(2*sqrt(exp(g2)*pi))
+ 2*w1*w2*dnorm((mu1-mu2)/sqrt(exp(g1)+exp(g2)))/sqrt(exp(g1)+exp(g2))
+
2*w1*w3*dnorm((mu1-mu3)/sqrt(exp(g1)+exp(g3)))/sqrt(exp(g1)+exp(g3))
+
2*w2*w3*dnorm((mu2-mu3)/sqrt(exp(g2)+exp(g3)))/sqrt(exp(g2)+exp(g3))
- (2/n)*(sum(w1*dnorm((x-mu1)/sqrt(exp(g1)))/sqrt(exp(g1))
+ w2*dnorm((x-mu2)/sqrt(exp(g2)))/sqrt(exp(g2))
+ w3*dnorm((x-mu3)/sqrt(exp(g3)))/sqrt(exp(g3)) )))
return(obj)
}
optim(theta0, fr2, method=BFGS", control = list (fnscale=10,
parscale=c(.01,.01,.01,.01,.01,1,1,1), maxit=10))
--
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http://www.nabble.com/How-to-improve-the-%22OPTIM%22-results-tp16509144p16509144.html
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Re: [R] How to improve the "OPTIM" results
Dear Katheryn:
I'm confused by your claim that, "Even though I used the true
parameter values as initial values, the results are not very good."
When I ran it, 'optim' quit with $value = -35835, substantially
less than fr2(theta0) = -0.3.
Could you please review your question, because I believe this will
answer it.
MORE GENERAL OPTIM ISSUES
It is known that 'optim' has problems. Perhaps the simplest thing
to do is to call 'optim' with each of the 'methods' in sequence, using
the 'optim' found by each 'method' as the starting value for the next.
When I do this, I often skip 'SANN', because it typically takes so much
more time than the other methods. However, if there might be multiple
local minima, then SANN may be the best way to find a global minimum,
though you may want to call 'optim' again with another method, starting
from optimal solution returned by 'SANN'.
Another relatively simple thing to do is to call optim with
hessian = TRUE and then compute eigen(optim(..., hessian=TRUE)$hessian,
symmetric=TRUE). If optim found an honest local minimum, all the
eigenvalues will be positive. For your example, the eigenvalues were as
follows:
19000, 11000,
0.06, 0.008, 0.003,
-0.0002, -0.06,
-6000
This says that locally, the "minimum" identified was really a
saddle point, being a parabola opening up in two dimensions (with
curvatures of 19000 and 11000 respectively), a parabola opening down in
one dimension (with curvature -6000), and relatively flat by comparison
in the other 5 dimensions. In cases like this, it should be moderately
easy and fast to explore the dimension with the largest negative
eigenvalue with the other dimensions fixed until local minima in each
direction were found. Then 'optim' could be restarted from both those
local minima, and the minimum of those two solutions could be returned.
If all eigenvalues were positive, it might then be wise to restart
with parscale = the square roots of the diagonal of the hessian; I
haven't tried this, but I believe it should work. Using 'parscale' can
fix convergence problems -- or create some where they did not exist
initially.
I'm considering creating a package 'optimMLE' that would automate
some of this and package it with common 'methods' that would assume that
sum(fn(...)) was either a log(likelihood) or the negative of a
log(likelihood), etc. However, before I do, I need to make more
progress on some of my other commitments, review RSiteSearch("optim",
"fun") to make sure I'm not duplicating something that already exists,
etc. If anyone is interested in collaborating on this, please contact
me off-line.
Hope this helps.
Spencer
kathie wrote:
> Dear R users,
>
> I used to "OPTIM" to minimize the obj. function below. Even though I used
> the true parameter values as initial values, the results are not very good.
>
> How could I improve my results? Any suggestion will be greatly appreciated.
