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I think the var data_line.standard_deviation ∝ 1/dloglikelihood_ddelta_cs. And data_line.standard_deviation can evaluate the noise, so using the var data_line.standard_deviation to calculate the Hessian will decrease the noisy center's influence(decrease the weight of it's Hessian).
I have seen the source code, I discover the calculation of Hessian does not use the gradient directly. In source code, you do not use the var dloglikelihood_ddelta_cs. But you use the var data_line.standard_deviation, Why? Do you use the Quasi-Newton method to solve the problem and use the var data_line.standard_deviation to approximate the Hessian? Thanks.