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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
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