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the label associated with x\\ Learning with example $(x_1,y_1)...(x_m,y_m) \quad \textit{training set} $\\\\ Training set is a set of examples with every algorithm can learn.......\\\\ Learning algorithm take training set as input and produces a predictor as output.\\\\ - ......DISEGNO \\\\ -With image recognition we use as measurement pixels.\\ +\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.8\linewidth]{../img/lez3-img1.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ +\\With image recognition we use as measurement pixels.\\ How do we measure the power of a predictor?\\ A learning algorithm will look at training set, algorithm and generate the predictor. Now the problem is verify the score. \\ Now we can consider a test set collection of example @@ -194,20 +200,29 @@ $ S is the traning set $(x_1,y_1)...(x_m,y_m) \\ x_t \in \barra{R}^d \qquad y_t \in \{-1,1\} \\\\ d = 2 \rightarrow \textit{2-dimensional vector}\\ $\\ -....-- DISEGNO --... -\\ where + and - are labels -\\\\ +\newpage \textbf{Point of test set} \\ If i want to predict this point? +\begin{figure}[h] + \centering + \includegraphics[width=0.4\linewidth]{../img/lez3-img2.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure} \\ Maybe if point is close to point with label i know then. Maybe they have the same label. \\ $\hat{y} = + \quad or \quad \hat{y} = - $ \\\\ -.....-- DISEGNO -- ... -\\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.4\linewidth]{../img/lez3-img3.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ +\\ I can came up with some sort of classifier. \\\\ Given $S$ training set, i can define $\hnn$ $X \rightarrow \{-1,1\}\\ 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 index ccee5d354..16779b5c9 100644 --- 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 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100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.tex +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture4.tex @@ -49,8 +49,12 @@ 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 ..-- -\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.4\linewidth]{../img/lez4-img1.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ Fix training set and test set\\ Accury as oppose to the error \\\\ @@ -83,6 +87,12 @@ 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! +\begin{figure}[h] + \centering + \includegraphics[width=0.5\linewidth]{../img/lez4-img2.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ \\ I have 3 features: \begin{itemize} @@ -90,17 +100,21 @@ I have 3 features: \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{figure}[h] + \centering + \includegraphics[width=0.3\linewidth]{../img/lez4-img3.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ \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 @@ -146,19 +160,37 @@ $ Y = \{-1, +1 \}$ \\\\ What's the simplest way?\\ Initial tree and correspond to a costant classifier -\\\\ --- DISEGNO -- -\\\\ +\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.2\linewidth]{../img/lez4-img4.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ \textbf{Majority of all example} -\\\\ --- DISEGNO -- -\\\\ +\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.2\linewidth]{../img/lez4-img5.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ $(x_1, y_1) ... (x_m, y_m)$ \\ $ 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 $\ell'$. +\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.8\linewidth]{../img/lez4-img6.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure}\\ +$ S_{\ell}$ and $ S’_{\ell}$ are given by the result of the test, not the labels and $\ell$ and $\ell'$.\\ +\begin{figure}[h] + \centering + \includegraphics[width=0.7\linewidth]{../img/lez4-img7.JPG} + \caption{Example of domain of $\knn$} + %\label{fig:} +\end{figure} \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/lecture5.aux b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial 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LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. @@ -1605,122 +253,52 @@ LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. -LaTeX Font Info: Checking defaults for U/ntxexa/m/n on input line 2. -LaTeX Font Info: Trying to load font information for U+ntxexa on input line -2. - -("C:\Program Files\MiKTeX 2.9\tex/latex/newtx\untxexa.fd" -File: untxexa.fd 2012/04/16 Fontinst v1.933 font definitions for U/ntxexa. -) +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 2. 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