>
> Regards,
>
> Kathryn Lord
>
> #--
>
> x = c(0.35938587, 0.34889725, 0.20577608, 0.1529, -4.24741146,
> -1.32943326,
> 0.29082527, -2.38156942, -6.62584473, -0.22596237, 6.97893687,
> 0.22001081,
>-1.39729222, -5.17860124, 0.52456484, 0.46791660, 0.03065136,
> 0.32155177,
>-1.12530013, 0.02608057, -0.22323154, 3.30955460, 0.54653982,
> 0.29403011,
> 0.47769874, 2.42216260, 3.93518355, 0.23237890, 0.09647044,
> -0.48768933,
> 0.37736377, 0.43739341, -0.02416010, 4.02788119, 0.07320802,
> -0.29393054,
> 0.25184609, 0.7608, -3.34121918, 1.16028677, -0.60352008,
> -2.86454069,
>-0.84411691, 0.24841071, -0.11764954, 5.92662106, 1.03932953,
> -6.21987657,
>-0.54763352, 0.20263192) # data
>
> theta0= c(log(2),0,c(0,-.3,.3),log(c(10,.05,.05))) # initial value(In fact,
> true parameter value)
> n = length(x)
>
> fr2 = function(theta)
> {
> a1 = theta[1]; a2 = theta[2]
> mu1 = theta[3]; mu2 = theta[4]; mu3 = theta[5]
> g1 = theta[6]; g2 = theta[7]; g3 = theta[8]
>
> w1=exp(a1)/(1+exp(a1)+exp(a2))
> w2=exp(a2)/(1+exp(a1)+exp(a2))
> w3=1-w1-w2
>
> obj =((w1^2)/(2*sqrt(exp(g1)*pi))
> + (w2^2)/(2*sqrt(exp(g2)*pi))
> + (w3^2)/(2*sqrt(exp(g2)*pi))
>
>+ 2*w1*w2*dnorm((mu1-mu2)/sqrt(exp(g1)+exp(g2)))/sqrt(exp(g1)+exp(g2))
> +
> 2*w1*w3*dnorm((mu1-mu3)/sqrt(exp(g1)+exp(g3)))/sqrt(exp(g1)+exp(g3))
> +
> 2*w2*w3*dnorm((mu2-mu3)/sqrt(exp(g2)+exp(g3)))/sqrt(exp(g2)+exp(g3))
>
> - (2/n)*(sum(w1*dnorm((x-mu1)/sqrt(exp(g1)))/sqrt(exp(g1))
> + w2*dnorm((x-mu2)/sqrt(exp(g2)))/sqrt(exp(g2))
> + w3*dnorm((x-mu3)/sqrt(exp(g3)))/sqrt(exp(g3)) )))
>
> return(obj)
> }
>
> optim(theta0, fr
Re: [R] How to improve the "OPTIM" results
Dear Spencer Graves,
Thank you for your comments and suggestions.
I knew that the true optimum values are about (0.69, 0.0, 0.0, -0.3, 0.3,
2.3, -3.0 ,-3.0). That's why I used these values as starting values.
Nonetheless, the last three estimates are so bad.
Regards,
Kathryn Lord
Spencer Graves wrote:
>
> Dear Katheryn:
>
> I'm confused by your claim that, "Even though I used the true
> parameter values as initial values, the results are not very good."
>
> When I ran it, 'optim' quit with $value = -35835, substantially
> less than fr2(theta0) = -0.3.
>
> Could you please review your question, because I believe this will
> answer it.
>
>
> MORE GENERAL OPTIM ISSUES
>
> It is known that 'optim' has problems. Perhaps the simplest thing
> to do is to call 'optim' with each of the 'methods' in sequence, using
> the 'optim' found by each 'method' as the starting value for the next.
> When I do this, I often skip 'SANN', because it typically takes so much
> more time than the other methods. However, if there might be multiple
> local minima, then SANN may be the best way to find a global minimum,
> though you may want to call 'optim' again with another method, starting
> from optimal solution returned by 'SANN'.
>
> Another relatively simple thing to do is to call optim with
> hessian = TRUE and then compute eigen(optim(..., hessian=TRUE)$hessian,
> symmetric=TRUE). If optim found an honest local minimum, all the
> eigenvalues will be positive. For your example, the eigenvalues were as
> follows:
>
> 19000, 11000,
> 0.06, 0.008, 0.003,
> -0.0002, -0.06,
> -6000
>
> This says that locally, the "minimum" identified was really a
> saddle point, being a parabola opening up in two dimensions (with
> curvatures of 19000 and 11000 respectively), a parabola opening down in
> one dimension (with curvature -6000), and relatively flat by comparison
> in the other 5 dimensions. In cases like this, it should be moderately
> easy and fast to explore the dimension with the largest negative
> eigenvalue with the other dimensions fixed until local minima in each
> direction were found. Then 'optim' could be restarted from both those
> local minima, and the minimum of those two solutions could be returned.
>
> If all eigenvalues were positive, it might then be wise to restart
> with parscale = the square roots of the diagonal of the hessian; I
> haven't tried this, but I believe it should work. Using 'parscale' can
> fix convergence problems -- or create some where they did not exist
> initially.
