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64 lines
4.3 KiB
TeX
64 lines
4.3 KiB
TeX
\babel@toc {english}{}
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\contentsline {chapter}{\numberline {1}Lecture 1 - 09-03-2020}{5}%
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\contentsline {section}{\numberline {1.1}Introduction of the course}{5}%
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\contentsline {section}{\numberline {1.2}Examples}{5}%
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\contentsline {subsection}{\numberline {1.2.1}Spam filtering}{8}%
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\contentsline {chapter}{\numberline {2}Lecture 2 - 07-04-2020}{9}%
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\contentsline {section}{\numberline {2.1}Argomento}{9}%
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\contentsline {section}{\numberline {2.2}Loss}{9}%
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\contentsline {subsection}{\numberline {2.2.1}Absolute Loss}{9}%
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\contentsline {subsection}{\numberline {2.2.2}Square Loss}{10}%
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\contentsline {subsection}{\numberline {2.2.3}Example of information of square loss}{11}%
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\contentsline {subsection}{\numberline {2.2.4}labels and losses}{12}%
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\contentsline {subsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{14}%
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\contentsline {chapter}{\numberline {3}Lecture 3 - 07-04-2020}{16}%
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\contentsline {section}{\numberline {3.1}Overfitting}{18}%
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\contentsline {subsection}{\numberline {3.1.1}Noise in the data}{18}%
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\contentsline {section}{\numberline {3.2}Underfitting}{20}%
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\contentsline {section}{\numberline {3.3}Nearest neighbour}{20}%
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\contentsline {chapter}{\numberline {4}Lecture 4 - 07-04-2020}{23}%
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\contentsline {section}{\numberline {4.1}Computing $h_{NN}$}{23}%
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\contentsline {section}{\numberline {4.2}Tree Predictor}{25}%
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\contentsline {chapter}{\numberline {5}Lecture 5 - 07-04-2020}{29}%
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\contentsline {section}{\numberline {5.1}Tree Classifier}{29}%
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\contentsline {section}{\numberline {5.2}Jensen’s inequality}{31}%
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\contentsline {section}{\numberline {5.3}Tree Predictor}{35}%
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\contentsline {section}{\numberline {5.4}Statistical model for Machine Learning}{36}%
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\contentsline {chapter}{\numberline {6}Lecture 6 - 07-04-2020}{38}%
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\contentsline {section}{\numberline {6.1}Bayes Optimal Predictor}{38}%
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\contentsline {subsection}{\numberline {6.1.1}Square Loss}{39}%
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\contentsline {subsection}{\numberline {6.1.2}Zero-one loss for binary classification}{40}%
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\contentsline {section}{\numberline {6.2}Bayes Risk}{43}%
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\contentsline {chapter}{\numberline {7}Lecture 7 - 07-04-2020}{45}%
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\contentsline {section}{\numberline {7.1}Chernoff-Hoffding bound}{45}%
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\contentsline {section}{\numberline {7.2}Union Bound}{46}%
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\contentsline {section}{\numberline {7.3}Studying overfitting of a ERM}{50}%
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\contentsline {chapter}{\numberline {8}Lecture 8 - 07-04-2020}{52}%
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\contentsline {section}{\numberline {8.1}The problem of estimating risk in practise}{53}%
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\contentsline {section}{\numberline {8.2}Cross-validation}{55}%
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\contentsline {section}{\numberline {8.3}Nested cross validation}{57}%
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\contentsline {chapter}{\numberline {9}Lecture 9 - 07-04-2020}{58}%
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\contentsline {section}{\numberline {9.1}Tree predictors}{58}%
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\contentsline {subsection}{\numberline {9.1.1}Catalan Number}{60}%
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\contentsline {chapter}{\numberline {10}Lecture 10 - 07-04-2020}{64}%
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\contentsline {section}{\numberline {10.1}TO BE DEFINE}{64}%
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\contentsline {section}{\numberline {10.2}MANCANO 20 MINUTI DI LEZIONE}{64}%
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\contentsline {section}{\numberline {10.3}Compare risk for zero-one loss}{66}%
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\contentsline {chapter}{\numberline {11}Lecture 11 - 20-04-2020}{68}%
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\contentsline {section}{\numberline {11.1}Analysis of $K_{NN}$}{68}%
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\contentsline {subsection}{\numberline {11.1.1}Study of $K_{NN}$}{71}%
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\contentsline {subsection}{\numberline {11.1.2}study of trees}{72}%
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\contentsline {section}{\numberline {11.2}Non-parametric Algorithms}{73}%
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\contentsline {subsection}{\numberline {11.2.1}Example of parametric algorithms}{74}%
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\contentsline {chapter}{\numberline {12}Lecture 12 - 21-04-2020}{75}%
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\contentsline {section}{\numberline {12.1}Non parametrics algorithms}{75}%
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\contentsline {subsection}{\numberline {12.1.1}Theorem: No free lunch}{75}%
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\contentsline {section}{\numberline {12.2}Highly Parametric Learning Algorithm}{77}%
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\contentsline {subsection}{\numberline {12.2.1}Linear Predictors}{77}%
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\contentsline {subsection}{\numberline {12.2.2}MinDisagreement}{81}%
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\contentsline {chapter}{\numberline {13}Lecture 17 - 12-05-2020}{82}%
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\contentsline {section}{\numberline {13.1}Kernel functions}{82}%
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\contentsline {subsection}{\numberline {13.1.1}Feature expansion}{82}%
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\contentsline {subsection}{\numberline {13.1.2}Kernels implements feature expansion (Efficiently}{83}%
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\contentsline {section}{\numberline {13.2}Gaussian Kernel}{84}%
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