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[]f\OML/cmm/m/it /12 outlook:humidity; windy\OMS/cmsy/m/n/12 g [] - + File: lectures/../img/lez4-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez4-img4.JPG used on input line 166. (pdftex.def) Requested size: 77.99881pt x 46.64948pt. - + File: lectures/../img/lez4-img5.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez4-img5.JPG used on input line 174. (pdftex.def) Requested size: 77.99881pt x 56.59116pt. - + File: lectures/../img/lez4-img6.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez4-img6.JPG used on input line 185. @@ -889,7 +889,7 @@ Package pdftex.def Info: lectures/../img/lez4-img6.JPG used on input line 185. 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LaTeX Font Warning: Command \small invalid in math mode on input line 11. @@ -1774,7 +1774,7 @@ Overfull \hbox (4.56644pt too wide) detected at line 53 cmr/m/n/12 = [] -[65 +[66 ] Overfull \hbox (17.46814pt too wide) detected at line 61 @@ -1797,7 +1797,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 77--80 [] - + File: lectures/../img/lez10-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez10-img1.JPG used on input line 84. @@ -1816,8 +1816,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 109--112 [] -[66] - +[67] + File: lectures/../img/lez10-img2.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez10-img2.JPG used on input line 131 @@ -1827,10 +1827,10 @@ Package pdftex.def Info: lectures/../img/lez10-img2.JPG used on input line 131 LaTeX Warning: `h' float specifier changed to `ht'. -) [67 <./lectures/../img/lez10-img1.JPG>] (lectures/lecture11.tex [68 <./lectur +) [68 <./lectures/../img/lez10-img1.JPG>] (lectures/lecture11.tex [69 <./lectur es/../img/lez10-img2.JPG>] Chapter 11. - + File: lectures/../img/lez11-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez11-img1.JPG used on input line 21. @@ -1851,10 +1851,10 @@ Underfull \hbox (badness 10000) in paragraph at lines 9--39 [] -[69 +[70 <./lectures/../img/lez11-img1.JPG>] - + File: lectures/../img/lez11-img2.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez11-img2.JPG used on input line 53. @@ -1891,8 +1891,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 123--125 [] -[70 <./lectures/../img/lez11-img2.JPG>] - +[71 <./lectures/../img/lez11-img2.JPG>] + File: lectures/../img/lez11-img3.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez11-img3.JPG used on input line 135 @@ -1913,7 +1913,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 166--170 [] -[71 <./lectures/../img/lez11-img3.JPG>] +[72 <./lectures/../img/lez11-img3.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 193--195 [] @@ -1971,7 +1971,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 233--251 [] -[72] +[73] Underfull \hbox (badness 10000) in paragraph at lines 253--256 [] @@ -2006,8 +2006,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 270--287 [] -[73] - +[74] + File: lectures/../img/lez11-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez11-img4.JPG used on input line 311 @@ -2048,7 +2048,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 296--333 [] -[74]) [75 <./lectures/../img/lez11-img4.JPG>] (lectures/lecture12.tex +[75]) [76 <./lectures/../img/lez11-img4.JPG>] (lectures/lecture12.tex Chapter 12. Underfull \hbox (badness 10000) in paragraph at lines 8--17 @@ -2060,7 +2060,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 8--17 [] - + File: lectures/../img/lez12-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img1.JPG used on input line 35. @@ -2079,19 +2079,19 @@ Underfull \hbox (badness 10000) in paragraph at lines 32--44 LaTeX Warning: `h' float specifier changed to `ht'. -[76 +[77 ] Underfull \hbox (badness 10000) in paragraph at lines 49--60 [] -[77 <./lectures/../img/lez12-img1.JPG>] +[78 <./lectures/../img/lez12-img1.