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03_neuralnetsimple.R
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03_neuralnetsimple.R
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# neuralnetsimple.R
# Neural Network from scratch in R
# Ilia 10.04.2017
################################################
## DATA FUNCTIONS
################################################
# Return train, test lists in format for NN from input-dataframe
train_test_from_df <- function(df, predict_col_index, train_ratio,
shuffle_input = TRUE, scale_input=TRUE)
{
# Helper functions
# Function to encode factor column as N-dummies
dmy <- function(df)
{
# Select only factor columns
factor_columns <- which(sapply(df, is.factor))
if (length(factor_columns) > 0)
{
# Split factors into dummies
dmy_enc <- model.matrix(~. + 0, data=df[factor_columns],
contrasts.arg = lapply(df[factor_columns], contrasts, contrasts=FALSE))
dmy_enc <- as.data.frame(dmy_enc)
# Attach factors to df
df <- cbind(df, dmy_enc)
# Delete original columns
df[c(factor_columns)] <- NULL
}
df
}
# Function to standarise inputs to range(0, 1)
scalemax <- function(df)
{
numeric_columns <- which(sapply(df, is.numeric))
if (length(numeric_columns)){df[numeric_columns] <- lapply(df[numeric_columns], function(x){
denom <- ifelse(max(x)==0, 1, max(x))
x/denom
})}
df
}
# Function to convert df to list of rows
listfromdf <- function(df){as.list(as.data.frame(t(df)))}
# Omit NAs (allow other options later)
df <- na.omit(df)
# Get list for X-data
if (scale_input){
X_data <- listfromdf(dmy(scalemax(df[-c(predict_col_index)])))
} else {
X_data <- listfromdf(dmy(df[-c(predict_col_index)]))
}
# Get list for y-data
y_data <- listfromdf(dmy(df[c(predict_col_index)]))
# Combine X,y
all_data <- list()
for (i in 1:length(X_data)){
all_data[[i]] <- c(X_data[i], y_data[i])
}
# Shuffle before splitting
if (shuffle_input) {all_data <- sample(all_data)}
# Split to training and test
tr_n <- round(length(all_data)*train_ratio)
# Return (training, testing)
list(all_data[c(1:tr_n)], all_data[-c(1:tr_n)])
}
################################################
## MATHS FUNCTIONS
################################################
# Calculate activation function
sigmoid <- function(z){1.0/(1.0+exp(-z))}
# Partial derivative of activation function
sigmoid_prime <- function(z){sigmoid(z)*(1-sigmoid(z))}
################################################
## NN FUNCTIONS
################################################
# Cost function derivative
cost_delta <- function(method, z, a, y) {if (method=='ce'){return (a-y)}}
feedforward <- function(a, biases, weights)
{
for (f in 1:length(biases)){
a <- matrix(a, nrow=length(a), ncol=1)
b <- biases[[f]]
w <- weights[[f]]
# (py) a = sigmoid(np.dot(w, a) + b)
# Equivalent of python np.dot(w,a)
w_a <- w%*%a
# Need to manually broadcast b to conform to np.dot(w,a)
b_broadcast <- matrix(b, nrow=dim(w_a)[1], ncol=dim(w_a)[-1])
a <- sigmoid(w_a + b_broadcast)
}
a
}
get_predictions <- function(test_X, biases, weights)
{
lapply(c(1:length(test_X)), function(i) {
which.max(feedforward(test_X[[i]], biases, weights))}
)
}
evaluate <- function(testing_data, biases, weights)
{
test_X <- lapply(testing_data, function(x) x[[1]])
test_y <- lapply(testing_data, function(x) x[[2]])
pred <- get_predictions(test_X, biases, weights)
truths <- lapply(test_y, function(x) which.max(x))
# Accuracy
correct <- sum(mapply(function(x,y) x==y, pred, truths))
total <- length(testing_data)
print(correct/total)
# Confusion
res <- as.data.frame(cbind(t(as.data.frame(pred)), t(as.data.frame(truths))))
colnames(res) <- c("Prediction", "Truth")
table(as.vector(res$Prediction), as.vector(res$Truth))
}
backprop <- function(x, y, C, sizes, num_layers, biases, weights)
{
# Initialise updates with zero vectors
listw <- sizes[1:length(sizes)-1]
listb <- sizes[-1]
# Initialise updates with zero vectors (for EACH mini-batch)
nabla_b_backprop <- lapply(seq_along(listb), function(idx){
r <- listb[[idx]]
matrix(0, nrow=r, ncol=1)
})
nabla_w_backprop <- lapply(seq_along(listb), function(idx){
c <- listw[[idx]]
r <- listb[[idx]]
matrix(0, nrow=r, ncol=c)
})
# First:
# Feed-forward (get predictions)
activation <- matrix(x, nrow=length(x), ncol=1)
activations <- list(matrix(x, nrow=length(x), ncol=1))
# z = f(w.x + b)
# So need zs to store all z-vectors
zs <- list()
for (f in 1:length(biases)){
b <- biases[[f]]
w <- weights[[f]]
w_a <- w%*%activation
b_broadcast <- matrix(b, nrow=dim(w_a)[1], ncol=dim(w_a)[-1])
z <- w_a + b
zs[[f]] <- z
activation <- sigmoid(z)
activations[[f+1]] <- activation # Activations already contain one element
}
# Second:
# Backwards (update gradient using errors)
# Last layer
delta <- cost_delta(method=C, z=zs[[length(zs)]], a=activations[[length(activations)]], y=y)
nabla_b_backprop[[length(nabla_b_backprop)]] <- delta
nabla_w_backprop[[length(nabla_w_backprop)]] <- delta %*% t(activations[[length(activations)-1]])
