Posted on December 6, 2019 by matsukat

広域システム特別講義II 教師あり学習1B

train.x = as.matrix(iris[,1:4])
train.y.temp = as.numeric(iris[,5])
train.y = matrix(0,nrow = nrow(train.x), ncol =3)
train.y[which(train.y.temp==1), 1]=1
train.y[which(train.y.temp==2), 2]=1
train.y[which(train.y.temp==3), 3]=1

init.network <- function(n.neurons){
  n.layer = length(n.neurons)
  W = list(); b = list()
  for (i.layer in 1:(n.layer-1)){
    W[[i.layer]] =
      matrix(rnorm(n.neurons[i.layer]*n.neurons[(i.layer+1)],sd = 0.1),nrow=n.neurons[i.layer])
    b[[i.layer]] =  matrix(rnorm(n.neurons[(i.layer+1)],sd = 0.1), nrow = 1)
  }
  return(list(W = W,b = b))
}

sigmoid.forwd <- function(x){
  return(1/(1+exp(-x)))
}

sigmoid.bckwd <- function(x, dout){
  y = sigmoid.forwd(x)
  return(dout*(1-y)*y)
}

affine.forwd <- function(x, W, b){
  return(x%*%W + matrix(1, nrow = nrow(x), ncol = 1)%*%b)
}

affine.bckwd <- function(x, W, b, dout){
  dx = dout%*%t(W)
  dW = t(x)%*%dout
  db = colSums(dout)
  return(list(dx = dx, dW = dW, db = db))
}

softmax.forwd <- function(x, target){
  max.x = apply(x,1,max)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  delta = 1e-7;
  R = nrow(as.matrix(y))
  return(-sum(target*log(y + delta))/R)
}

softmax.bckwd <- function(x, target,  dout = 1){
  max.x = apply(x, 1, max)
  R = nrow(x)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  return((y-target)/R)
}

params = init.network(c(4,15,3))
batch_size = 50; n.iter =5000; lambda =0.05
n.train = nrow(train.x)
loss = rep(0,n.iter)
for (i.iter in 1:n.iter){
  batch_mask = sample(1:n.train, batch_size)
  x.batch = train.x[batch_mask,]
  t.batch = train.y[batch_mask,]
  a1 = affine.forwd(x.batch,params$W[[1]],params$b[[1]])
  z1 = sigmoid.forwd(a1)
  a2 = affine.forwd(z1,params$W[[2]],params$b[[2]])
  z2 = softmax.forwd(a2,t.batch)
  loss[i.iter] = z2
  dwSM = softmax.bckwd(a2, t.batch, 1)
  dwA2 = affine.bckwd(a1,params$W[[2]],params$b[[2]],dwSM)
  dwSG = sigmoid.bckwd(a1,dwA2$dx)
  dwA1 = affine.bckwd(x.batch,params$W[[1]],params$b[[1]],dwSG)
  params$W[[2]] = params$W[[2]] - lambda*dwA2$dW
  params$b[[2]] = params$b[[2]] - lambda*dwA2$db
  params$W[[1]] = params$W[[1]] - lambda*dwA1$dW
  params$b[[1]] = params$b[[1]] - lambda*dwA1$db
}
loss.dat = data.frame(trial = 1:length(loss), loss = loss)
ggplot(loss.dat,aes(x = trial, y = loss)) +
  geom_smooth(se=F)

### methods to improve effeciency
func02R = function(x){
  return(1/20*x[1]^2 + x[2]^2)
}
numerical.grad <- function(func, x){
  h = 1e-4
  R = nrow(x)
  C = ncol(x)
  grad = matrix(0, R, C)
  for (i.col in 1:C){
    for (i.row in 1:R){
      temp.x = x[i.row,i.col]
      x[i.row, i.col] = temp.x + h
      plusH = do.call(func, list(x))
      x[i.row, i.col] = temp.x - h
      minusH = do.call(func,list(x))
      grad[i.row, i.col] = (plusH - minusH)/(2*h)
      x[i.row, i.col] = temp.x
    }
  }
  return(grad)
}

