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![> f <- function (x) (x - 1 / 3)^2
> (xmin <- optimize(f, c(0, 1), tol =
0.0001)
$minimum
[1] 0.3333333
$objective
[1] 0
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-20-320.jpg)
![R
•
•R
log_likelihood_for_norm <- function(x){
return(function(par){
mu <- par[1]
sigma2 <- par[2]
- length(x) / 2 * log(sigma2) - 1 / 2 *
sum((x - mu)^2) / sigma2
})
(x) μ σ
}
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-22-320.jpg)
![: sapply&rapply
> invisible(sapply(1:3, function(x) { cat("x
is", x, fill=TRUE) }))
x is 1
x is 2
x is 3
> rapply(list(list(c("a", "b"), list(1:10)),
matrix(1:10, 2, 5)),
+ function(x) {
+ class(x)
+ }
+ )
[1] "character" "integer" "matrix"
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-24-320.jpg)
![R
•
•R
log_likelihood_for_norm <- function(x){
return(function(par){
mu <- par[1]
sigma2 <- par[2]
- length(x) / 2 * log(sigma2) - 1 / 2 *
sum((x - mu)^2) / sigma2
})
(x) μ σ
}
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-25-320.jpg)
![optim
•
=> cars$speed
> optim(par = c(5, 10), fn = log_likelihood_for_norm(cars$speed),
control = list(fnscale = -1))
$par
[1] 15.39812 27.40184 ( )
$value
[1] -107.7636
$counts
function gradient
75 NA
optim
$convergence
fnscale=-1
[1] 0
$message
NULL
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-26-320.jpg)
![?
> optim(par = c(5, 10), fn = log_likelihood_for_norm(cars$speed),
control = list(fnscale = -1))
$par
[1] 15.39812 27.40184
$value
[1] -107.7636
> mean(cars$speed)
[1] 15.4
$counts
> var(cars$speed)
function gradient
[1] 27.95918
75 NA
$convergence
[1] 0 !!
$message
NULL
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-27-320.jpg)
![!!
result <- lm(dist~speed, data=cars)
plot(cars)
coef <- result$coef
abline(coef[1], coef[2], col="red")
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-28-320.jpg)
![> obj_func <- function(x, y) {
+ function(par) {
+ a <- par[1]; b <- par[2]
+ sum((y - (a + b * x))^2)
+ }
+ }
>
> result <- optim(par = c(0, 5),
fn = obj_func(cars$speed, cars
$dist))
> result$par
[1] -17.579625 3.932217
> lm(dist~speed, data=cars)$coef
(Intercept) speed
!!
-17.579095 3.932409
Saturday, March 27, 2010](https://image.slidesharecdn.com/optimizationinr-100326145028-phpapp01/85/Optimization-In-R-29-320.jpg)
Optimization In R
- 1. Optimization in R id:syou6162 Saturday, March 27, 2010
- 2. Agenda • • GSoC Tsukuba.R • Optimization in R(R ) • • R • Saturday, March 27, 2010
- 3. • (id:syou6162 @syou6162) • http://syou6162.sakura.ne.jp/ • => • & Saturday, March 27, 2010
- 4. Google Summer of Code • 3/29 • NoSQL interface for R • Dirk Eddelbuettel • Saturday, March 27, 2010
- 5. Tsukuba.R • ( ) R • R • (Tokyo Osaka Nagoya) • 2008 7 #6 Saturday, March 27, 2010
- 6. (1) • • plot • • R • • apply family • ggplot2 animation Saturday, March 27, 2010
- 7. (2) • • R C • openCV C R • R • • Twitter Saturday, March 27, 2010
- 8.
- 9.
- 10.
- 11.
- 12.
- 13.