# Second to second-to-last-layer
# If no hidden-layer reduces to multinomial logit
if (num_layers > 2) {
for (k in 2:(num_layers-1)) {
sp <- sigmoid_prime(zs[[length(zs)-(k-1)]])
delta <- (t(weights[[length(weights)-(k-2)]]) %*% delta) * sp
nabla_b_backprop[[length(nabla_b_backprop)-(k-1)]] <- delta
testyy <- t(activations[[length(activations)-k]])
nabla_w_backprop[[length(nabla_w_backprop)-(k-1)]] <- delta %*% testyy
}
}
return_nabla <- list(nabla_b_backprop, nabla_w_backprop)
return_nabla
}
update_mini_batch <- function(mini_batch, lr, C, sizes, num_layers, biases, weights)
{
nmb <- length(mini_batch)
listw <- sizes[1:length(sizes)-1]
listb <- sizes[-1]
# Initialise updates with zero vectors (for EACH mini-batch)
nabla_b <- lapply(seq_along(listb), function(idx){
r <- listb[[idx]]
matrix(0, nrow=r, ncol=1)
})
nabla_w <- lapply(seq_along(listb), function(idx){
c <- listw[[idx]]
r <- listb[[idx]]
matrix(0, nrow=r, ncol=c)
})
# Go through mini_batch
for (i in 1:nmb){
x <- mini_batch[[i]][[1]]
y <- mini_batch[[i]][[-1]]
# Back propogation will return delta
# Backprop for each obeservation in mini-batch
delta_nablas <- backprop(x, y, C, sizes, num_layers, biases, weights)
delta_nabla_b <- delta_nablas[[1]]
delta_nabla_w <- delta_nablas[[-1]]
# Add on deltas to nabla
nabla_b <- lapply(seq_along(biases),function(j)
unlist(nabla_b[[j]])+unlist(delta_nabla_b[[j]]))
nabla_w <- lapply(seq_along(weights),function(j)
unlist(nabla_w[[j]])+unlist(delta_nabla_w[[j]]))
}
# After mini-batch has finished update biases and weights:
# i.e. weights = weights - (learning-rate/numbr in batch)*nabla_weights
# Opposite direction of gradient
weights <- lapply(seq_along(weights), function(j)
unlist(weights[[j]])-(lr/nmb)*unlist(nabla_w[[j]]))
biases <- lapply(seq_along(biases), function(j)
unlist(biases[[j]])-(lr/nmb)*unlist(nabla_b[[j]]))
# Return
list(biases, weights)
}
SGD <- function(training_data, epochs, mini_batch_size, lr, C, sizes, num_layers, biases, weights,
verbose=FALSE, validation_data)
{
start.time <- Sys.time()
# Every epoch
for (j in 1:epochs){
# Stochastic mini-batch (shuffle data)
training_data <- sample(training_data)
# Partition set into mini-batches
mini_batches <- split(training_data,
ceiling(seq_along(training_data)/mini_batch_size))
# Feed forward (and back) all mini-batches
for (k in 1:length(mini_batches)) {
# Update biases and weights
res <- update_mini_batch(mini_batches[[k]], lr, C, sizes, num_layers, biases, weights)
biases <- res[[1]]
weights <- res[[-1]]
}
# Logging
if(verbose){if(j %% 1 == 0){
cat("Epoch: ", j, " complete")
# Print acc and hide confusion matrix
confusion <- evaluate(validation_data, biases, weights)
}}
}
time.taken <- Sys.time() - start.time
if(verbose){cat("Training complete in: ", time.taken)}
cat("Training complete")
# Return trained biases and weights
list(biases, weights)
}
neuralnetwork <- function(sizes, training_data, epochs, mini_batch_size, lr, C,
verbose=FALSE, validation_data=training_data)
{
num_layers <- length(sizes)
listw <- sizes[1:length(sizes)-1] # Skip last (weights from 1st to 2nd-to-last)
listb <- sizes[-1] # Skip first element (biases from 2nd to last)
# Initialise with gaussian distribution for biases and weights
biases <- lapply(seq_along(listb), function(idx){
r <- listb[[idx]]
matrix(rnorm(n=r), nrow=r, ncol=1)
})
weights <- lapply(seq_along(listb), function(idx){
c <- listw[[idx]]
r <- listb[[idx]]
matrix(rnorm(n=r*c), nrow=r, ncol=c)/sqrt(c)
})
SGD(training_data, epochs, mini_batch_size, lr, C,
sizes, num_layers, biases, weights, verbose, validation_data)
}
##################################################################################################################
## TEST HARNESSES
##################################################################################################################
##################################################################################################################
## Example MNIST - 97% Accuracy
##################################################################################################################
# Train
mnist <- read.table('https://iliadl.blob.core.windows.net/nnet/mnist_train.csv', sep=",", header = FALSE)
mnist$V1 <- factor(mnist$V1)
training_data <- train_test_from_df(df = mnist, predict_col_index = 1, train_ratio = 1)[[1]]
# Test
mnist <- read.table('https://iliadl.blob.core.windows.net/nnet/mnist_test.csv', sep=",", header = FALSE)
mnist$V1 <- factor(mnist$V1)
testing_data <- train_test_from_df(df = mnist, predict_col_index = 1, train_ratio = 1)[[1]]
# Input and output neurons
in_n <- length(training_data[[1]][[1]])
out_n <- length(training_data[[1]][[-1]])
# MNIST: 784, 100, 10 (one hidden-layer)
print("THIS WILL TAKE 20-30 MINUTES...")
trained_net <- neuralnetwork(
sizes=c(in_n, 100, out_n),
training_data=training_data,
epochs=30,
mini_batch_size=10,
lr=3,
C='ce',
verbose=TRUE,
validation_data=testing_data
)