Concept02_poly_regression.md

Ch 03: Concept 02

Polynomial regression

Import the relevant libraries and initialize the hyper-parameters

library(tensorflow)

learning_rate <- 0.01
training_epochs <- 40

Set up some fake raw input data

trX <- seq.int(-1, 1, length.out = 101)

Set up raw output data based on a degree 6 polynomial

num_coeffs <- 6
trY_coeffs <- c(1, 2, 3, 4, 5, 6)
trY <- 0
for(i in 1:num_coeffs){
    trY <- trY + trY_coeffs[i] * trX^(i-1)
}

Add some noise

trY <- trY +rnorm(length(trX), mean = 0, sd=1.3) * 1.5

Plot the raw data

plot(trX, trY)

X <- tf$placeholder("float")
Y <- tf$placeholder("float")

Define our polynomial model

model <- function(X, w){
    terms <- list()
    for(i in 0:(num_coeffs-1)){
        term <- tf$multiply(w[i], tf$pow(X, i))
        terms[[i+1]] <- term 
    }
    return(tf$add_n(terms))
}

Set up the parameter vector to all zero

w <- tf$Variable(tf$zeros(num_coeffs,dtype = 'float'), name="parameters")
y_model <- model(X, w)

Define the cost function just as before

cost <- tf$reduce_sum(tf$square(Y-y_model))
train_op <- tf$train$GradientDescentOptimizer(learning_rate)$minimize(cost)

Set up the session and run the learning algorithm just as before

sess <- tf$Session()
init <- tf$global_variables_initializer()
sess$run(init)

for(epoch in 1:training_epochs){
    for(i in 1:length(trX)){
        sess$run(train_op, feed_dict=dict(X= trX[i], Y= trY[i]))
    }
}

w_val <- sess$run(w)
print(w_val)

## [1] 0.9349267 1.1665890 4.3310685 4.6033034 3.7153454 5.1843162

Close the session when done

sess$close()

Plot the result

plot(trX, trY)
trY2 <- 0
for(i in 1:num_coeffs){
    trY2 <- trY2 + w_val[i] * trX^(i-1)
}
lines(trX, trY2, col='red')