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 65--67 [] - + File: lectures/../img/lez12-img2.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img2.JPG used on input line 83. @@ -2102,7 +2102,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 80--88 [] - + File: lectures/../img/lez12-img3.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img3.JPG used on input line 108 @@ -2111,14 +2111,14 @@ Package pdftex.def Info: lectures/../img/lez12-img3.JPG used on input line 108 LaTeX Warning: `h' float specifier changed to `ht'. - + File: lectures/../img/lez12-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img4.JPG used on input line 124 . (pdftex.def) Requested size: 155.99762pt x 130.43692pt. -[78 <./lectures/../img/lez12-img2.JPG>] - +[79 <./lectures/../img/lez12-img2.JPG>] + File: lectures/../img/lez12-img5.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img5.JPG used on input line 147 @@ -2128,8 +2128,8 @@ Package pdftex.def Info: lectures/../img/lez12-img5.JPG used on input line 147 LaTeX Warning: `h' float specifier changed to `ht'. -[79 <./lectures/../img/lez12-img3.JPG> <./lectures/../img/lez12-img4.JPG>] - +[80 <./lectures/../img/lez12-img3.JPG> <./lectures/../img/lez12-img4.JPG>] + File: lectures/../img/lez12-img6.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img6.JPG used on input line 156 @@ -2140,8 +2140,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 173--176 [] -[80 <./lectures/../img/lez12-img5.JPG> <./lectures/../img/lez12-img6.JPG>] - +[81 <./lectures/../img/lez12-img5.JPG> <./lectures/../img/lez12-img6.JPG>] + File: lectures/../img/lez12-img7.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez12-img7.JPG used on input line 180 @@ -2167,7 +2167,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 199--210 [] -[81 <./lectures/../img/lez12-img7.JPG>]) [82] (lectures/lecture13.tex +[82 <./lectures/../img/lez12-img7.JPG>]) [83] (lectures/lecture13.tex Chapter 13. 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(pdftex.def) Requested size: 77.99881pt x 83.57153pt. - + File: lectures/../img/lez13-img3.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez13-img3.JPG used on input line 74. @@ -2252,8 +2252,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 59--81 LaTeX Warning: `h' float specifier changed to `ht'. -[84 <./lectures/../img/lez13-img1.JPG> <./lectures/../img/lez13-img2.JPG>] - +[85 <./lectures/../img/lez13-img1.JPG> <./lectures/../img/lez13-img2.JPG>] + File: lectures/../img/lez13-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez13-img4.JPG used on input line 93. @@ -2269,8 +2269,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 86--100 [] -[85 <./lectures/../img/lez13-img3.JPG> <./lectures/../img/lez13-img4.JPG>] - +[86 <./lectures/../img/lez13-img3.JPG> <./lectures/../img/lez13-img4.JPG>] + File: lectures/../img/lez13-img5.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez13-img5.JPG used on input line 120 @@ -2291,7 +2291,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 102--127 [] -[86 <./lectures/../img/lez13-img5.JPG>] +[87 <./lectures/../img/lez13-img5.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 134--138 [] @@ -2311,7 +2311,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 143--148 [] - + File: lectures/../img/lez13-img6.