loco

Author: cxy0714

notes/Master.bib

@@ -1,9 +1,18 @@
+
 @article{chen2025identification,
   title={Identification and Debiased Learning of Causal Effects with General Instrumental Variables},
   author={Chen, Shuyuan and Zhang, Peng and Cui, Yifan},
   journal={arXiv preprint arXiv:2510.20404},
   year={2025}
 }
+
+@article{wang2024multi,
+  title={Multi-source stable variable importance measure via adversarial machine learning},
+  author={Wang, Zitao and Si, Nian and Guo, Zijian and Liu, Molei},
+  journal={arXiv preprint arXiv:2409.07380},
+  year={2024}
+}
+
 @article{barber2015controlling,
   title  = {Controlling the false discovery rate via knockoffs},
   author = {Barber, Rina Foygel and Cand{\`e}s, Emmanuel J},
@@ -27244,7 +27253,16 @@ @article{hoeffding1948class
   year      = {1948},
   publisher = {Institute of Mathematical Statistics}
 }
-
+@article{lei2018distribution,
+  title={Distribution-free predictive inference for regression},
+  author={Lei, Jing and G’Sell, Max and Rinaldo, Alessandro and Tibshirani, Ryan J and Wasserman, Larry},
+  journal={Journal of the American Statistical Association},
+  volume={113},
+  number={523},
+  pages={1094--1111},
+  year={2018},
+  publisher={Taylor \& Francis}
+}
 @article{lei2014distribution,
   title     = {Distribution-free prediction bands for non-parametric regression},
   author    = {Lei, Jing and Wasserman, Larry},

notes/main.typ

@@ -314,7 +314,21 @@ S8 in @graham2024towards
 ==== Nuisance tangent space
 
 
+== Neyman orthogonality
 
+@wang2024multi used a little different neyman orthogonality. Their problem can be summarized by following:
+
+When the model is $X ~ PP_( theta, overline(eta))$ where $overline(eta)$ is the (nuisance) parameter and $theta$ is the finite dimensional parameter of interest and $ theta = R( overline(eta) ) = limits("max")_(eta) R( eta )$ where $ R(eta) = EE_(X)L(X;eta)$ and $L$ is a loss function.
+
+$ theta =   EE_(X) L(X; overline(eta) )  = limits("max")_(eta) EE_(X) L(X; eta) $
+
+Then $ psi (X;eta) :=  L(X;eta)$ naturally satisfies that the Gâteaux derivative of $eta$ is always zero in $overline(eta)$:
+
+$ & frac(partial EE_(X) [psi (X; eta_0 + t(eta - eta_0))] , partial t) |_(t = 0) =0, forall eta. \ $
+
+The parameterization need to check, if in above setting, $theta$ is totally determined by $overline(eta)$.
+
+Their paper mentioned the indenfication of $theta$, need to check.
 
 === Higher order influence function
 
@@ -374,4 +388,22 @@ Their another work is consider the inference after variable selection, using the
 )
 
 e-valuede 的#link("https://sas.uwaterloo.ca/~wang/")[王若度]（U of Waterloo，  Chair profess） 曾经是星际争霸职业选手。
+
+
+= Machine Learning
+
+== Why named black box model?
+
+#link("https://slds-lmu.github.io/iml_methods_limitations/introduction.html")[Introduction of #emph("Limitations of ML Interpretability")] give a good review to ML Interpretability. Black box model is because the model is based algorithm not as generalized linear model have a simple representation. As @breiman2001statistical saying, two cultures of modeling.
+
+== Varibale importance
+
+=== Leave-One-Covariate-Out(LOCO) 
+
+@lei2018distribution give a measure named loco:
+$ I_x = l( y, f(x,z) ) - l( y, f(z) ) $
+to measure the importance of variable $x$ by comparing the loss when including $x$ versus excluding $x$.
+
+@wang2024multi proposed an extension of LOCO under multiple source data and using semiparametric theory to provide the inference of their measure.
+
 #bibliography("Master.bib")