- 14. • Tsukuba.R • Saturday, March 27, 2010
- 15. Optimization in R id:syou6162 Saturday, March 27, 2010
- 16. R • 2 !! • optim optimize • optim optimize 1 • ? Saturday, March 27, 2010
- 17. ? •R • => !! • • ? Saturday, March 27, 2010
- 18. : (= ) !! http://ja.wikipedia.org/wiki/ Saturday, March 27, 2010
- 19. • ( ) • • • !! Saturday, March 27, 2010
- 20. > f <-function (x) (x - 1 / 3)^2 > (xmin <- optimize(f, c(0, 1), tol = 0.0001) $minimum [1] 0.3333333 $objective [1] 0 Saturday, March 27, 2010
- 21. • • • ( ) • Saturday, March 27, 2010
- 22. R • •R log_likelihood_for_norm <- function(x){ return(function(par){ mu <- par[1] sigma2 <- par[2] - length(x) / 2 * log(sigma2) - 1 / 2 * sum((x - mu)^2) / sigma2 }) (x) μ σ } Saturday, March 27, 2010
- 23. : •R • • •R : apply family • apply tapply sapply mapply rapply eapply lapply Saturday, March 27, 2010
- 24. : sapply&rapply > invisible(sapply(1:3, function(x) { cat("x is", x, fill=TRUE) })) x is 1 x is 2 x is 3 > rapply(list(list(c("a", "b"), list(1:10)), matrix(1:10, 2, 5)), + function(x) { + class(x) + } + ) [1] "character" "integer" "matrix" Saturday, March 27, 2010
- 25. R • •R log_likelihood_for_norm <- function(x){ return(function(par){ mu <- par[1] sigma2 <- par[2] - length(x) / 2 * log(sigma2) - 1 / 2 * sum((x - mu)^2) / sigma2 }) (x) μ σ } Saturday, March 27, 2010
- 26. optim • => cars$speed > optim(par = c(5, 10), fn = log_likelihood_for_norm(cars$speed), control = list(fnscale = -1)) $par [1] 15.39812 27.40184 ( ) $value [1] -107.7636 $counts function gradient 75 NA optim $convergence fnscale=-1 [1] 0 $message NULL Saturday, March 27, 2010
- 27. ? > optim(par = c(5, 10), fn = log_likelihood_for_norm(cars$speed), control = list(fnscale = -1)) $par [1] 15.39812 27.40184 $value [1] -107.7636 > mean(cars$speed) [1] 15.4 $counts > var(cars$speed) function gradient [1] 27.95918 75 NA $convergence [1] 0 !! $message NULL Saturday, March 27, 2010
- 28. !! result <- lm(dist~speed, data=cars) plot(cars) coef <- result$coef abline(coef[1], coef[2], col="red") Saturday, March 27, 2010
- 29. > obj_func <-function(x, y) { + function(par) { + a <- par[1]; b <- par[2] + sum((y - (a + b * x))^2) + } + } > > result <- optim(par = c(0, 5), fn = obj_func(cars$speed, cars $dist)) > result$par [1] -17.579625 3.932217 > lm(dist~speed, data=cars)$coef (Intercept) speed !! -17.579095 3.932409 Saturday, March 27, 2010
- 30. ... • optim method • CG SANN B BFGS Nelder-Mead L-BFGS- • Saturday, March 27, 2010
- 31. CG( ) • • 2 • • n 2 n • CG • http://ja.wikipedia.org/wiki/ Saturday, March 27, 2010
- 32. BFGS • <= • => 2 => • • => 2 ( ) • • Saturday, March 27, 2010
- 33. Nelder-Mead • N N+1 • • • • http://ibisforest.org/index.php?Nelder-Mead Saturday, March 27, 2010
- 34. Nelder-Mead optim (method ) Saturday, March 27, 2010
- 35. R • optim • etc • Nelder-Mead SANN • BFGS CG Saturday, March 27, 2010
- 36.
- 37. R ? • • • C C++ • Tsukuba.R#4 • http://d.hatena.ne.jp/ syou6162/20090301/1235890688 Saturday, March 27, 2010
- 38. ? • CG BFGS • ( ) • optim • Saturday, March 27, 2010
- 39. • • Writing R Extentions !! Saturday, March 27, 2010
- 40. • • GSoC Tsukuba.R • Optimization in R(R ) • • R • Saturday, March 27, 2010