From 7e652dabff0e4b8b4c0c2e4534284cfc5c7f188b Mon Sep 17 00:00:00 2001 From: mhjensen Date: Sat, 2 Nov 2019 17:47:47 +0100 Subject: [PATCH] material to decision tree --- .../html/DecisionTrees-reveal.html | 31 ++++++++++++++++ .../html/DecisionTrees-solarized.html | 29 +++++++++++++++ doc/pub/DecisionTrees/html/DecisionTrees.html | 29 +++++++++++++++ .../DecisionTrees/ipynb/DecisionTrees.ipynb | 33 ++++++++++++++++++ .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 195 -> 194 bytes .../pdf/DecisionTrees-minted.pdf | Bin 274455 -> 285062 bytes doc/src/DecisionTrees/DecisionTrees.do.txt | 23 ++++++++++++ 7 files changed, 145 insertions(+) diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html index 5b1289cc6..92835cc5e 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html @@ -1800,11 +1800,42 @@ Example will be added here.

Boosting, a Bird'e Eye

+ +

+The basic idea is to combine weak classifiers in order to create a good +classifier. With a weak classifier we often intend a classifier which +produces results which are only slightly better than we would get by +random guesses. + +

+This is done by applying in an iterative way a weak (or a standard +classifier like decision trees) to modify the data. In each iteration +we emphasize those observations which are misclassified by weighting +them with a factor.

Adaptive boosting: AdaBoost, Basic Algorithm

+ +

+The algorithm here is rather straightforward. Assume that our weak +classifier is a decision tree and we consider a binary set of outputs +with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of +observations. Our design matrix is given in terms of the +feature/predictor vectors +\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1} \). Finally, we define also a +classifier determined by our data via a function \( G(\boldsymbol{X}) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \). + +

+We can then define the misclassification error \( \mathrm{err} \) as +

 
+$$ +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(\boldsymbol{X}_{i*}), +$$ +

 
+ +where the function \( I() \) is one if we misclassify and zero if we classify correctly.

diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html index 160958595..a1f7b3344 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -1778,11 +1778,40 @@ Example will be added here.

Boosting, a Bird'e Eye

+

+The basic idea is to combine weak classifiers in order to create a good +classifier. With a weak classifier we often intend a classifier which +produces results which are only slightly better than we would get by +random guesses. + +

+This is done by applying in an iterative way a weak (or a standard +classifier like decision trees) to modify the data. In each iteration +we emphasize those observations which are misclassified by weighting +them with a factor. +











Adaptive boosting: AdaBoost, Basic Algorithm

+

+The algorithm here is rather straightforward. Assume that our weak +classifier is a decision tree and we consider a binary set of outputs +with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of +observations. Our design matrix is given in terms of the +feature/predictor vectors +\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1} \). Finally, we define also a +classifier determined by our data via a function \( G(\boldsymbol{X}) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \). + +

+We can then define the misclassification error \( \mathrm{err} \) as +$$ +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(\boldsymbol{X}_{i*}), +$$ + +where the function \( I() \) is one if we misclassify and zero if we classify correctly. +











diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html index dc47b1555..f6c752b84 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -1783,11 +1783,40 @@ Example will be added here.

Boosting, a Bird'e Eye

+

+The basic idea is to combine weak classifiers in order to create a good +classifier. With a weak classifier we often intend a classifier which +produces results which are only slightly better than we would get by +random guesses. + +

+This is done by applying in an iterative way a weak (or a standard +classifier like decision trees) to modify the data. In each iteration +we emphasize those observations which are misclassified by weighting +them with a factor. +











Adaptive boosting: AdaBoost, Basic Algorithm

+

+The algorithm here is rather straightforward. Assume that our weak +classifier is a decision tree and we consider a binary set of outputs +with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of +observations. Our design matrix is given in terms of the +feature/predictor vectors +\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1} \). Finally, we define also a +classifier determined by our data via a function \( G(\boldsymbol{X}) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \). + +

+We can then define the misclassification error \( \mathrm{err} \) as +$$ +\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(\boldsymbol{X}_{i*}), +$$ + +where the function \( I() \) is one if we misclassify and zero if we classify correctly. +











diff --git a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb index 3739cfe22..5a6dac0b3 100644 --- a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb +++ b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb @@ -1825,11 +1825,44 @@ "\n", "## Boosting, a Bird'e Eye\n", "\n", + "The basic idea is to combine weak classifiers in order to create a good\n", + "classifier. With a weak classifier we often intend a classifier which\n", + "produces results which are only slightly better than we would get by\n", + "random guesses.\n", "\n", + "This is done by applying in an iterative way a weak (or a standard\n", + "classifier like decision trees) to modify the data. In each iteration\n", + "we emphasize those observations which are misclassified by weighting\n", + "them with a factor.\n", "\n", "\n", "## Adaptive boosting: AdaBoost, Basic Algorithm\n", "\n", + "The algorithm here is rather straightforward. Assume that our weak\n", + "classifier is a decision tree and we consider a binary set of outputs\n", + "with $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n", + "observations. Our design matrix is given in terms of the\n", + "feature/predictor vectors\n", + "$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}$. Finally, we define also a\n", + "classifier determined by our data via a function $G(\\boldsymbol{X})$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n", + "\n", + "We can then define the misclassification error $\\mathrm{err}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(\\boldsymbol{X}_{i*}),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where the function $I()$ is one if we misclassify and zero if we classify correctly. \n", "\n", "## AdaBoost Examples" ] diff --git a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz index cc84654c373b9919009e62dbf1803a4e4fc3b795..b20c240525f08ab0d96a3909dc91c658e915c020 100644 GIT binary patch delta 174 zcmV;f08#(L0m1!6n&!iv z`4xEPpD0^lV6z)+t0YKeu~O;`IUa-&N|qYYM4}sH1+_vmHbCR87aD=f0eD>t>x%pm cc3K@ZznUog^-rGXdER#q2y7a?FaQVu0KI=p7ytkO delta 175 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