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sec-4: change order of images

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Aleso add a ε=0.5 plot in the KDE slide.
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Giù Marcer 2020-06-12 22:18:11 +02:00 committed by rnhmjoj
parent 9476aab2f1
commit e02e4a9557
1 changed files with 109 additions and 110 deletions
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slides/sections/4.md
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@ -20,48 +20,46 @@ How to estimate sample median, mode and FWHM?
\Begin{block}{Algorithm} \Begin{block}{Algorithm}
::: incremental ::: incremental
1. Sort sample in ascending order 1. Sample points
2. 2. Sort sample in ascending order
3.
Take middle element if odd Take middle element if odd
Take average of two middle elements if even Take average of two middle elements if even
::: :::
\End{block} \End{block}
. . .
\setbeamercovered{} \setbeamercovered{}
\begin{center} \begin{center}
\begin{tikzpicture}[remember picture, >=Stealth] \begin{tikzpicture}[remember picture, >=Stealth]
% place holder
\draw [ultra thick, white] (-0.35,0.7) -- (-0.35,-0.7);
% line % line
\draw [line width=3, ->, cyclamen] (-5,0) -- (5,0); \draw <1-> [line width=3, ->, cyclamen] (-5,0) -- (5,0);
\node [right] at (5,0) {$x$}; \node <1-> [right] at (5,0) {$x$};
% points % points
\draw [yellow!50!black, fill=yellow] (-4.6,-0.1) rectangle (-4.8,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-4.6,-0.1) rectangle (-4.8,0.1);
\draw [yellow!50!black, fill=yellow] (-4,-0.1) rectangle (-4.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-4,-0.1) rectangle (-4.2,0.1);
\draw [yellow!50!black, fill=yellow] (-3.3,-0.1) rectangle (-3.5,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-3.3,-0.1) rectangle (-3.5,0.1);
\draw [yellow!50!black, fill=yellow] (-2.3,-0.1) rectangle (-2.5,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-2.3,-0.1) rectangle (-2.5,0.1);
\draw [yellow!50!black, fill=yellow] (-0.6,-0.1) rectangle (-0.8,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-0.6,-0.1) rectangle (-0.8,0.1);
\draw [yellow!50!black, fill=yellow] (-0.1,-0.1) rectangle (0.1,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-0.1,-0.1) rectangle (0.1,0.1);
\draw [yellow!50!black, fill=yellow] (1.1,-0.1) rectangle (1.3,0.1); \draw <1-> [yellow!50!black, fill=yellow] (1.1,-0.1) rectangle (1.3,0.1);
\draw [yellow!50!black, fill=yellow] (2,-0.1) rectangle (2.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (2,-0.1) rectangle (2.2,0.1);
\draw [yellow!50!black, fill=yellow] (2.7,-0.1) rectangle (2.9,0.1); \draw <1-> [yellow!50!black, fill=yellow] (2.7,-0.1) rectangle (2.9,0.1);
\draw [yellow!50!black, fill=yellow] (4,-0.1) rectangle (4.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (4,-0.1) rectangle (4.2,0.1);
\pause
% nodes % nodes
\node [below] at (-4.7,-0.1) {1}; \node <2-> [below] at (-4.7,-0.1) {1};
\node [below] at (-4.1,-0.1) {2}; \node <2-> [below] at (-4.1,-0.1) {2};
\node [below] at (-3.4,-0.1) {3}; \node <2-> [below] at (-3.4,-0.1) {3};
\node [below] at (-2.4,-0.1) {4}; \node <2-> [below] at (-2.4,-0.1) {4};
\node [below] at (-0.7,-0.1) {5}; \node <2-> [below] at (-0.7,-0.1) {5};
\node [below] at ( 0 ,-0.1) {6}; \node <2-> [below] at ( 0 ,-0.1) {6};
\node [below] at ( 1.2,-0.1) {7}; \node <2-> [below] at ( 1.2,-0.1) {7};
\node [below] at ( 2.1,-0.1) {8}; \node <2-> [below] at ( 2.1,-0.1) {8};
\node [below] at ( 2.8,-0.1) {9}; \node <2-> [below] at ( 2.8,-0.1) {9};
\node [below] at ( 4.1,-0.1) {10}; \node <2-> [below] at ( 4.1,-0.1) {10};
\pause \draw <3-> [ultra thick] (-0.35,0.7) -- (-0.35,-0.7);
\draw [ultra thick] (-0.35,0.7) -- (-0.35,-0.7);
\end{tikzpicture} \end{tikzpicture}
\end{center} \end{center}
\setbeamercovered{transparent} \setbeamercovered{transparent}
@ -73,67 +71,42 @@ How to estimate sample median, mode and FWHM?
