COMMunication
RESearch.NET

# the above no gradient

gradient <- function(x, v){
    residuals = x - v
    # y = (sum(x-v)^2)/n 혹은 (mean(x-v)^2) 
    # 의 식이 ms값을 구하는 식인데 
    # 이를 v에 대해서 미분하면 chain rule을 써야 한다
    # 자세한 것은 http://commres.net/wiki/estimated_standard_deviation
    # 문서 중에 미분 부분 참조
    # dy/dv = ( 2(x-v)*-1 ) / n chain rule
    # dy/dv = -2 (x-v) / n = -2 (mean(residual)) 
    dx = -2 * mean(residuals)
    # return(list("ds" = dx))
    return(dx)
} # function returns ds value

zx <- (x-mean(x))/sd(x)
# pick one random v in (x-v)
v <- rnorm(1)

# Train the model with scaled features
learning.rate = 1e-1

msrs <- c()
vs <- c()

msr <- function(x, v) {
    residuals <- (x - v)
    return((mean(residuals^2)))
}

nlen <- 75
for (epoch in 1:nlen) {
    residual <- residuals(zx, v)
    msr.x <- msr(zx, v)
    msrs <- append(msrs, msr.x)
    
    grad <- gradient(zx, v)
    step.v <- grad * learning.rate # 
    v <- v - step.v # 그 다음 v값
    vs <- append(vs, v) # v값 저장
}

tail(msrs)
tail(vs)

plot(vs, msrs, type='b')

# scaled
vs # 변화하는 v 값들의 집합 
vs.orig <- (vs*sd(x))+mean(x) 
vs.orig

# 마지막 v값이 최소값에 근접한 값
v 
v.orig <- (v*sd(x))+mean(x) 
v.orig

plot(vs.orig, msrs, type='b')