diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture2.tex b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture2.tex index bbf57446d..a50f853e9 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture2.tex +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture2.tex @@ -1,3 +1,6 @@ +\documentclass[../main.tex]{subfiles} + +\begin{document} \section{Lecture 2 - 07-04-2020} \subsection{Argomento} @@ -193,3 +196,5 @@ We want to replace this process with a predictor (so we don’t have to bored a person).\\ y is the ground truth for x $\rightarrow$ mean reality!\\ If i want to predict stock for tomorrow, i will wait tomorrow to see the ground truth. + +\end{document} \ No newline at end of file diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.log b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.log index d01c8103d..9dfd39648 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.log +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 2020.4.12) 12 APR 2020 15:16 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 2020.4.12) 12 APR 2020 15:20 entering extended mode **./lecture3.tex (lecture3.tex @@ -354,7 +354,7 @@ MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmsy10.pfb> -Output written on lecture3.pdf (6 pages, 135512 bytes). +Output written on lecture3.pdf (6 pages, 135258 bytes). 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Learning/lectures/lecture3.synctex.gz index 9a4cb0b27..4a3e67dc8 100644 Binary files a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.synctex.gz and b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.synctex.gz differ diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.tex b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.tex index 0891f38ab..dc1248325 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.tex +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture3.tex @@ -210,9 +210,9 @@ $\hat{y} = + \quad or \quad \hat{y} = - $ \\\ I can came up with some sort of classifier. \\\\ -Given $S$ training set, i can define $h_NN X \rightarrow \{-1,1\}\\ +Given $S$ training set, i can define $\hnn$ $X \rightarrow \{-1,1\}\\ $ -$h_NN(x) = $ label $y_t$ of the point $x_t$ in $S$ closest to $X$\\ +$\hnn(x) = $ label $y_t$ of the point $x_t$ in $S$ closest to $X$\\ \textbf{(the breaking rule for ties)} \\ For the closest we mean euclidian distance diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.aux b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.aux new file mode 100644 index 000000000..ccee5d354 --- /dev/null +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.aux @@ -0,0 +1,4 @@ +\relax +\@writefile{toc}{\contentsline {section}{\numberline {1}Lecture 4 - 07-04-2020}{1}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Computing $h_{NN}$}{1}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Tree Predictor}{2}\protected@file@percent } diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.log b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.log new file mode 100644 index 000000000..90305c222 --- /dev/null +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.log @@ -0,0 +1,292 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 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Second point doesn’t switch and third will +be classify to positive and we have training mistake.\\ +Switches corresponds to border of voronoi partition. +$$\knn \qquad \textit{For multiclass classification}$$\\ +$$ +(|Y| > 2 ) \qquad \textit{for regression } Y\equiv \barra{R} +$$ +\\ +Average of labels of $K$ neighbours $\rightarrow$ i will get a number with prediction. +\\ +I can weight average by distance +\\ +You can vary this algorithm as you want.\\\\ +Let’s go back to Binary classification.\\ +The $k$ parameter is the effect of making the structure of classifier more +complex and less complex for small value of $k$.\\\\ +--.. DISEGNO ..-- +\\ +Fix training set and test set\\ +Accury as oppose to the error +\\\\ +Show a plot. Training error is 0 at $k = 0$.\\ +As i go further training error is higher and test error goes down. At some point +after which training and set met and then after that training and test error goes +up (accuracy goes down).\\ +If i run algorithm is going to be overfitting: training error and test error is high and also underfitting since testing and training are close and both high. +Trade off point is the point in $x = 23$ (more or less).\\ +There are some heuristic to run NN algorithm without value of $k$. +\\\\ +\textbf{History} +\begin{itemize} +\item $\knn$: from 1960 $\rightarrow$ $X \equiv \barra{R}^d$ +\item Tree predictor: from 1980 +\\ +\end{itemize} + +\subsection{Tree Predictor} +If a give you data not welled defined in a Euclidean space. +\\ +$X = X_1 \cdot x \cdot ... \cdot X_d \cdot x$ \qquad Medical Record +\\ +$X_1 = \{Male, Female\}$\\ +$X_2 = \{Yes, No\}$ +\\ +so we have different data +\\\\ +I want to avoid comparing $x_i$ with $x_j$, $i\neq j $\\ +so comparing different feature and we want to compare each feature with +each self. I don’t want to mix them up.\\ +We can use a tree! +\\ +I have 3 features: +\begin{itemize} +\item outlook $= \{sunny, overcast, rain\}$ +\item humidity $= \{[0,100]\}$ +\item windy $ = \{yes,no\}$ +\end{itemize} +... -- DISEGNO -- ...\\\\ +Tree is a natural way of doing decision and abstraction of decision process of +one person. It is a good way to deal with categorical variables.\\ +What kind of tree we are talking about?