require(plot3D)
x = seq(-10,10,0.5)
y = seq(-10,10,0.5)
M = mesh(x,y)
R = nrow(M$x)
C = nrow(M$x)
scaling = 0.05
plot(c(),c(),xlim = c(-10,10),ylim=c(-10,10))
for (i.col in 1:C){
  for (i.row in 1:R){
    ng = numerical.grad("func02R",matrix(c(M$x[i.row,i.col],M$y[i.row,i.col]),nrow=1))
    arrows(M$x[i.row,i.col],M$y[i.row,i.col],
           (M$x[i.row,i.col]-ng[1]*scaling),(M$y[i.row,i.col]-ng[2]*scaling),
           length = 0.05)
  }
}

x = seq(-10,10,0.2)
y = seq(-10,10,0.2)
M = mesh(x,y)
Z = as.vector(1/20*M$x^2)+as.vector(M$y^2)
Z.mesh = matrix(Z,nrow(M$x))
contour(x,y,Z.mesh,drawlabels = F,nlevels=40)

grad.desc <- function(func, init.x, lr, n.iter){
  x = init.x
  x.hist = init.x
  for (i.iter in 1:n.iter) {
    grad = numerical.grad(func, x)
    x = x - lr*grad
    x.hist = rbind(x.hist,x)
  }
  return(x.hist)
}
x.init = matrix(c(-7,2),nrow = 1)
gd = grad.desc("func02R",x.init,0.9,100)
lines(gd,type='o',col = 'green',pch=20)

gd.moment <- function(func, init.x, lr, moment, n.iter){
  x = init.x
  x.hist = init.x
  grad.hist = rep(0,length(x))
  for (i.iter in 1:n.iter) {
    grad = numerical.grad(func, x)
    x = x - lr*grad+moment*grad.hist
    x.hist = rbind(x.hist,x)
    grad.hist = -lr*grad
  }
  return(x.hist)
}
x.init = matrix(c(-7,2),nrow = 1)
gdm = gd.moment("func02R",x.init,0.9,0.3,100)
lines(gdm,type='o',col = 'blue',pch=20)

adaGrad <- function(func, init.x, eta, n.iter){
  x = init.x
  x.hist = init.x
  h = rep(0,length(x))
  for (i.iter in 1:n.iter) {
    grad = numerical.grad(func, x)
    h = h + grad*grad
    x = x - eta*(1/(sqrt(h)+1e-7))*grad
    x.hist = rbind(x.hist,x)
  }
  return(x.hist)
}
x.init = matrix(c(-7,2),nrow = 1)
adaGrad = adaGrad("func02R",x.init,0.9,100)
contour(x,y,Z.mesh,drawlabels = F,nlevels=40)
lines(adaGrad,type='o',col = 'red',pch=20)


adam <- function(func, init.x, eta, beta1, beta2, epsilon, n.iter){
  x = init.x
  x.hist = init.x
  m = rep(0,length(x))
  v = rep(0,length(x))
  for (i.iter in 1:n.iter) {
    grad = numerical.grad(func, x)
    m = beta1*m + (1-beta1)*grad
    v = beta2*v + (1-beta2)*grad*grad
    m.hat = m/(1-beta1)
    v.hat = v/(1-beta2)
    x = x - eta/((sqrt(v.hat)+epsilon))*m.hat
    x.hist = rbind(x.hist,x)
  }
  return(x.hist)
}
x.init = matrix(c(-7,2),nrow = 1)
adam = adam("func02R",x.init,0.2,0.9,0.999,1e-8,100)
contour(x,y,Z.mesh,drawlabels = F,nlevels=40)
lines(adam,type='o',col = 'red',pch=20)

### w/ functions
relu.forwd <- function(x){
  return(pmax(x,0))
}
relu.bckwd <- function(z, dout){
  dout[which(z <= 0)] = 0
  return(dout)
}
# sigmoid
sigmoid.forwd <- function(x){
  return(1/(1+exp(-x)))
}
sigmoid.bckwd <- function(z, dout){
  return(dout*(1-z)*z)
}
# Affine
affine.forwd <- function(x, W, b){
  return(x%*%W + matrix(1, nrow = nrow(x), ncol = 1)%*%b)
}
affine.bckwd <- function(x, W, dout){
  dx = dout%*%t(W)
  dW = t(x)%*%dout
  db = colSums(dout)
  return(list(dx = dx, dW = dW, db = db))
}
# softmax with CE
softmax.forwd <- function(x, target){
  max.x = apply(x,1,max)
  C = ncol(x)
  x = x - max.x%*%matrix(1,nrow=1,ncol=C)
  y = exp(x)/rowSums(exp(x))
  delta = 1e-7;
  R = nrow(as.matrix(y))
  return(list(smx = y, ce = -sum(target*log(y + delta))/R))
}
softmax.bckwd <- function(smx, target){
  R = nrow(smx)
  return((smx-target)/R)
}

activation <- function(A, target, actFun){
  if (actFun == "sigmoid"){
    return(sigmoid.forwd(A))
  }
  if (actFun == "relu"){
    return(relu.forwd(A))
  }
  if (actFun == "softmax"){
    return(softmax.forwd(A, target))
  }
}