>
> I'm considering creating a package 'optimMLE' that would automate
> some of this and package it with common 'methods' that would assume that
> sum(fn(...)) was either a log(likelihood) or the negative of a
> log(likelihood), etc. However, before I do, I need to make more
> progress on some of my other commitments, review RSiteSearch("optim",
> "fun") to make sure I'm not duplicating something that already exists,
> etc. If anyone is interested in collaborating on this, please contact
> me off-line.
>
> Hope this helps.
> Spencer
>
> kathie wrote:
>> Dear R users,
>>
>> I used to "OPTIM" to minimize the obj. function below. Even though I
>> used
>> the true parameter values as initial values, the results are not very
>> good.
>>
>> How could I improve my results? Any suggestion will be greatly
>> appreciated.
>>
>> Regards,
>>
>> Kathryn Lord
>>
>> #--
>>
>> x = c(0.35938587, 0.34889725, 0.20577608, 0.1529, -4.24741146,
>> -1.32943326,
>> 0.29082527, -2.38156942, -6.62584473, -0.22596237, 6.97893687,
>> 0.22001081,
>>-1.39729222, -5.17860124, 0.52456484, 0.46791660, 0.03065136,
>> 0.32155177,
>>-1.12530013, 0.02608057, -0.22323154, 3.30955460, 0.54653982,
>> 0.29403011,
>> 0.47769874, 2.42216260, 3.93518355, 0.23237890, 0.09647044,
>> -0.48768933,
>> 0.37736377, 0.43739341, -0.02416010, 4.02788119, 0.07320802,
>> -0.29393054,
>> 0.25184609, 0.7608, -3.34121918, 1.16028677, -0.60352008,
>> -2.86454069,
>>-0.84411691, 0.24841071, -0.11764954, 5.92662106, 1.03932953,
>> -6.21987657,
>>-0.54763352, 0.20263192) # data
>>
>> theta0= c(log(2),0,c(0,-.3,.3),log(c(10,.05,.05))) # initial value(In
>> fact,
>> true parameter value)
>> n = length(x)
>>
>> fr2 = function(theta)
>> {
>> a1 = theta[1]; a2 = theta[2]
>> mu1 = theta[3]; mu2 = theta[4]; mu3 = theta[5]
>> g1 = theta[6]; g2 = theta[7]; g3 = theta[8]
>>
>> w1=exp(a1)/(1+exp(a1)+exp(a2))
>> w2=exp(a2)/(1+exp(a1)+exp(a2))
>> w3=1-w1-w2
>>
>> obj =((w1^2)/(2*sqrt(exp(g1)*pi))
>> + (w2^2)/(2*sqrt(exp(g2)*pi))
>> + (w3^2)/(2*sqrt(exp(g2)*pi))
>>
>> + 2*w1*w2*d
Re: [R] How to improve the "OPTIM" results
> MORE GENERAL OPTIM ISSUES
>
> I'm considering creating a package 'optimMLE' that would automate
> some of this and package it with common 'methods' that would assume that
> sum(fn(...)) was either a log(likelihood) or the negative of a
> log(likelihood), etc. However, before I do, I need to make more
> progress on some of my other commitments, review RSiteSearch("optim",
> "fun") to make sure I'm not duplicating something that already exists,
> etc. If anyone is interested in collaborating on this, please contact
> me off-line.
>
> Hope this helps.
> Spencer
Thanks for your tips on using `optim()'. I believe `optim' is a reasonable good
implementation of numerical optimization techniques such as quasi-Newton BFGS or
conjugate gradients. Maybe methods using modern line searches or trust regions
can follow someday.
Everybody applying `optim' should be aware that it is a *Local Optimization*
(LO) approach. What you describe appears to be a step towards *Global
Optimization* (GO) in R. And indeed more and more requests in to the R-help list
are about `optim' as a tool for global optimization, not always being fully
aware of the differences.
I am wondering whether it would be more useful to provide one or two global
optimization approaches to the R community. And as this is an active research
area, there are many and with different advantages and drawbacks.
I would like to propose IPOPT as one of he newer and more advanced methods for
global optimization. This powerful software package is open source and available
through the COIN-OR initiative and its Web pages:
http://www.coin-or.org/Ipopt/documentation/
``Ipopt (Interior Point OPTimizer, pronounced I-P-Opt) is a software
package
for large-scale nonlinear optimization. Ipopt is written in C++ and is
released as open source code under the Common Public License (CPL). It is
available from the COIN-OR initiative. The code has been written by Carl
Laird (Carnegie Mellon University) and Andreas Wachter (IBM's T.J. Watson
Research Center), who is the COIN project leader for Ipopt.''