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez13-img6.JPG used on input line 152 @@ -2327,12 +2327,12 @@ Underfull \hbox (badness 10000) in paragraph at lines 149--167 [] -[87 <./lectures/../img/lez13-img6.JPG>] +[88 <./lectures/../img/lez13-img6.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 194--197 [] -) [88] [89] (lectures/lecture14.tex +) [89] [90] (lectures/lecture14.tex Chapter 14. Underfull \hbox (badness 10000) in paragraph at lines 7--13 @@ -2369,14 +2369,14 @@ Underfull \hbox (badness 10000) in paragraph at lines 56--75 [] -[90 +[91 ] Underfull \hbox (badness 10000) in paragraph at lines 76--79 [] - + File: lectures/../img/lez14-img1.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez14-img1.JPG used on input line 93. @@ -2397,7 +2397,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 81--100 [] -[91 <./lectures/../img/lez14-img1.JPG>] +[92 <./lectures/../img/lez14-img1.JPG>] Underfull \hbox (badness 10000) in paragraph at lines 106--109 [] @@ -2417,8 +2417,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 137--152 [] -[92] - +[93] + File: lectures/../img/lez14-img2.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez14-img2.JPG used on input line 161 @@ -2434,8 +2434,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 157--172 [] -[93 <./lectures/../img/lez14-img2.JPG>] - +[94 <./lectures/../img/lez14-img2.JPG>] + File: lectures/../img/lez14-img3.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez14-img3.JPG used on input line 180 @@ -2451,8 +2451,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 191--196 [] -[94 <./lectures/../img/lez14-img3.JPG>] - +[95 <./lectures/../img/lez14-img3.JPG>] + File: lectures/../img/lez14-img4.JPG Graphic file (type jpg) Package pdftex.def Info: lectures/../img/lez14-img4.JPG used on input line 207 @@ -2473,7 +2473,7 @@ mm/m/it/12 w[] x `[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 w\OT1/cmr/m/n/12 ) = \OML r/m/n/12 )[] [] -) [95 <./lectures/../img/lez14-img4.JPG>] (lectures/lecture15.tex +) [96 <./lectures/../img/lez14-img4.JPG>] (lectures/lecture15.tex Chapter 15. Underfull \hbox (badness 10000) in paragraph at lines 7--9 @@ -2485,39 +2485,126 @@ Underfull \hbox (badness 10000) in paragraph at lines 14--20 [] -[96 +[97 ] - + File: lectures/../img/lez15-img1.JPG Graphic file (type jpg) -Package pdftex.def Info: lectures/../img/lez15-img1.JPG used on input line 44. +Package pdftex.def Info: lectures/../img/lez15-img1.JPG used on input line 45. (pdftex.def) Requested size: 117.00119pt x 54.50513pt. -! Missing $ inserted. - - $ -l.50 \end{document} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. 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f80012c77..b0c9cdaeb 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/Machine Learning/main.toc +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/Machine Learning/main.toc @@ -1,80 +1,80 @@ \babel@toc {english}{} -\contentsline {chapter}{\numberline {1}Lecture 1 - 09-03-2020}{6}% -\contentsline {section}{\numberline {1.1}Introduction of the course}{6}% -\contentsline {section}{\numberline {1.2}Examples}{6}% -\contentsline {subsection}{\numberline {1.2.1}Spam filtering}{9}% -\contentsline {chapter}{\numberline {2}Lecture 2 - 10-03-2020}{10}% -\contentsline {section}{\numberline {2.1}Argomento}{10}% -\contentsline {section}{\numberline {2.2}Loss}{10}% -\contentsline {subsection}{\numberline {2.2.1}Absolute Loss}{10}% -\contentsline {subsection}{\numberline {2.2.2}Square Loss}{11}% -\contentsline {subsection}{\numberline {2.2.3}Example