Dact <- function(z, smx, target, dout, actFun){
  if (actFun == "sigmoid"){
    return(sigmoid.bckwd(z, dout))
  }
  if (actFun == "relu"){
    return(relu.bckwd(z, dout))
  }
  if (actFun == "softmax"){
    return(softmax.bckwd(smx, target))
  }
}

# function for initialization
init.network <- function(n.neurons, actFun, Opt, sdv){
  n.layer = length(n.neurons)
  W = list(); b = list();
  mW = list(); mb = list();    # momentum
  hW = list(); hb = list();    # adaGrad
  aMW = list(); aMb = list();  # adam M
  aVW = list(); aVb = list();  # adam V
  for (i.layer in 1:(n.layer-1)){
    if (nargs() == 3) {
      if (actFun[i.layer]=="sigmoid"){
        # Xavier
        sdv = 1/sqrt(n.neurons[i.layer])
      } else {
        # He - assumes ReLU
        sdv = sqrt(2/n.neurons[i.layer])
      }
    }
    W[[i.layer]] = matrix(rnorm(n.neurons[i.layer]*n.neurons[(i.layer+1)], sd = sdv),
                          nrow=n.neurons[i.layer])
    b[[i.layer]] =  matrix(rnorm(n.neurons[(i.layer+1)], sd = sdv), nrow = 1)
    if (Opt == "momentum"){
      mW[[i.layer]] = matrix(0, nrow=n.neurons[i.layer], ncol=n.neurons[(i.layer+1)])
      mb[[i.layer]] = matrix(0, nrow = 1, ncol=n.neurons[(i.layer+1)])
    }
    if (Opt == "adagrad"){
      hW[[i.layer]] = matrix(0, nrow=n.neurons[i.layer], ncol=n.neurons[(i.layer+1)])
      hb[[i.layer]] = matrix(0, nrow = 1, ncol=n.neurons[(i.layer+1)])
    }
    if (Opt == "adam"){
      aMW[[i.layer]] = matrix(0, nrow=n.neurons[i.layer], ncol=n.neurons[(i.layer+1)])
      aMb[[i.layer]] = matrix(0, nrow = 1, ncol=n.neurons[(i.layer+1)])
      aVW[[i.layer]] = matrix(0, nrow=n.neurons[i.layer], ncol=n.neurons[(i.layer+1)])
      aVb[[i.layer]] = matrix(0, nrow = 1, ncol=n.neurons[(i.layer+1)])
    }
  }
  return(list(W = W, b = b, actFun = actFun, optimizer = Opt,
              mW=mW, mb=mb,
              hW=hW, hb=hb,
              aMW=aMW,aMb=aMb,aVW=aVW))
}

OPT<-function(net, Daff, HP){
  if (net$optimizer == "momentum"){
    return(Opt.mom(net, Daff, HP))
  }
  if (net$optimizer == "adagrad"){
    return(Opt.adagrad(net, Daff, HP))
  }
  if (net$optimizer == "adam"){
    return(Opt.adam(net, Daff, HP))
  }
}

Opt.mom <- function(net, Daff, HP) {
  # HP[3] = learning rate
  # HP[4] = weight decay
  # HP[5] = momentum
  n.layer <- length(net$W)
  for (i.layer in 1:n.layer) {
    net$mW[[i.layer]] = HP[5]*net$mW[[i.layer]] - HP[3]*Daff[[i.layer]]$dW - HP[4]*net$W[[i.layer]]
    net$mb[[i.layer]] = HP[5]*net$mb[[i.layer]] - HP[3]*Daff[[i.layer]]$db - HP[4]*net$b[[i.layer]]
    net$W[[i.layer]] = net$W[[i.layer]] + net$mW[[i.layer]]
    net$b[[i.layer]] = net$b[[i.layer]] + net$mb[[i.layer]]
  }
  return(net=net)
}