PERHAPS the COIN project would agree for IPOPT to be integrated into the open
source project R as a package. For testing it right now there is an AMPL-based
interface to IPOPT at the NEOS solver:
http://neos.mcs.anl.gov/neos/solvers/nco:Ipopt/AMPL.html
There may be other rewarding projects in the COIN-OR initiative, such as
`SYMPHONY' for solving mixed-integer linear programs (MILP, stronger than `glpk'
and `lp-solve'), or the BONMIN open source *non-linear* mixed integer
programming (MINLP) solver. I could imagine R to be a good platform for
integrating some of these algorithms.
Hans W. Borchers
Control and Optimization Group
ABB Corporate Research Germany
[EMAIL PROTECTED]
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and provide commented, minimal, self-contained, reproducible code.
Re: [R] How to improve the "OPTIM" results
try to use method "L-BFGS-B" and give boudary condition to the parameters in
use so that the algorithm search is limited to a particular region as it
seems u have to many parameters.
On Fri, 4 Apr 2008 22:10:20 -0700 (PDT) kathie wrote:
>
> Dear R users,
>
> I used to "OPTIM" to minimize the obj. function below. Even though I used
> the true parameter values as initial values, the results are not very
good.
>
> How could I improve my results? Any suggestion will be greatly
appreciated.
>
> Regards,
>
> Kathryn Lord
>
>
#---
---
>
> x = c(0.35938587, 0.34889725, 0.20577608, 0.1529, -4.24741146,
> -1.32943326,
> 0.29082527, -2.38156942, -6.62584473, -0.22596237, 6.97893687,
>! ; 0.22001081,
> -1.39729222, -5.17860124, 0.52456484, 0.46791660, 0.03065136,
> 0.32155177,
> -1.12530013, 0.02608057, -0.22323154, 3.30955460, 0.54653982,
> 0.29403011,
> 0.47769874, 2.42216260, 3.93518355, 0.23237890, 0.09647044,
> -0.48768933,
> 0.37736377, 0.43739341, -0.02416010, 4.02788119, 0.07320802,
> -0.29393054,
> 0.25184609, 0.7608, -3.34121918, 1.16028677, -0.60352008,
> -2.86454069,
> -0.84411691, 0.24841071, -0.11764954, 5.92662106, 1.03932953,
> -6.21987657,
> -0.54763352, 0.20263192) # data
>
> theta0= c(log(2),0,c(0,-.3,.3),log(c(10,.05,.05))) # initial value(In
fact,
> true parameter value)
> n = length(x)
>
> fr2 = function(theta)
> {
> a1 = theta[1]; a2 = theta[2]
> mu1 = theta[3]; mu2 = theta[4]; mu3 = theta[5]
> g1 = theta[6]; g2 = theta[7]; g3! = theta[8]
>
> w1=exp(a1)/(1+exp(a1)+exp(a2))
> w2=exp(a2)/(1+exp(a1)+exp(a2))
> w3=1-w1-w2
>
> obj =((w1^2)/(2*sqrt(exp(g1)*pi))
> + (w2^2)/(2*sqrt(exp(g2)*pi))
> + (w3^2)/(2*sqrt(exp(g2)*pi))
>
> + 2*w1*w2*dnorm((mu1-mu2)/sqrt(exp(g1)+exp(g2)))/sqrt(exp(g1)+exp(g2))
> +
> 2*w1*w3*dnorm((mu1-mu3)/sqrt(exp(g1)+exp(g3)))/sqrt(exp(g1)+exp(g3))
> +
> 2*w2*w3*dnorm((mu2-mu3)/sqrt(exp(g2)+exp(g3)))/sqrt(exp(g2)+exp(g3))
>
> - (2/n)*(sum(w1*dnorm((x-mu1)/sqrt(exp(g1)))/sqrt(exp(g1))
> + w2*dnorm((x-mu2)/sqrt(exp(g2)))/sqrt(exp(g2))
> + w3*dnorm((x-mu3)/sqrt(exp(g3)))/sqrt(exp(g3)) )))
>
> return(obj)
> }
>
> optim(theta0, fr2, method=BFGS", control = list (fnscale=10,
> parscale=c(.01,.01,.01,.01,.01,1,1,1), maxit=10))
>
> --
> View this message in context:
> http://www.nabble.com/How-to-impr!
ove-the-%22OPTIM%22-results-tp16509144p16509144.html
> Sent from the R help mailing list archive at Nabble.com.
>
> __
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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