Gradient descent in R (using the cost function)

GradientDescent.r

assertThat  <- function(actualValue, expectedValue) {
  if (as.character(actualValue) == as.character(expectedValue)) {
    print("TEST PASSED: actual and expected values match.")
  } else {
    print("TEST FAILED: actual and expected values do not match.")
  }
}

is         <- function(value) {
  return(value)
}

equalTo    <- is

source('./supportingFunctions.r')

houseSizes  <- c( 2104,  1416,  1534,  852)      ## x
housePrices <- c(460000, 232000, 315000, 178000) ## y

houseSizes  <- c( 2,  3,  4,  5) ## x
housePrices <- c( 1,  2,  3,  4) ## y

theta0      <- 0 ### expected 50
theta1      <- 0  ### expected 0.06
ZERO        <- 0

numberOfItemsInTheTrainingSet <- function(inTrainingSet) {
  return(length(inTrainingSet))
}



#
# Cost function: Linear regression model
#
#  hypothesis: h_thetaOf_x = theta0 + (theta1 * x)
#  parameters: theta0, theta1
#  J_of_theta0_theta1 = (1 / 2m) * sumOf(1..m)Of(h_thetaOf_x_i - y_i) square
#

costFunctionHypothesis  <- function(inTheta0, inTheta1, inX) {
  h_theta_Of_x <- (inTheta0 + (inTheta1 * inX))
  return(h_theta_Of_x)  
}

costFunction <- function(inTheta0, inTheta1, inX, inY) {
  m          <- numberOfItemsInTheTrainingSet(inX)  
  partA      <- 1 / (2 * m)
  
  result     <- 0
  for(i in c(1: m)) {
    x        <- inX[i]
    y        <- inY[i]
    partB    <- (costFunctionHypothesis(inTheta0, inTheta1, x) - y)
    result   <- result + (partB ^ 2)
  }
  
  result   <- partA * result
  return(result)
}

derivativeOfCostFunctionTheta0 <- function(inTheta0, inTheta1, inX, inY) {
  m        <- numberOfItemsInTheTrainingSet(inX)  
  partA    <- 1 / m  

  result <- 0
  for(i in c(1: m)) {
    x <- inX[i]
    y <- inY[i]
    partB    <- (costFunctionHypothesis(inTheta0, inTheta1, x) - y)
    result   <- result + partB
  }
  
  result   <- partA * result
  return(result)
}

derivativeOfCostFunctionTheta1 <- function(inTheta0, inTheta1, inX, inY) {
  m        <- numberOfItemsInTheTrainingSet(inX)  
  partA    <- 1 / m  
  
  result <- 0
  for(i in c(1: m)) {
    x <- inX[i]
    y <- inY[i]
    partB    <- (costFunctionHypothesis(inTheta0, inTheta1, x) - y) * x
    result   <- result + partB
  }
  
  result   <- partA * result
  return(result)
}


convergeGradientDecent <- function() {
  alpha      <- 0.1
  
  newTheta0 <- 5
  newTheta1 <- 5
  ctr       <- 0
  while( ((newTheta0 - theta0) != ZERO)  && ((newTheta1 - theta1) != ZERO)) {
    theta0    <- newTheta0
    theta1    <- newTheta1
    
    print(paste("theta0:", theta0, "theta1:", theta1, "newTheta0:", newTheta0, "newTheta1:", newTheta1))    
    
    derivativeValueTheta0 <- derivativeOfCostFunctionTheta0(theta0, theta1, houseSizes, housePrices)
    newTheta0 <- newTheta0 - (alpha * derivativeValueTheta0)
    
    derivativeValueTheta1 <- derivativeOfCostFunctionTheta1(theta0, theta1, houseSizes, housePrices)
    newTheta1 <- newTheta1 - (alpha * derivativeValueTheta1)
    
    #print(paste("(theta0-newTheta0)^2:", abs(theta0-newTheta0)^2, "(theta1-newTheta1)^2:", abs(theta1-newTheta1)^2))
    
    #result <- costFunction(newTheta0, newTheta1, houseSizes, housePrices)
    #print(paste("Original cost function:", result))
    
    print(paste("derivativeValueTheta0:", derivativeValueTheta0, "derivativeValueTheta1:", derivativeValueTheta1))
    
    ctr <- ctr + 1
    
    #if (ctr > 10000) {
    #  break
    #}
  }
}