Opt.adagrad <- function(net, Daff, HP) {
  # HP[3] = learning rate
  # HP[4] = weight decay
  n.layer <- length(net$W)
  for (i.layer in 1:n.layer) {
    net$hW[[i.layer]] = net$hW[[i.layer]] + Daff[[i.layer]]$dW*Daff[[i.layer]]$dW
    net$hb[[i.layer]] = net$hb[[i.layer]] + Daff[[i.layer]]$db*Daff[[i.layer]]$db
    net$W[[i.layer]] = net$W[[i.layer]]-HP[3]/(sqrt(net$hW[[i.layer]])+1e-7)*Daff[[i.layer]]$dW - HP[4]*net$W[[i.layer]]
    net$b[[i.layer]] = net$b[[i.layer]]-HP[3]/(sqrt(net$hb[[i.layer]])++1e-7)*Daff[[i.layer]]$db - HP[4]*net$b[[i.layer]]
  }
  return(net=net)
}
cu.nnet = function(train.x, train.y, net, HP = c(10,1000,0.05,0.01,0.1,0.999,0.9)){
  # HP: Hyperparameters
  # HP[1] = batch size
  # HP[2] = n iteration
  # HP[3] = learning rate
  # HP[4] = weight decay
  # HP[5] = momentum
  # HP[6] = beta1 (adam)
  # HP[7] = beta2 (adam)
  n.layer <- length(net$W)
  loss = rep(0,HP[2])
  A = list(); z = list(); Dact = list(); Daff = list()
  for (i.iter in 1:HP[2]){
    batch_mask = sample(1:nrow(train.x), HP[1])
    x.batch = train.x[batch_mask,]
    t.batch = train.y[batch_mask,]
    for (i.layer in 1:n.layer){
      if (i.layer == 1){
        x = x.batch
      } else {
        x = z[[(i.layer - 1)]]
      }
      A[[i.layer]] = affine.forwd(x, net$W[[i.layer]], net$b[[i.layer]])
      z[[i.layer]] = activation(A[[i.layer]], t.batch, net$actFun[i.layer])
    }
    loss[i.iter] = z[[i.layer]]$ce
    smx = z[[i.layer]]$smx
    for (i.layerR in n.layer:1){
      if (i.layerR == n.layer){
        dout = 1
      } else {
        dout = Daff[[(i.layerR+1)]]$dx
      }
      Dact[[i.layerR]] = Dact(z[[i.layerR]], smx, t.batch, dout, net$actFun[i.layerR])
      if (i.layerR==1){
        x = x.batch
      } else {
        x = A[[(i.layerR-1)]]
      }
      Daff[[i.layerR]] = affine.bckwd(x, net$W[[i.layerR]], Dact[[i.layerR]])
    }
    net = OPT(net, Daff, HP)
  }
  return(list(loss = loss, net = net))
}

train.x = as.matrix(iris[,1:4])
train.y.temp = as.numeric(iris[,5])
train.y = matrix(0,nrow = nrow(train.x), ncol =3)
train.y[which(train.y.temp==1), 1]=1
train.y[which(train.y.temp==2), 2]=1
train.y[which(train.y.temp==3), 3]=1
actF = c("relu","softmax")
network = init.network(c(4,15,3), actF, "momentum")
res = cu.nnet(train.x, train.y, network, HP=c(15,1000,0.01,0.0001,0.9,0.999,0.9))
hist(res$net$W[[1]])
plot(res$loss,type='l')

MNIST.dat<-read.csv("http://www.matsuka.info/univ/course_folder/MNSTtrain.csv")

train <- data.matrix(MNIST.dat)
train.x <- as.matrix(train[,-1]/255)
train.y.temp <- train[,1]
train.y = matrix(0,nrow = nrow(train), ncol = 10)
for (i in 1:nrow(train.x)){
  train.y[i,(train.y.temp[i]+1)]=1
}
actF = c("relu","relu","softmax")
network = init.network(c(784,100,50,10), actF, "momentum")
res = cu.nnet(train.x, train.y, network,HP=c(100,2000,0.1,0.001,0.8,0.999,0.9))
plot(res$loss,type='l')

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