Questions tagged [taylor-series]

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28
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1answer
8k views

XGBoost Loss function Approximation With Taylor Expansion

As an example, take the objective function of the XGBoost model on the $t$'th iteration: $$\mathcal{L}^{(t)}=\sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)}+f_t(\mathbf{x}_i))+\Omega(f_t)$$ where $\ell$ is ...
2
votes
3answers
823 views

Best basis set for polynomial expansion

I want to do a regression of x onto y: $$f(y)=c_{1}x+c_{2}x^{2}+c_{3}x^{3}\cdots$$ Obviously a plain Taylor expansion as above is suboptimal since the coefficients will not be orthogonal/...
5
votes
0answers
869 views

Why is Fisher Scoring easier to compute?

In practice, the observed information matrix (Newton-Raphson) is usually replaced by its expectation, known as Fisher scoring. Link: https://en.wikipedia.org/wiki/Scoring_algorithm#Fisher_scoring ...
5
votes
1answer
2k views

Are Maximum Likelihood Estimators asymptotically unbiased?

I can follow the proofs in which the asymptotic normal-distribution of a maximum likelihood estimator $\tilde{\theta}_n$ is derived. however, does this already imply that the maximum likelihood ...
1
vote
1answer
83 views

xgboost tayler expansion detail [duplicate]

This is the objective function for Xgboost. I have no idea where $g_{i}$ and $h_{i}$ came from is some one explain how this two terms came form? or direct me to the related tutorial page then I ...