\\ +Tree has inner node and leaves. Leaves are associated with labels $(Y)$ and +inner nodes are associated with test. +\begin{itemize} +\item Inner node $\rightarrow$ test +\item Leaves $\rightarrow$ label in Y +\end{itemize} +%... -- DISEGNO -- ... +Test if a function $f$ (NOT A PREDICTOR!) \\ +Test $ \qquad f_i \, X_i \rightarrow \{1,...,k\}$ +\\ where $k$ is the number of children (inner node) to which test is assigned +\\ +In a tree predictor we have: +\begin{itemize} +\item Root node +\item Children are ordered(i know the order of each branch that come out from the node) +\end{itemize} +$$ +X = \{Sunny, 50\%, No \} \quad \rightarrow \quad \textit{are the parameters for } \{outlook. humidity, windy \} +$$ +\\ +$ +f_i = +\begin{cases} +1, & \mbox{if } x_2 \in [30 \%,60 \% ] +\\ +2, & \mbox{if } otherwise \end{cases} +$ +\\ where the numbers 1 and 2 are the children +\\ +A test is partitioning the range of values of a certain attribute in a number of +elements equal to number of children of of the node to which the test is +assigned. +\\ +$h_T(x)$ is always the label of a leaf of T\\ +This leaf is the leaf to which $x$ is \textbf{routed} +\\ +Data space for this problem (outlook,..) is partitioned in the leaves of the tree. +It won’t be like voronoi graph. +How do I build a tree given a training set? +How do i learn a tree predictor given a training set? +\begin{itemize} +\item Decide tree structure (how • many node, leaves ecc..) +\item Decide test on inner nodes +\item Decide labels on leaves +\end{itemize} +We have to do this all together and process will be more dynamic. +For simplicity binary classification and fix two children for each inner node.\\\\ +$ Y = \{-1, +1 \}$ +\\ $2$ children for each inner node +\\\\ +What's the simplest way?\\ +Initial tree and correspond to a costant classifier +\\\\ +-- DISEGNO -- +\\\\ +\textbf{Majority of all example} +\\\\ +-- DISEGNO -- +\\\\ +$(x_1, y_1) ... (x_m, y_m)$ \\ +$ x_t \in X$ \qquad $ y_t \in \{-1,+1\}$\\ +Training set $S = \{ (x,y) \in S$, x is routed to $\ell\}$\\ +$S_{\ell}^+$ +\\\\ +-- DISEGNO -- +\\\\ +$ S_{\ell}$ and $ S’_{\ell}$ are given by the result of the test, not the labels and $\ell$ and $\ell'$. +\end{document} \ No newline at end of file diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log index db0c92b86..1b5000a6b 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 2020.4.12) 12 APR 2020 15:12 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 2020.4.12) 12 APR 2020 15:21 entering extended mode **./main.tex (main.tex @@ -177,111 +177,111 @@ Underfull \hbox (badness 10000) in paragraph at lines 99--139 [] [4]) [5] (lectures/lecture2.tex -Underfull \hbox (badness 10000) in paragraph at lines 4--13 +Underfull \hbox (badness 10000) in paragraph at lines 7--16 [] -Underfull \hbox (badness 10000) in paragraph at lines 14--27 +Underfull \hbox (badness 10000) in paragraph at lines 17--30 [] -Underfull \hbox (badness 10000) in paragraph at lines 14--27 +Underfull \hbox (badness 10000) in paragraph at lines 17--30 [] -Underfull \hbox (badness 10000) in paragraph at lines 29--32 +Underfull \hbox (badness 10000) in paragraph at lines 32--35 [] [6] -Underfull \hbox (badness 10000) in paragraph at lines 46--49 +Underfull \hbox (badness 10000) in paragraph at lines 49--52 [] -Underfull \hbox (badness 10000) in paragraph at lines 46--49 +Underfull \hbox (badness 10000) in paragraph at lines 49--52 [] -Underfull \hbox (badness 10000) in paragraph at lines 60--78 +Underfull \hbox (badness 10000) in paragraph at lines 63--81 [] [7] -Underfull \hbox (badness 10000) in paragraph at lines 78--83 +Underfull \hbox (badness 10000) in paragraph at lines 81--86 [] -Underfull \hbox (badness 10000) in paragraph at lines 86--106 +Underfull \hbox (badness 10000) in paragraph at lines 89--109 [] -Underfull \hbox (badness 10000) in paragraph at lines 86--106 +Underfull \hbox (badness 10000) in paragraph at lines 89--109 [] -Underfull \hbox (badness 10000) in paragraph at lines 86--106 +Underfull \hbox (badness 10000) in paragraph at lines 89--109 [] -Underfull \hbox (badness 10000) in paragraph at lines 107--112 +Underfull \hbox (badness 10000) in paragraph at lines 110--115 [] [8] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] -Underfull \hbox (badness 10000) in paragraph at lines 115--153 +Underfull \hbox (badness 10000) in paragraph at lines 118--156 [] [9] -Underfull \hbox (badness 10000) in paragraph at lines 161--168 +Underfull \hbox (badness 10000) in paragraph at lines 164--171 [] [10] -Underfull \hbox (badness 10000) in paragraph at lines 169--179 +Underfull \hbox (badness 10000) in paragraph at lines 172--182 [] -) -Underfull \hbox (badness 10000) in paragraph at lines 186--33 + +Underfull \hbox (badness 10000) in paragraph at lines 189--199 [] -[11] (lectures/lecture3.tex +) [11] (lectures/lecture3.tex Underfull \hbox (badness 10000) in paragraph at lines 5--7 [] @@ -457,7 +457,12 @@ Underfull \hbox (badness 10000) in paragraph at lines 187--223 [] -[16]) [17] (lectures/lecture4.tex) [18] (lectures/lecture5.tex) [19] +[16] +Underfull \hbox (badness 10000) in paragraph at lines 225--226 + + [] + +) [17] (lectures/lecture4.tex) [18] (lectures/lecture5.tex) [19] (lectures/lecture6.tex) [20] (lectures/lecture7.tex) [21] (lectures/lecture8.tex) [22] (lectures/lecture9.tex) [23] (lectures/lecture10.tex @@ -561,7 +566,7 @@ c/amsfonts/cm/cmsy6.pfb> -Output written on main.pdf (27 pages, 198551 bytes). +Output written on main.pdf (27 pages, 198691 bytes). 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