Logistic regression for orange vs grapefruit

logistic_regression_grapefruit.m

% data
x = [1, 2, 3, 4, 5, 6];
y = [0, 0, 0, 1, 1, 1];

% function to calculate the predicted value
function result = h(x, t0, t1)
  result = sigmoid(t0 + t1 * x);
end

% sigmoid function
function result = sigmoid(z)
  result = 1 / (1 + e ^ (-z));
end

% given a theta_0 and theta_1, this function calculates
% their cost. We don't need this function, strictly speaking...
% but it is nice to print out the costs as gradient descent iterates.
% We should see the cost go down every time the values of theta get updated.
function distance = cost(theta_0, theta_1, x, y)
  distance = 0;
  for i = 1:length(x) % arrays in octave are indexed starting at 1
    if (y(i) == 1)
      distance += -log(h(x(i), theta_0, theta_1));
    else
      distance += -log(1 - h(x(i), theta_0, theta_1));
    end
  end
  % get how far off we were on average
  distance = distance / length(x);
end

alpha = 0.1;
iters = 1500;
m = length(x);

% initial values
theta_0 = 0;
theta_1 = 0;

for i = 1:iters
  % we store this calculation in temporary variables,
  % because theta_0 and theta_1 must be updated *together*.
  % i.e. we can't update theta_0 and use the new theta_0 value
  % while updating theta_1.
  cost_0 = 0;
  for i = 1:m
    cost_0 += (h(x(i), theta_0, theta_1) - y(i));
  end
  temp_0 = theta_0 - alpha * 1/m * cost_0;

  cost_1 = 0;
  for i = 1:m
    cost_1 += ((h(x(i), theta_0, theta_1) - y(i)) * x(i));
  end
  temp_1 = theta_1 - alpha * 1/m * cost_1;

  theta_0 = temp_0;
  theta_1 = temp_1;

  % print out the new values of theta for each iteration,
  % as well as the new, lower cost
  disp([theta_0, theta_1, cost(theta_0, theta_1, x, y)]);
end

% print out predictions for numbers 1 to 10
for i = 1:10
  disp([i, h(i, theta_0, theta_1) * 100]);
end