\Begin{block}{Algorithm} \Begin{block}{Algorithm}
::: incremental ::: incremental
1. Find the smallest interval containing half points 1. Sample points
2. Repeat on the new interval (called modal) 2. Find the smallest interval containing half points
3. If the interval has less than two points, take average 3. Repeat on the new interval (iterative)
4. If less than four points, take average of the closest two
::: :::
\End{block} \End{block}
. . .
\centering \centering
\setbeamercovered{} \setbeamercovered{}
\begin{tikzpicture}[remember picture, >=Stealth] \begin{tikzpicture}[remember picture, >=Stealth]
% line % line
\draw [line width=3, ->, cyclamen] (-5,0) -- (5,0); \draw <1-> [line width=3, ->, cyclamen] (-5,0) -- (5,0);
\node [right] at (5,0) {$x$}; \node <1-> [right] at (5,0) {$x$};
% points % points
\draw [yellow!50!black, fill=yellow] (-4.6,-0.1) rectangle (-4.8,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-4.6,-0.1) rectangle (-4.8,0.1);
\draw [yellow!50!black, fill=yellow] (-4,-0.1) rectangle (-4.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-4,-0.1) rectangle (-4.2,0.1);
\draw [yellow!50!black, fill=yellow] (-3.3,-0.1) rectangle (-3.5,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-3.3,-0.1) rectangle (-3.5,0.1);
\draw [yellow!50!black, fill=yellow] (-2.3,-0.1) rectangle (-2.5,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-2.3,-0.1) rectangle (-2.5,0.1);
\draw [yellow!50!black, fill=yellow] (-0.6,-0.1) rectangle (-0.8,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-0.6,-0.1) rectangle (-0.8,0.1);
\draw [yellow!50!black, fill=yellow] (-0.1,-0.1) rectangle (0.1,0.1); \draw <1-> [yellow!50!black, fill=yellow] (-0.1,-0.1) rectangle (0.1,0.1);
\draw [yellow!50!black, fill=yellow] (1.1,-0.1) rectangle (1.3,0.1); \draw <1-> [yellow!50!black, fill=yellow] (1.1,-0.1) rectangle (1.3,0.1);
\draw [yellow!50!black, fill=yellow] (2,-0.1) rectangle (2.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (2,-0.1) rectangle (2.2,0.1);
\draw [yellow!50!black, fill=yellow] (2.7,-0.1) rectangle (2.9,0.1); \draw <1-> [yellow!50!black, fill=yellow] (2.7,-0.1) rectangle (2.9,0.1);
\draw [yellow!50!black, fill=yellow] (4,-0.1) rectangle (4.2,0.1); \draw <1-> [yellow!50!black, fill=yellow] (4,-0.1) rectangle (4.2,0.1);
% future nodes % nodes
\node at (-1,-0.3) (1a) {}; \node <1-> at (-1,-0.3) (1a) {};
\node at (3.1,0.3) (1b) {}; \node <1-> at (3.1,0.3) (1b) {};
\node at (0.9,-0.3) (2a) {}; \node <1-> at (0.9,-0.3) (2a) {};
\node at (1.8,-0.3) (3a) {}; \node <1-> at (1.8,-0.3) (3a) {};
% result nodes \node <1-> at (2.45,-0.7) (f1) {};
\node at (2.45,-0.7) (f1) {}; \node <1-> at (2.45,0.7) (f2) {};
\node at (2.45,0.7) (f2) {}; % algorithm
\end{tikzpicture} \draw <2-> [gray, fill=gray, opacity=0.5] (1a) rectangle (1b);
\draw <3-> [gray, fill=gray, opacity=0.6] (2a) rectangle (1b);
. . . \draw <4-> [cyclamen, thick] (3a) rectangle (1b);
\draw <5-> [ultra thick] (f1) -- (f2);
\begin{tikzpicture}[remember picture, overlay]
% region
\draw [gray, fill=gray, opacity=0.5] (1a) rectangle (1b);
\end{tikzpicture}
. . .
