Thesis.toc

\contentsline {chapter}{Abstract}{v}{}%
\contentsline {chapter}{\numberline {1}Introduction}{1}{}%
\contentsline {section}{\numberline {1.1}The robustness challenge}{1}{}%
\contentsline {subsection}{\numberline {1.1.1}Adversarial setting}{2}{}%
\contentsline {subsection}{\numberline {1.1.2}Out-of-distribution setting}{4}{}%
\contentsline {section}{\numberline {1.2}Related work}{6}{}%
\contentsline {section}{\numberline {1.3}Objectives}{7}{}%
\contentsline {chapter}{\numberline {2}Theoretical background }{9}{}%
\contentsline {section}{\numberline {2.1}The learning framework}{9}{}%
\contentsline {section}{\numberline {2.2}Learning with neural networks}{10}{}%
\contentsline {section}{\numberline {2.3}Posterior agreement}{11}{}%
\contentsline {subsection}{\numberline {2.3.1}Posterior distribution}{12}{}%
\contentsline {subsection}{\numberline {2.3.2}Generalization error}{13}{}%
\contentsline {subsection}{\numberline {2.3.3}Maximum posterior agreement}{14}{}%
\contentsline {chapter}{\numberline {3}Experimental setup}{17}{}%
\contentsline {section}{\numberline {3.1}Problem formulation}{17}{}%
\contentsline {section}{\numberline {3.2}Robustness under covariate shift}{18}{}%
\contentsline {section}{\numberline {3.3}Adversarial setting}{20}{}%
\contentsline {section}{\numberline {3.4}Domain generalization setting}{21}{}%
\contentsline {section}{\numberline {3.5}Robust learners}{22}{}%
\contentsline {section}{\numberline {3.6}Robustness assessment with posterior agreement}{23}{}%
\contentsline {subsection}{\numberline {3.6.1}Posterior in classification tasks}{23}{}%
\contentsline {subsection}{\numberline {3.6.2}The posterior agreement kernel}{24}{}%
\contentsline {subsection}{\numberline {3.6.3}Implementation}{27}{}%
\contentsline {chapter}{\numberline {4}Robustness assessment}{29}{}%
\contentsline {section}{\numberline {4.1}In-distribution setting}{29}{}%
\contentsline {section}{\numberline {4.2}Adversarial setting}{33}{}%
\contentsline {section}{\numberline {4.3}Out-of-distribution setting}{43}{}%
\contentsline {paragraph}{Experiment 5a.}{44}{}%
\contentsline {paragraph}{Experiment 5b.}{46}{}%
\contentsline {paragraph}{Experiment 5c.}{48}{}%
\contentsline {chapter}{\numberline {5}Model selection}{51}{}%
\contentsline {section}{\numberline {5.1}DiagVib-6 Benchmark}{52}{}%
\contentsline {paragraph}{Experiment 6.}{52}{}%
\contentsline {section}{\numberline {5.2}In-distribution DiagVib-6}{56}{}%
\contentsline {paragraph}{Experiment 7.}{56}{}%
\contentsline {section}{\numberline {5.3}WILDS Benchmark}{59}{}%
\contentsline {paragraph}{Experiment 8.}{59}{}%
\contentsline {paragraph}{Experiment 9.}{60}{}%
\contentsline {paragraph}{Experiment 10.}{60}{}%
\contentsline {chapter}{\numberline {6}Conclusions}{63}{}%
\newpage 
\contentsline {chapter}{\numberline {A}Theoretical Proofs and Derivations}{67}{}%
\contentsline {section}{\numberline {A.1}Proof of problem formulation}{67}{}%
\contentsline {section}{\numberline {A.2}Properties of the PA kernel}{69}{}%
\contentsline {chapter}{\numberline {B}Supplementary Results}{73}{}%
\contentsline {section}{\numberline {B.1}Robustness assessment}{73}{}%
\contentsline {subsection}{\numberline {B.1.1}In-distribution setting}{73}{}%
\contentsline {subsection}{\numberline {B.1.2}Adversarial setting}{76}{}%
\contentsline {section}{\numberline {B.2}Model Selection}{82}{}%
\contentsline {subsection}{\numberline {B.2.1}DiagVib-6 Benchmark}{82}{}%
\contentsline {subsection}{\numberline {B.2.2}In-distribution DiagVib-6}{83}{}%
\contentsline {chapter}{\numberline {C}Dataset reference}{84}{}%
\contentsline {section}{\numberline {C.1}Robustness assessment}{85}{}%
\contentsline {section}{\numberline {C.2}Model selection}{85}{}%
\contentsline {subsection}{\numberline {C.2.1}DiagVib-6 Benchmark}{85}{}%
\contentsline {subsection}{\numberline {C.2.2}In-distribution DiagVib-6}{87}{}%