ml_fund_1.R

library(modelr)
library(dplyr)
library(ggplot2)
library(animation)
library(gganimate)

options(scipen = 999)

n     <- 200 # number of observations
bias  <- 4
slope <- 3.5
dot   <- `%*%` # defined for personal preference 

x   <- rnorm(n) * 2
x_b <- cbind(x, rep(1, n))
y   <- bias + slope * x + rnorm(n)
df  <- data_frame(x = x,  y = y)

learning_rate <- 0.05
n_iterations  <- 100
theta         <- matrix(c(20, 20))

b0    <- vector("numeric", length = n_iterations)
b1    <- vector("numeric", length = n_iterations)
sse_i <- vector("numeric", length = n_iterations)

for (iteration in seq_len(n_iterations)) { 
  
  residuals_b        <- dot(x_b, theta) - y
  gradients          <- 2/n * dot(t(x_b), residuals_b)
  theta              <- theta - learning_rate * gradients
  
  sse_i[[iteration]] <- sum((y - dot(x_b, theta))**2)
  b0[[iteration]]    <- theta[2]
  b1[[iteration]]    <- theta[1]
  
}

model_i <- data.frame(model_iter = 1:n_iterations, 
                      sse = sse_i, 
                      b0 = b0, 
                      b1 = b1)

model_i$affine <- model_iter

p1 <- df %>% 
  ggplot(aes(x=x, y=y)) + 
  geom_abline(aes(intercept = b0, 
                  slope = b1, 
                  colour = -sse, 
                  frame = model_iter), 
              data = model_i, 
              alpha = .50 
  ) +
  geom_point(alpha = 0.4) + 
  geom_abline(aes(intercept = b0, 
                  slope = b1), 
              data = model_i[100, ], 
              alpha = 0.5, 
              size = 2, 
              colour = "dodger blue") +
  geom_abline(aes(intercept = b0, 
                  slope = b1),
              data = model_i[1, ],
              colour = "red", 
              alpha = 0.5,
              size = 2) + 
  scale_color_continuous(low = "red", high = "grey") +
  guides(colour = FALSE) +
  theme_minimal()

p_gif <- df  %>% 
  ggplot(aes(x=x, y=y)) + 
  geom_abline(aes(intercept = b0, 
                  slope = b1, 
                  colour = -sse, 
                  frame = model_iter), 
              data = model_i[1:30, ], 
              alpha = .50, 
              size = 2
  ) +
  geom_point(alpha = 0.4) + 
  scale_color_continuous(low = "red", high = "dodger blue")

library(gganimate)
gganimate(p_gif, interval = 0.2, "lr_output.gif")

p2 <- model_i[1:30,] %>%
  ggplot(aes(model_iter, sse, colour = -sse)) + 
  geom_point(alpha = 0.4) +
  theme_minimal() +
  labs(x = "Model iteration", 
       y = "Sum of Sqaured errors") + 
  scale_color_continuous(low = "red", high = "dodger blue") +
  guides(colour = FALSE)