線性梯度迴歸，使用octave實現

function [initw] = lineGred()
  x = randi(10,20,2)
  realw = [2 3]
  y =  x* realw'
  initw = [1 1]

  j = sum(power((x * initw' - y),2)) / size(x,1)
  while j > 0.001
    swapw = sum((x * initw' - y).*x) / size(x,1)
    initw = initw -  0.01*swapw
    j = sum(power((x * initw' - y),2)) / size(x,1)
  end
  disp(initw)
end

 

結果：

initw = [2.0087   2.9896]

 

多項式：

function [initw] = lineGredPow2()
  realw = [2 3]
  x1 = randi(10,20,1)
  x2 = x1 .^2;
  x = [x1,x2]
  y =   x* realw'
  initw = [1 2]
  j = sum(power((x * initw' - y),2)) / size(x,1)
  while j > 0.001
    swapw = sum((x * initw' - y).*x) / size(x,1)
    initw = initw -  0.0001*swapw
    j = sum(power((x * initw' - y),2)) / size(x,1)
  end
end

 

結果：1.9787   3.0026

 

直接求解

function [initw] = normalLine()
  x = randi(10,20,2)
  realw = [2 3]
  y =  x* realw'
  w = pinv(x'*x)*x'*y
 
end