weight_update_Huber.py

def update_weights_Huber(m, b, X, Y, delta, learning_rate):
    m_deriv = 0
    b_deriv = 0
    N = len(X)
    for i in range(N):
        # derivative of quadratic for small values and of linear for large values
        if abs(Y[i] - m*X[i] - b) <= delta:
          m_deriv += -X[i] * (Y[i] - (m*X[i] + b))
          b_deriv += - (Y[i] - (m*X[i] + b))
        else:
          m_deriv += delta * X[i] * ((m*X[i] + b) - Y[i]) / abs((m*X[i] + b) - Y[i])
          b_deriv += delta * ((m*X[i] + b) - Y[i]) / abs((m*X[i] + b) - Y[i])
    
    # We subtract because the derivatives point in direction of steepest ascent
    m -= (m_deriv / float(N)) * learning_rate
    b -= (b_deriv / float(N)) * learning_rate

    return m, b