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"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">AdaBoost</span><span class=\"p\">(</span><span class=\"n\">L</span><span class=\"p\">,</span> <span class=\"n\">K</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 18.34]"""</span>\n",
" <span class=\"k\">def</span> <span class=\"nf\">train</span><span class=\"p\">(</span><span class=\"n\">dataset</span><span class=\"p\">):</span>\n",
" <span class=\"n\">examples</span><span class=\"p\">,</span> <span class=\"n\">target</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">examples</span><span class=\"p\">,</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">target</span>\n",
" <span class=\"n\">N</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">examples</span><span class=\"p\">)</span>\n",
" <span class=\"n\">epsilon</span> <span class=\"o\">=</span> <span class=\"mf\">1.</span> <span class=\"o\">/</span> <span class=\"p\">(</span><span class=\"mi\">2</span> <span class=\"o\">*</span> <span class=\"n\">N</span><span class=\"p\">)</span>\n",
" <span class=\"n\">w</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mf\">1.</span> <span class=\"o\">/</span> <span class=\"n\">N</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">N</span>\n",
" <span class=\"n\">h</span><span class=\"p\">,</span> <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"p\">[],</span> <span class=\"p\">[]</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">K</span><span class=\"p\">):</span>\n",
" <span class=\"n\">h_k</span> <span class=\"o\">=</span> <span class=\"n\">L</span><span class=\"p\">(</span><span class=\"n\">dataset</span><span class=\"p\">,</span> <span class=\"n\">w</span><span class=\"p\">)</span>\n",
" <span class=\"n\">h</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">h_k</span><span class=\"p\">)</span>\n",
" <span class=\"n\">error</span> <span class=\"o\">=</span> <span class=\"nb\">sum</span><span class=\"p\">(</span><span class=\"n\">weight</span> <span class=\"k\">for</span> <span class=\"n\">example</span><span class=\"p\">,</span> <span class=\"n\">weight</span> <span class=\"ow\">in</span> <span class=\"nb\">zip</span><span class=\"p\">(</span><span class=\"n\">examples</span><span class=\"p\">,</span> <span class=\"n\">w</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">example</span><span class=\"p\">[</span><span class=\"n\">target</span><span class=\"p\">]</span> <span class=\"o\">!=</span> <span class=\"n\">h_k</span><span class=\"p\">(</span><span class=\"n\">example</span><span class=\"p\">))</span>\n",
" <span class=\"c1\"># Avoid divide-by-0 from either 0% or 100% error rates:</span>\n",
" <span class=\"n\">error</span> <span class=\"o\">=</span> <span class=\"n\">clip</span><span class=\"p\">(</span><span class=\"n\">error</span><span class=\"p\">,</span> <span class=\"n\">epsilon</span><span class=\"p\">,</span> <span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">epsilon</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">j</span><span class=\"p\">,</span> <span class=\"n\">example</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">examples</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">example</span><span class=\"p\">[</span><span class=\"n\">target</span><span class=\"p\">]</span> <span class=\"o\">==</span> <span class=\"n\">h_k</span><span class=\"p\">(</span><span class=\"n\">example</span><span class=\"p\">):</span>\n",
" <span class=\"n\">w</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">*=</span> <span class=\"n\">error</span> <span class=\"o\">/</span> <span class=\"p\">(</span><span class=\"mf\">1.</span> <span class=\"o\">-</span> <span class=\"n\">error</span><span class=\"p\">)</span>\n",
" <span class=\"n\">w</span> <span class=\"o\">=</span> <span class=\"n\">normalize</span><span class=\"p\">(</span><span class=\"n\">w</span><span class=\"p\">)</span>\n",
" <span class=\"n\">z</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">math</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">((</span><span class=\"mf\">1.</span> <span class=\"o\">-</span> <span class=\"n\">error</span><span class=\"p\">)</span> <span class=\"o\">/</span> <span class=\"n\">error</span><span class=\"p\">))</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">WeightedMajority</span><span class=\"p\">(</span><span class=\"n\">h</span><span class=\"p\">,</span> <span class=\"n\">z</span><span class=\"p\">)</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">train</span>\n",
"</pre></div>\n",
"</body>\n",
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]
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"metadata": {},
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],
"source": [
"psource(AdaBoost)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"AdaBoost takes as inputs: **L** and *K* where **L** is the learner and *K* is the number of hypotheses to be generated. The learner **L** takes in as inputs: a dataset and the weights associated with the examples in the dataset. But the `PerceptronLearner` doesnot handle weights and only takes a dataset as its input. \n",
"To remedy that we will give as input to the PerceptronLearner a modified dataset in which the examples will be repeated according to the weights associated to them. Intuitively, what this will do is force the learner to repeatedly learn the same example again and again until it can classify it correctly. \n",
"\n",
"To convert `PerceptronLearner` so that it can take weights as input too, we will have to pass it through the **`WeightedLearner`** function."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"psource(WeightedLearner)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `WeightedLearner` function will then call the `PerceptronLearner`, during each iteration, with the modified dataset which contains the examples according to the weights associated with them."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example\n",
"\n",
"We will pass the `PerceptronLearner` through `WeightedLearner` function. Then we will create an `AdaboostLearner` classifier with number of hypotheses or *K* equal to 5."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
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"source": [
"WeightedPerceptron = WeightedLearner(PerceptronLearner)\n",
"AdaboostLearner = AdaBoost(WeightedPerceptron, 5)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"iris2 = DataSet(name=\"iris\")\n",
"iris2.classes_to_numbers()\n",
"\n",
"adaboost = AdaboostLearner(iris2)\n",
"\n",
"adaboost([5, 3, 1, 0.1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is the correct answer. Let's check the error rate of adaboost with perceptron."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error ratio for adaboost: 0.046666666666666634\n"
]
}
],
"source": [
"print(\"Error ratio for adaboost: \", err_ratio(adaboost, iris2))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"It reduced the error rate considerably. Unlike the `PerceptronLearner`, `AdaBoost` was able to learn the complexity in the iris dataset."
]
}
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