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Similar to Optimization In R (6)
Optimization In R
- 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
- 14. •
Tsukuba.R
•
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
- 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