\begin{tikzpicture}[remember picture, overlay]
% region
\draw [gray, fill=gray, opacity=0.6] (2a) rectangle (1b);
\end{tikzpicture}
. . .
\begin{tikzpicture}[remember picture, overlay]
% region
\draw [gray, fill=gray, opacity=0.7] (3a) rectangle (1b);
\end{tikzpicture}
. . .
\begin{tikzpicture}[remember picture, overlay]
% region
\draw [ultra thick] (f1) -- (f2);
\end{tikzpicture} \end{tikzpicture}
@ -157,41 +130,67 @@ $$
G \left( \frac{x-x_i}{\varepsilon} \right) G \left( \frac{x-x_i}{\varepsilon} \right)
$$ $$
- The parameter $\varepsilon$ controls the strength of the smoothing - The parameter $\varepsilon$ controls the
sharpness of the empirical PDF
::: :::
::: {.column width=50%} ::: {.column width=50%}
\setbeamercovered{} \setbeamercovered{}
\begin{center} \begin{center}
\begin{tikzpicture} \begin{tikzpicture}
% placeholder
\draw [white] (-2.7,-0.2) rectangle (3,3.3);
% bandwidth 1
\node <4,5> [left] at (2.9,3) {$\epsilon = 1$};
% points % points
\draw [yellow!50!black, fill=yellow] (-2,-0.1) rectangle (-1.8,0.1); \draw <3-> [yellow!50!black, fill=yellow] (-1.2,-0.2) rectangle (-1,0);
\draw [yellow!50!black, fill=yellow] (-0.1,-0.1) rectangle (0.1,0.1); \draw <3-> [yellow!50!black, fill=yellow] (-0.1,-0.2) rectangle (0.1,0);
\draw [yellow!50!black, fill=yellow] (1.3,-0.1) rectangle (1.5,0.1); \draw <3-> [yellow!50!black, fill=yellow] (0.7,-0.2) rectangle (0.9,0);
\draw [yellow!50!black, fill=yellow] (0.7,-0.1) rectangle (0.9,0.1); \draw <3-> [yellow!50!black, fill=yellow] (1.3,-0.2) rectangle (1.5,0);
\pause % lines 1
% lines \draw <4,5> [cyclamen, dashed] (-1.1,0.1) -- (-1.1,1);
\draw [cyclamen, dashed] (-1.9,0.1) -- (-1.9,1); \draw <4,5> [cyclamen, dashed] (0,0.1) -- (0,1);
\draw [cyclamen, dashed] (0,0.1) -- (0,1); \draw <4,5> [cyclamen, dashed] (1.4,0.1) -- (1.4,1);
\draw [cyclamen, dashed] (1.4,0.1) -- (1.4,1); \draw <4,5> [cyclamen, dashed] (0.8,0.1) -- (0.8,1);
\draw [cyclamen, dashed] (0.8,0.1) -- (0.8,1); % Gaussians 1
% Gaussians \draw <4,5> [domain=-2.6:0.4, smooth, variable=\x, cyclamen, very thick]
\draw[domain=-3.4:-0.4, smooth, variable=\x, cyclamen, very thick] plot ({\x}, {exp(-(\x + 1.1)*(\x + 1.1)) + 0.1});
plot ({\x}, {exp(-(\x + 1.9)*(\x + 1.9)) + 0.1}); \draw <4,5> [domain=-1.5:1.5, smooth, variable=\x, cyclamen, very thick]