of information of square loss}{12}% -\contentsline {subsection}{\numberline {2.2.4}labels and losses}{13}% -\contentsline {subsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{15}% -\contentsline {chapter}{\numberline {3}Lecture 3 - 16-03-2020}{17}% -\contentsline {section}{\numberline {3.1}Overfitting}{19}% -\contentsline {subsection}{\numberline {3.1.1}Noise in the data}{19}% -\contentsline {section}{\numberline {3.2}Underfitting}{21}% -\contentsline {section}{\numberline {3.3}Nearest neighbour}{21}% -\contentsline {chapter}{\numberline {4}Lecture 4 - 17-03-2020}{24}% -\contentsline {section}{\numberline {4.1}Computing $h_{NN}$}{24}% -\contentsline {section}{\numberline {4.2}Tree Predictor}{26}% -\contentsline {chapter}{\numberline {5}Lecture 5 - 23-03-2020}{30}% -\contentsline {section}{\numberline {5.1}Tree Classifier}{30}% -\contentsline {section}{\numberline {5.2}Jensen’s inequality}{32}% -\contentsline {section}{\numberline {5.3}Tree Predictor}{36}% -\contentsline {section}{\numberline {5.4}Statistical model for Machine Learning}{37}% -\contentsline {chapter}{\numberline {6}Lecture 6 - 24-03-2020}{39}% -\contentsline {section}{\numberline {6.1}Bayes Optimal Predictor}{39}% -\contentsline {subsection}{\numberline {6.1.1}Square Loss}{40}% -\contentsline {subsection}{\numberline {6.1.2}Zero-one loss for binary classification}{41}% -\contentsline {section}{\numberline {6.2}Bayes Risk}{44}% -\contentsline {chapter}{\numberline {7}Lecture 7 - 30-03-2020}{46}% -\contentsline {section}{\numberline {7.1}Chernoff-Hoffding bound}{46}% -\contentsline {section}{\numberline {7.2}Union Bound}{47}% -\contentsline {section}{\numberline {7.3}Studying overfitting of a ERM}{51}% -\contentsline {chapter}{\numberline {8}Lecture 8 - 31-03-2020}{53}% -\contentsline {section}{\numberline {8.1}The problem of estimating risk in practise}{54}% -\contentsline {section}{\numberline {8.2}Cross-validation}{56}% -\contentsline {section}{\numberline {8.3}Nested cross validation}{58}% -\contentsline {chapter}{\numberline {9}Lecture 9 - 06-04-2020}{59}% -\contentsline {section}{\numberline {9.1}Tree predictors}{59}% -\contentsline {subsection}{\numberline {9.1.1}Catalan Number}{61}% -\contentsline {chapter}{\numberline {10}Lecture 10 - 07-04-2020}{65}% -\contentsline {section}{\numberline {10.1}TO BE DEFINE}{65}% -\contentsline {section}{\numberline {10.2}MANCANO 20 MINUTI DI LEZIONE}{65}% -\contentsline {section}{\numberline {10.3}Compare risk for zero-one loss}{67}% -\contentsline {chapter}{\numberline {11}Lecture 11 - 20-04-2020}{69}% -\contentsline {section}{\numberline {11.1}Analysis of $K_{NN}$}{69}% -\contentsline {subsection}{\numberline {11.1.1}Study of $K_{NN}$}{72}% -\contentsline {subsection}{\numberline {11.1.2}study of trees}{73}% -\contentsline {section}{\numberline {11.2}Non-parametric Algorithms}{74}% -\contentsline {subsection}{\numberline {11.2.1}Example of parametric algorithms}{75}% -\contentsline {chapter}{\numberline {12}Lecture 12 - 21-04-2020}{76}% -\contentsline {section}{\numberline {12.1}Non parametrics algorithms}{76}% -\contentsline {subsection}{\numberline {12.1.1}Theorem: No free lunch}{76}% -\contentsline {section}{\numberline {12.2}Highly Parametric Learning Algorithm}{78}% -\contentsline {subsection}{\numberline {12.2.1}Linear Predictors}{78}% -\contentsline {subsection}{\numberline {12.2.2}MinDisagreement}{82}% -\contentsline {chapter}{\numberline {13}Lecture 13 - 27-04-2020}{83}% -\contentsline {section}{\numberline {13.1}Linear prediction}{83}% -\contentsline {subsection}{\numberline {13.1.1}MinDisOpt}{83}% -\contentsline {section}{\numberline {13.2}The Perception Algorithm}{86}% -\contentsline {subsection}{\numberline {13.2.1}Perception convergence Theorem}{87}% -\contentsline {chapter}{\numberline {14}Lecture 14 - 28-04-2020}{90}% -\contentsline {section}{\numberline {14.1}Linear Regression}{90}% -\contentsline {subsection}{\numberline {14.1.1}The problem of linear regression}{90}% -\contentsline {subsection}{\numberline {14.1.2}Ridge regression}{91}% -\contentsline {section}{\numberline {14.2}Percetron}{92}% -\contentsline {subsection}{\numberline {14.2.1}Online Learning }{93}% -\contentsline {subsection}{\numberline {14.2.2}Online Gradiant Descent (OGD)}{95}% -\contentsline {chapter}{\numberline {15}Lecture 15 - 04-05-2020}{96}% -\contentsline {section}{\numberline {15.1}Regret analysis of OGD}{96}% -\contentsline {subsection}{\numberline {15.1.1}Projected OGD}{97}% -\contentsline {chapter}{\numberline {16}Lecture 16 - 05-05-2020}{98}% -\contentsline {chapter}{\numberline {17}Lecture 17 - 11-05-2020}{99}% -\contentsline {chapter}{\numberline {18}Lecture 18 - 12-05-2020}{100}% -\contentsline {section}{\numberline {18.1}Kernel functions}{100}% -\contentsline {subsection}{\numberline {18.1.1}Feature expansion}{100}% -\contentsline {subsection}{\numberline {18.1.2}Kernels implements feature expansion (Efficiently}{101}% -\contentsline {section}{\numberline {18.2}Gaussian Kernel}{102}% +\contentsline {chapter}{\numberline {1}Lecture 1 - 09-03-2020}{7}% +\contentsline {section}{\numberline {1.1}Introduction of the course}{7}% +\contentsline {section}{\numberline {1.2}Examples}{7}% +\contentsline {subsection}{\numberline {1.2.1}Spam filtering}{10}% +\contentsline {chapter}{\numberline {2}Lecture 2 - 10-03-2020}{11}% +\contentsline {section}{\numberline {2.1}Argomento}{11}% +\contentsline {section}{\numberline {2.2}Loss}{11}% +\contentsline {subsection}{\numberline {2.2.1}Absolute Loss}{11}% +\contentsline {subsection}{\numberline {2.2.2}Square Loss}{12}% +\contentsline {subsection}{\numberline {2.2.3}Example of information of square loss}{13}% +\contentsline {subsection}{\numberline {2.2.4}labels and losses}{14}% +\contentsline {subsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{16}% +\contentsline {chapter}{\numberline {3}Lecture 3 - 16-03-2020}{18}% +\contentsline {section}{\numberline {3.1}Overfitting}{20}% +\contentsline {subsection}{\numberline {3.1.1}Noise in the data}{20}% +\contentsline {section}{\numberline {3.2}Underfitting}{22}% +\contentsline {section}{\numberline {3.3}Nearest neighbour}{22}% +\contentsline {chapter}{\numberline {4}Lecture 4 - 17-03-2020}{25}% +\contentsline {section}{\numberline {4.1}Computing $h_{NN}$}{25}% +\contentsline {section}{\numberline {4.2}Tree Predictor}{27}% +\contentsline {chapter}{\numberline {5}Lecture 5 - 23-03-2020}{31}% +\contentsline {section}{\numberline {5.1}Tree Classifier}{31}% +\contentsline {section}{\numberline {5.2}Jensen’s inequality}{33}% +\contentsline {section}{\numberline {5.3}Tree Predictor}{37}% +\contentsline {section}{\numberline {5.4}Statistical model for Machine Learning}{38}% +\contentsline {chapter}{\numberline {6}Lecture 6 - 24-03-2020}{40}% +\contentsline {section}{\numberline {6.1}Bayes Optimal Predictor}{40}% +\contentsline {subsection}{\numberline {6.1.1}Square Loss}{41}% +\contentsline {subsection}{\numberline {6.1.2}Zero-one loss for binary classification}{42}% +\contentsline {section}{\numberline {6.2}Bayes Risk}{45}% +\contentsline {chapter}{\numberline {7}Lecture 7 - 30-03-2020}{47}% +\contentsline {section}{\numberline {7.1}Chernoff-Hoffding bound}{47}% +\contentsline {section}{\numberline {7.2}Union Bound}{48}% +\contentsline {section}{\numberline {7.3}Studying overfitting of a ERM}{52}% +\contentsline {chapter}{\numberline {8}Lecture 8 - 31-03-2020}{54}% +\contentsline {section}{\numberline {8.1}The problem of estimating risk in practise}{55}% +\contentsline {section}{\numberline {8.2}Cross-validation}{57}% +\contentsline {section}{\numberline {8.3}Nested cross validation}{59}% +\contentsline {chapter}{\numberline {9}Lecture 9 - 06-04-2020}{60}% +\contentsline {section}{\numberline {9.1}Tree predictors}{60}% +\contentsline {subsection}{\numberline {9.1.1}Catalan Number}{62}% +\contentsline {chapter}{\numberline {10}Lecture 10 - 07-04-2020}{66}% +\contentsline {section}{\numberline {10.1}TO BE DEFINE}{66}% +\contentsline {section}{\numberline {10.2}MANCANO 20 MINUTI DI LEZIONE}{66}% +\contentsline {section}{\numberline {10.3}Compare risk for zero-one loss}{68}% +\contentsline {chapter}{\numberline {11}Lecture 11 - 20-04-2020}{70}% +\contentsline {section}{\numberline {11.1}Analysis of $K_{NN}$}{70}% +\contentsline {subsection}{\numberline {11.1.1}Study of $K_{NN}$}{73}% +\contentsline {subsection}{\numberline {11.1.2}study of trees}{74}% +\contentsline {section}{\numberline {11.2}Non-parametric Algorithms}{75}% +\contentsline {subsection}{\numberline {11.2.1}Example of parametric algorithms}{76}% +\contentsline {chapter}{\numberline {12}Lecture 12 - 21-04-2020}{77}% +\contentsline {section}{\numberline {12.1}Non parametrics algorithms}{77}% +\contentsline {subsection}{\numberline {12.1.1}Theorem: No free lunch}{77}% +\contentsline {section}{\numberline {12.2}Highly Parametric Learning Algorithm}{79}% +\contentsline {subsection}{\numberline {12.2.1}Linear Predictors}{79}% +\contentsline {subsection}{\numberline {12.2.2}MinDisagreement}{83}% +\contentsline {chapter}{\numberline {13}Lecture 13 - 27-04-2020}{84}% +\contentsline {section}{\numberline {13.1}Linear prediction}{84}% +\contentsline {subsection}{\numberline {13.1.1}MinDisOpt}{84}% +\contentsline {section}{\numberline {13.2}The Perception Algorithm}{87}% +\contentsline {subsection}{\numberline {13.2.1}Perception convergence Theorem}{88}% +\contentsline {chapter}{\numberline {14}Lecture 14 - 28-04-2020}{91}% +\contentsline {section}{\numberline {14.1}Linear Regression}{91}% +\contentsline {subsection}{\numberline {14.1.1}The problem of linear regression}{91}% +\contentsline {subsection}{\numberline {14.1.2}Ridge regression}{92}% +\contentsline {section}{\numberline {14.2}Percetron}{93}% +\contentsline {subsection}{\numberline {14.2.1}Online Learning }{94}% +\contentsline {subsection}{\numberline {14.2.2}Online Gradiant Descent (OGD)}{96}% +\contentsline {chapter}{\numberline {15}Lecture 15 - 04-05-2020}{97}% +\contentsline {section}{\numberline {15.1}Regret analysis of OGD}{97}% +\contentsline {subsection}{\numberline {15.1.1}Projected OGD}{98}% +\contentsline {chapter}{\numberline {16}Lecture 16 - 05-05-2020}{102}% +\contentsline {chapter}{\numberline {17}Lecture 17 - 11-05-2020}{103}% +\contentsline {chapter}{\numberline {18}Lecture 18 - 12-05-2020}{104}% +\contentsline {section}{\numberline {18.1}Kernel functions}{104}% +\contentsline {subsection}{\numberline {18.1.1}Feature expansion}{104}% +\contentsline {subsection}{\numberline {18.1.2}Kernels implements feature expansion (Efficiently}{105}% +\contentsline {section}{\numberline {18.2}Gaussian Kernel}{106}%

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