egonSchiele/logistic_regression_grapefruit.m

## 68 changes: 68 additions & 0 deletions logistic_regression_grapefruit.m
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    % data
% data

    x = [1, 2, 3, 4, 5, 6];
x = [1, 2, 3, 4, 5, 6];

    y = [0, 0, 0, 1, 1, 1];
y = [0, 0, 0, 1, 1, 1];


    % function to calculate the predicted value
% function to calculate the predicted value

    function result = h(x, t0, t1)
function result = h(x, t0, t1)

      result = sigmoid(t0 + t1 * x);
  result = sigmoid(t0 + t1 * x);

    end
end


    % sigmoid function
% sigmoid function

    function result = sigmoid(z)
function result = sigmoid(z)

      result = 1 / (1 + e ^ (-z));
  result = 1 / (1 + e ^ (-z));

    end
end


    % given a theta_0 and theta_1, this function calculates
% given a theta_0 and theta_1, this function calculates

    % their cost. We don't need this function, strictly speaking...
% their cost. We don't need this function, strictly speaking...

    % but it is nice to print out the costs as gradient descent iterates.
% 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.
% We should see the cost go down every time the values of theta get updated.

    function distance = cost(theta_0, theta_1, x, y)
function distance = cost(theta_0, theta_1, x, y)

      distance = 0;
  distance = 0;

      for i = 1:length(x) % arrays in octave are indexed starting at 1
  for i = 1:length(x) % arrays in octave are indexed starting at 1

        if (y(i) == 1)
    if (y(i) == 1)

          distance += -log(h(x(i), theta_0, theta_1));
      distance += -log(h(x(i), theta_0, theta_1));

        else
    else

          distance += -log(1 - h(x(i), theta_0, theta_1));
      distance += -log(1 - h(x(i), theta_0, theta_1));

        end
    end

      end
  end

      % get how far off we were on average
  % get how far off we were on average

      distance = distance / length(x);
  distance = distance / length(x);

    end
end


    alpha = 0.1;
alpha = 0.1;

    iters = 1500;
iters = 1500;

    m = length(x);
m = length(x);


    % initial values
% initial values

    theta_0 = 0;
theta_0 = 0;

    theta_1 = 0;
theta_1 = 0;


    for i = 1:iters
for i = 1:iters

      % we store this calculation in temporary variables,
  % we store this calculation in temporary variables,

      % because theta_0 and theta_1 must be updated *together*.
  % 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
  % i.e. we can't update theta_0 and use the new theta_0 value

      % while updating theta_1.
  % while updating theta_1.

      cost_0 = 0;
  cost_0 = 0;

      for i = 1:m
  for i = 1:m

        cost_0 += (h(x(i), theta_0, theta_1) - y(i));
    cost_0 += (h(x(i), theta_0, theta_1) - y(i));

      end
  end

      temp_0 = theta_0 - alpha * 1/m * cost_0;
  temp_0 = theta_0 - alpha * 1/m * cost_0;


      cost_1 = 0;
  cost_1 = 0;

      for i = 1:m
  for i = 1:m

        cost_1 += ((h(x(i), theta_0, theta_1) - y(i)) * x(i));
    cost_1 += ((h(x(i), theta_0, theta_1) - y(i)) * x(i));

      end
  end

      temp_1 = theta_1 - alpha * 1/m * cost_1;
  temp_1 = theta_1 - alpha * 1/m * cost_1;


      theta_0 = temp_0;
  theta_0 = temp_0;

      theta_1 = temp_1;
  theta_1 = temp_1;


      % print out the new values of theta for each iteration,
  % print out the new values of theta for each iteration,

      % as well as the new, lower cost
  % as well as the new, lower cost

      disp([theta_0, theta_1, cost(theta_0, theta_1, x, y)]);
  disp([theta_0, theta_1, cost(theta_0, theta_1, x, y)]);

    end
end


    % print out predictions for numbers 1 to 10
% print out predictions for numbers 1 to 10

    for i = 1:10
for i = 1:10

      disp([i, h(i, theta_0, theta_1) * 100]);
  disp([i, h(i, theta_0, theta_1) * 100]);

    end
end