鲁棒学习：Tukey损失最小化

clear; clc;
n = 10; 
N = 1000; 
x = linspace(-3, 3, n)'; 
X = linspace(-4, 4, N)';
rng('default');
y = x + 0.1*randn(n,1); 
y(n) = -4;     % 异常值
y(n - 1) = -4;
y(2) = -4;
p(:, 1) = ones(n, 1); 
p(:, 2) = x; 
t0 = p\y;   % 计算拟合系数
e = 1;    % 阈值设定
for o = 1 : 1000
  r = abs(p*t0 - y);   % 残差
  w = zeros(n, 1); 
  w(r <= e) = (1 - r(r <= e) .^ 2) .^ 2;   % 残差小于阈值的情况
  t = (p'*(repmat(w, 1, 2) .* p)) \ (p'*(w.*y));
  if norm(t - t0) < 1e-3
      break
  end
  t0 = t;
end
P(:, 1) = ones(N, 1); 
P(:, 2) = X; 
F = P*t;
hold on; 
axis([-4 4 -4.5 3.5]);
plot(X, F, 'g', 'LineWidth', 2); 
plot(x, y, 'ob', 'LineWidth', 2);
hold off