Chapter 6: Adaptive rare event estimation using Bernstein copula

josephmure commented 10 months ago

Remarque préliminaire sur le titre de chapitre : à mon avis il faudrait écrire "using Bernstein copulaS".

Contrairement à ce que j'ai fait pour l'introduction et le chapitre 1, je vais découper ici par section, pour que les passages soient plus faciles à retrouver pour toi en cas de changement de la pagination.

6.1 Introduction

[ ] system ~exceeding~ crossing the threshold Techniquement, il s'agit de dépasser par en-dessous, donc le terme franchir me paraît plus approprié.
[ ] FORM/SORM methods do not provide ~a lot of~ much statistical information
[ ] becomes rapidly intractable ~rapidly~
[ ] such as ~the~ Subset Simulation
[ ] In Subset Simulation, the idea is to write the rare event probability pf
[ ] The main drawback of ~the~ Cross-Entropy Adaptive Importance Sampling is its limited flexibility ~not allowing it to perform well~ which makes it perform badly
[ ] and a fit of their copula with the Empirial Bernstein Copula (EBC) ajouter l'acronyme ici
[ ] Additionally, unlike SS, the proposed method ~proposed~ ... ~unlike SS~
[ ] the BANCS ~algortihm~ algorithm
[ ] and illustrate ~their~ its estimation on samples

josephmure commented 10 months ago

6.2 Bernstein adaptive nonparametric conditional sampling

[ ] the BANCS method does not require any iso-probabilistic transform.
[ ] either a scaling parameter for the KDE bizarre que ça n'apparaisse pas dans l'algorithme 1, d'autant qu'il me semble que tu n'utilises pas les options par défaut d'OpenTURNS.
[ ] (considered equal for all dimensionS) for the EBC. In the BANCS algorithm
[ ] Dans l'algorithme 1, il faut préciser à mon avis que $\hat{f}_{[0]} = f_X$ à la ligne 9.
[ ] Dernier paragraphe : tu parles à 2 reprises de "sharp fit" mais je ne comprends pas bien ce que tu veux dire, surtout quand ce fit sharp doit être "around this border".
[ ] Il manque un point entre "overfitting the data" et "At the second iteration"

josephmure commented 10 months ago

6.3 Numerical experiments

[ ] ~The size N of each intermediate samples (i.e., subset) evolves in the following set N ∈ {300, 500, 700, 1000, 2000, 5000, 10000}.~ We experiment with the following intermediate sample sizes N: 300, 500, 700, 1000, 2000, 5000, 10000.
[ ] Let us ~reming~ recall that the EBC tuning is setup ce mot existe-t-il dans ce sens ? J'aurais mis "set" to minimize the AMISE~, such that~ with m=...

josephmure commented 10 months ago

6.3.1 Analytical toy-cases

[ ] The distribution of the input random vector X~,~ is defined as a product of marginals following the distributions defined in Table 6.1
[ ] ~Such~ This visualization allows to perceive the nonlinearity

josephmure commented 10 months ago

6.3.2 Benchmark results and analysis

[ ] the benchmark is conducted on test-case #2 (fourbranch problem with d = 2), test-case #4 (with d = 7)~,~ and test-case #5 (oscillator problem with d = 8).
[ ] as it ~fits~ separately fits the copula and the marginals
[ ] For test-case #4, the NAIS implementation used does not support input distributions with bounded domains and was therefore removed. C'est quelque chose que je ne comprends pas, à discuter. D'ailleurs n'est-ce pas plutôt le test case #5 ?
[ ] On this rare and complex case (notice the nonlinearity in the cross-cut in Fig. 6.3), SS is more accurate for small-sized samples (i.e., N ≤ 103) but becomes equivalent to BANCS for larger sample sizes. A mon avis, il faut renverser la formulation, c'est BANCS qui est comparé aux autres donc il faut plutôt dire "BANCS is less accurate than SS for small-sized... but becomes equivalent to SS for larger...

josephmure commented 10 months ago

6.4 Reliability-oriented sensitivity analysis

[ ] The importance factors are a ~first~ local ROSA measure
[ ] the use of Hilbert-Schmidt indepencence criterion (HSIC) estimators
[ ] ~which~ . This idea was further explored by Marrel and Chabridon (2021)
[ ] TSA measuring / CSA studying: choisis un verbe et utilise le même pour TSA et CSA

josephmure commented 10 months ago

6.4.1 Target and conditional HSIC

[ ] In our case, the target-HSIC (T-HSIC) and ~their~ its respective
[ ] However, the asymptotic approach no longer holdS for CSA
[ ] Note that the HSIC generally do not require independence of the samples je ne comprends pas cette phrase, de quoi parles-tu ?

josephmure commented 10 months ago

6.4.2 ROSA as a post-processing of BANCS reliability analysis

[ ] The target and conditional sensitivity analysis are presented via their respective HSIC and the p-value of their independence test. il faut être plus précis, tu n'as pas accès aux HSIC mais seulement à des estimations des HSIC. Ou alors il faut dire à un moment que tu fais cet abus de langage, mais je n'y suis pas favorable, car il n'est pas dificile de dire rigoureusement les choses.
[ ] X1 has an interesting behavior as the problem becomes rarer ???

josephmure commented 10 months ago

6.5 Conclusion

[ ] with other methods ~as~ mettre des double points : SS and NAIS
[ ] similar to what is done for surrogate models
[ ] ~allows capturing~ captures multimodal problems
[ ] ~the~ ROSA was investigated
[ ] (~in the vein of~ following the work of Marrel and Chabridon, 2021) je n'ai trouvé aucune utilisation de l'expression in the vein of sur le net, l'expression ne semle pas idiomatique
[ ] tools ~for understanding~ to understand problems
[ ] is ~an~ important ~tool~ to understand

efekhari27 commented 10 months ago

Hi Joseph, I have taken into account all your remarks, thanks for this very good feedback. Regards, Elias

efekhari27 / thesis