\draw[domain=-1.5:1.5, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-\x*\x + 0.1}); plot ({\x}, {exp(-\x*\x + 0.1});
\draw[domain=-0.1:2.9, smooth, variable=\x, cyclamen, very thick] \draw <4,5> [domain=-0.7:2.3, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 1.4)*(\x - 1.4)) + 0.1});
\draw[domain=-0.7:2.3, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 0.8)*(\x - 0.8)) + 0.1}); plot ({\x}, {exp(-(\x - 0.8)*(\x - 0.8)) + 0.1});
\pause \draw <4,5> [domain=-0.1:2.9, smooth, variable=\x, cyclamen, very thick]
% sum plot ({\x}, {exp(-(\x - 1.4)*(\x - 1.4)) + 0.1});
\draw [fill=white, white, opacity=0.5] (-3.5,0.1) rectangle (3,1.3); % sum 1
\draw[domain=-3.4:3.4, smooth, variable=\x, yellow, very thick] \draw <5> [fill=white, white, opacity=0.5] (-2.7,0.1) rectangle (3,2.7);
plot ({\x}, {exp(-(\x + 1.9)*(\x + 1.9)) + \draw <5> [domain=-2.6:2.9, smooth, variable=\x, yellow, very thick]
plot ({\x}, {exp(-(\x + 1.1)*(\x + 1.1)) +
exp(-\x*\x) + exp(-\x*\x) +
exp(-(\x - 1.4)*(\x - 1.4)) + exp(-(\x - 1.4)*(\x - 1.4)) +
exp(-(\x - 0.8)*(\x - 0.8)) + 0.1}); exp(-(\x - 0.8)*(\x - 0.8)) + 0.1});
% bandwidth 2
\node <6> [left] at (2.9,3) {$\epsilon = 0.5$};
% lines 2
\draw <6> [cyclamen, dashed] (-1.1,0.1) -- (-1.1,2);
\draw <6> [cyclamen, dashed] (0,0.1) -- (0,2);
\draw <6> [cyclamen, dashed] (1.4,0.1) -- (1.4,2);
\draw <6> [cyclamen, dashed] (0.8,0.1) -- (0.8,2);
% Gaussians 2
\draw <6> [domain=-2.6:0.4, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x + 1.1)*(\x + 1.1)/0.25)/0.5 + 0.1});
\draw <6> [domain=-1.5:1.5, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-\x*\x/0.25)/0.5 + 0.1});
\draw <6> [domain=-0.7:2.3, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 0.8)*(\x - 0.8)/0.25)/0.5 + 0.1});
\draw <6> [domain=-0.1:2.9, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 1.4)*(\x - 1.4)/0.25)/0.5 + 0.1});
% sum
\draw <6> [fill=white, white, opacity=0.5] (-2.7,0.1) rectangle (3,2.7);
\draw <6> [domain=-2.6:2.9, smooth, variable=\x, yellow, very thick]
plot ({\x}, {exp(-(\x + 1.1)*(\x + 1.1)/0.25)/0.5 +
exp(-\x*\x/0.25)/0.5 +
exp(-(\x - 1.4)*(\x - 1.4)/0.25)/0.5 +
exp(-(\x - 0.8)*(\x - 0.8)/0.25)/0.5 + 0.1});
\end{tikzpicture} \end{tikzpicture}
\end{center} \end{center}
\setbeamercovered{transparent} \setbeamercovered{transparent}