\babel@toc {english}{}
\contentsline {chapter}{\numberline {1}Lecture 1 - 09-03-2020}{4}%
\contentsline {section}{\numberline {1.1}Introduction of the course}{4}%
\contentsline {section}{\numberline {1.2}Examples}{4}%
\contentsline {subsection}{\numberline {1.2.1}Spam filtering}{7}%
\contentsline {chapter}{\numberline {2}Lecture 2 - 07-04-2020}{8}%
\contentsline {section}{\numberline {2.1}Argomento}{8}%
\contentsline {section}{\numberline {2.2}Loss}{8}%
\contentsline {subsection}{\numberline {2.2.1}Absolute Loss}{8}%
\contentsline {subsection}{\numberline {2.2.2}Square Loss}{9}%
\contentsline {subsection}{\numberline {2.2.3}Example of information of square loss}{9}%
\contentsline {subsection}{\numberline {2.2.4}labels and losses}{10}%
\contentsline {subsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{12}%
\contentsline {chapter}{\numberline {3}Lecture 3 - 07-04-2020}{14}%
\contentsline {section}{\numberline {3.1}Overfitting}{16}%
\contentsline {subsection}{\numberline {3.1.1}Noise in the data}{16}%
\contentsline {section}{\numberline {3.2}Underfitting}{17}%
\contentsline {section}{\numberline {3.3}Nearest neighbour}{18}%
\contentsline {chapter}{\numberline {4}Lecture 4 - 07-04-2020}{20}%
\contentsline {section}{\numberline {4.1}Computing $h_{NN}$}{20}%
\contentsline {section}{\numberline {4.2}Tree Predictor}{21}%
\contentsline {chapter}{\numberline {5}Lecture 5 - 07-04-2020}{24}%
\contentsline {section}{\numberline {5.1}Tree Classifier}{24}%
\contentsline {section}{\numberline {5.2}Jensen’s inequality}{25}%
\contentsline {section}{\numberline {5.3}Tree Predictor}{27}%
\contentsline {section}{\numberline {5.4}Statistical model for Machine Learning}{28}%
\contentsline {chapter}{\numberline {6}Lecture 6 - 07-04-2020}{30}%
\contentsline {section}{\numberline {6.1}Bayes Optimal Predictor}{30}%
\contentsline {subsection}{\numberline {6.1.1}Square Loss}{31}%
\contentsline {subsection}{\numberline {6.1.2}Zero-one loss for binary classification}{32}%
\contentsline {section}{\numberline {6.2}Bayes Risk}{34}%
\contentsline {chapter}{\numberline {7}Lecture 7 - 07-04-2020}{35}%
\contentsline {section}{\numberline {7.1}Chernoff-Hoffding bound}{35}%
\contentsline {section}{\numberline {7.2}Union Bound}{36}%
\contentsline {section}{\numberline {7.3}Studying overfitting of a ERM}{40}%
\contentsline {chapter}{\numberline {8}Lecture 8 - 07-04-2020}{42}%
\contentsline {section}{\numberline {8.1}The problem of estimating risk in practise}{43}%
\contentsline {section}{\numberline {8.2}Cross-validation}{45}%
\contentsline {section}{\numberline {8.3}Nested cross validation}{47}%
\contentsline {chapter}{\numberline {9}Lecture 9 - 07-04-2020}{48}%
\contentsline {section}{\numberline {9.1}Tree predictors}{48}%
\contentsline {subsection}{\numberline {9.1.1}Catalan Number}{50}%
\contentsline {chapter}{\numberline {10}Lecture 10 - 07-04-2020}{54}%
\contentsline {section}{\numberline {10.1}TO BE DEFINE}{54}%
\contentsline {section}{\numberline {10.2}MANCANO 20 MINUTI DI LEZIONE}{54}%
\contentsline {section}{\numberline {10.3}Compare risk for zero-one loss}{56}%
\contentsline {chapter}{\numberline {11}Lecture 11 - 20-04-2020}{58}%
\contentsline {section}{\numberline {11.1}Analysis of $K_{NN}$}{58}%
\contentsline {subsection}{\numberline {11.1.1}Study of $K_{NN}$}{61}%
\contentsline {subsection}{\numberline {11.1.2}study of trees}{62}%
\contentsline {section}{\numberline {11.2}Non-parametric Algorithms}{63}%
\contentsline {subsection}{\numberline {11.2.1}Example of parametric algorithms}{64}%
\contentsline {chapter}{\numberline {12}Lecture 12 - 21-04-2020}{65}%
\contentsline {section}{\numberline {12.1}Non parametrics algorithms}{65}%