Dear All,
I am using optim() for a relatively simple task: a linear model where
instead of minimizing the sum of the squared errors, I minimize the sum
of the squared relative errors.
However, I notice that the default algorithm is very sensitive to the
choice of the initial fit parameters, whereas I get much more stable
(and therefore better?) results with the BFGS algorithm.
I would like to have some feedback on this (perhaps I made a mistake
somewhere).
I provide a small self-contained example.
You can download a tiny data set from the link
https://www.dropbox.com/s/tmbj3os4ev3d4y8/data-instability.csv?dl=0
whereas I paste the script I am using at the end of the email.
Any feedback is really appreciated.
Many thanks
Lorenzo
################################################################
min.perc_error <- function(data, par) {
with(data, sum(((par[1]*x1 + par[2]*x2+par[3]*x3 -
y)/y)^2))
}
par_ini1 <- c(.3,.1, 1e-3)
par_ini2 <- c(1,1, 1)
data <- read.csv("data-instability.csv")
mm_def1 <-optim(par = par_ini1
, min.perc_error, data = data)
mm_bfgs1 <-optim(par = par_ini1
, min.perc_error, data = data, method="BFGS")
print("fit parameters with the default algorithms and the first seed
")
print(mm_def1$par)
print("fit parameters with the BFGS algorithms and the first seed ")
print(mm_bfgs1$par)
mm_def2 <-optim(par = par_ini2
, min.perc_error, data = data)
mm_bfgs2 <-optim(par = par_ini2
, min.perc_error, data = data, method="BFGS")
print("fit parameters with the default algorithms and the second seed
")
print(mm_def2$par)
print("fit parameters with the BFGS algorithms and the second seed ")
print(mm_bfgs2$par)
Tyipcally the parameters being optimized should be the same order of magnitude or else you can expect numerical problems. That is what the fnscale control parameter is for. On Sat, Nov 14, 2015 at 10:15 AM, Lorenzo Isella <lorenzo.isella at gmail.com> wrote:> Dear All, > I am using optim() for a relatively simple task: a linear model where > instead of minimizing the sum of the squared errors, I minimize the sum > of the squared relative errors. > However, I notice that the default algorithm is very sensitive to the > choice of the initial fit parameters, whereas I get much more stable > (and therefore better?) results with the BFGS algorithm. > I would like to have some feedback on this (perhaps I made a mistake > somewhere). > I provide a small self-contained example. > You can download a tiny data set from the link > > https://www.dropbox.com/s/tmbj3os4ev3d4y8/data-instability.csv?dl=0 > > whereas I paste the script I am using at the end of the email. > Any feedback is really appreciated. > Many thanks > > Lorenzo > > ################################################################ > > min.perc_error <- function(data, par) { > with(data, sum(((par[1]*x1 + par[2]*x2+par[3]*x3 - > y)/y)^2)) > } > > par_ini1 <- c(.3,.1, 1e-3) > > par_ini2 <- c(1,1, 1) > > > data <- read.csv("data-instability.csv") > > mm_def1 <-optim(par = par_ini1 > , min.perc_error, data = data) > > mm_bfgs1 <-optim(par = par_ini1 > , min.perc_error, data = data, method="BFGS") > > print("fit parameters with the default algorithms and the first seed > ") > print(mm_def1$par) > > print("fit parameters with the BFGS algorithms and the first seed ") > print(mm_bfgs1$par) > > > > mm_def2 <-optim(par = par_ini2 > , min.perc_error, data = data) > > mm_bfgs2 <-optim(par = par_ini2 > , min.perc_error, data = data, method="BFGS") > > > > > print("fit parameters with the default algorithms and the second seed > ") > print(mm_def2$par) > > print("fit parameters with the BFGS algorithms and the second seed ") > print(mm_bfgs2$par) > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.-- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com
I meant the parscale parameter. On Sat, Nov 14, 2015 at 10:30 AM, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:> Tyipcally the parameters being optimized should be the same order of > magnitude or else you can expect numerical problems. That is what the > fnscale control parameter is for. > > On Sat, Nov 14, 2015 at 10:15 AM, Lorenzo Isella > <lorenzo.isella at gmail.com> wrote: >> Dear All, >> I am using optim() for a relatively simple task: a linear model where >> instead of minimizing the sum of the squared errors, I minimize the sum >> of the squared relative errors. >> However, I notice that the default algorithm is very sensitive to the >> choice of the initial fit parameters, whereas I get much more stable >> (and therefore better?) results with the BFGS algorithm. >> I would like to have some feedback on this (perhaps I made a mistake >> somewhere). >> I provide a small self-contained example. >> You can download a tiny data set from the link >> >> https://www.dropbox.com/s/tmbj3os4ev3d4y8/data-instability.csv?dl=0 >> >> whereas I paste the script I am using at the end of the email. >> Any feedback is really appreciated. >> Many thanks >> >> Lorenzo >> >> ################################################################ >> >> min.perc_error <- function(data, par) { >> with(data, sum(((par[1]*x1 + par[2]*x2+par[3]*x3 - >> y)/y)^2)) >> } >> >> par_ini1 <- c(.3,.1, 1e-3) >> >> par_ini2 <- c(1,1, 1) >> >> >> data <- read.csv("data-instability.csv") >> >> mm_def1 <-optim(par = par_ini1 >> , min.perc_error, data = data) >> >> mm_bfgs1 <-optim(par = par_ini1 >> , min.perc_error, data = data, method="BFGS") >> >> print("fit parameters with the default algorithms and the first seed >> ") >> print(mm_def1$par) >> >> print("fit parameters with the BFGS algorithms and the first seed ") >> print(mm_bfgs1$par) >> >> >> >> mm_def2 <-optim(par = par_ini2 >> , min.perc_error, data = data) >> >> mm_bfgs2 <-optim(par = par_ini2 >> , min.perc_error, data = data, method="BFGS") >> >> >> >> >> print("fit parameters with the default algorithms and the second seed >> ") >> print(mm_def2$par) >> >> print("fit parameters with the BFGS algorithms and the second seed ") >> print(mm_bfgs2$par) >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. > > > > -- > Statistics & Software Consulting > GKX Group, GKX Associates Inc. > tel: 1-877-GKX-GROUP > email: ggrothendieck at gmail.com-- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com
> On 14 Nov 2015, at 16:15, Lorenzo Isella <lorenzo.isella at gmail.com> wrote: > > Dear All, > I am using optim() for a relatively simple task: a linear model where > instead of minimizing the sum of the squared errors, I minimize the sum > of the squared relative errors. > However, I notice that the default algorithm is very sensitive to the > choice of the initial fit parameters, whereas I get much more stable > (and therefore better?) results with the BFGS algorithm. > I would like to have some feedback on this (perhaps I made a mistake > somewhere). > I provide a small self-contained example. > You can download a tiny data set from the link > > https://www.dropbox.com/s/tmbj3os4ev3d4y8/data-instability.csv?dl=0 > > whereas I paste the script I am using at the end of the email. > Any feedback is really appreciated. > Many thanks >The initial parameter values for the percentage error variant are not very good. If you print min.perc_error(data,par_ini2) you can see that. Try par_ini2 <- c(1e-4,1e-4,1e-4) and you'll get results that are closer to each other. The rest is up to you. Berend> Lorenzo > > ################################################################ > > min.perc_error <- function(data, par) { > with(data, sum(((par[1]*x1 + par[2]*x2+par[3]*x3 - > y)/y)^2)) > } > > par_ini1 <- c(.3,.1, 1e-3) > > par_ini2 <- c(1,1, 1) > > > data <- read.csv("data-instability.csv") > > mm_def1 <-optim(par = par_ini1 > , min.perc_error, data = data) > > mm_bfgs1 <-optim(par = par_ini1 > , min.perc_error, data = data, method="BFGS") > > print("fit parameters with the default algorithms and the first seed > ") > print(mm_def1$par) > > print("fit parameters with the BFGS algorithms and the first seed ") > print(mm_bfgs1$par) > > > > mm_def2 <-optim(par = par_ini2 > , min.perc_error, data = data) > > mm_bfgs2 <-optim(par = par_ini2 > , min.perc_error, data = data, method="BFGS") > > > > > print("fit parameters with the default algorithms and the second seed > ") > print(mm_def2$par) > > print("fit parameters with the BFGS algorithms and the second seed ") > print(mm_bfgs2$par) > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.
> On 14 Nov 2015, at 17:02, Berend Hasselman <bhh at xs4all.nl> wrote: > >> >> On 14 Nov 2015, at 16:15, Lorenzo Isella <lorenzo.isella at gmail.com> wrote: >> >> Dear All, >> I am using optim() for a relatively simple task: a linear model where >> instead of minimizing the sum of the squared errors, I minimize the sum >> of the squared relative errors. >> However, I notice that the default algorithm is very sensitive to the >> choice of the initial fit parameters, whereas I get much more stable >> (and therefore better?) results with the BFGS algorithm. >> I would like to have some feedback on this (perhaps I made a mistake >> somewhere). >> I provide a small self-contained example. >> You can download a tiny data set from the link >> >> https://www.dropbox.com/s/tmbj3os4ev3d4y8/data-instability.csv?dl=0 >> >> whereas I paste the script I am using at the end of the email. >> Any feedback is really appreciated. >> Many thanks >> > > The initial parameter values for the percentage error variant are not very good. > If you print min.perc_error(data,par_ini2) you can see that. > > Try > > par_ini2 <- c(1e-4,1e-4,1e-4) > > and you'll get results that are closer to each other. > The rest is up to you.Try this at the end of your script: # Original min.perc_error(data,par_ini2) # Much better par_ini3 <- c(1e-4,1e-4,1e-4) min.perc_error(data,par_ini3) mm_def3 <-optim(par = par_ini3 , min.perc_error, data = data) mm_bfgs3 <-optim(par = par_ini3 , min.perc_error, data = data, method="BFGS") print("fit parameters with the default algorithms and the second seed ") print(mm_def3$par) min.perc_error(data,mm_def3$par) print("fit parameters with the BFGS algorithms and the second seed ") print(mm_bfgs3$par) min.perc_error(data,mm_bfgs3$par) and rejoice! Berend