mirror-github-bspeice/bspeice.github.io
1
0
Fork 0
mirror of https://github.com/bspeice/bspeice.github.io synced 2024-12-21 22:18:07 -05:00
Code Issues Releases Wiki Activity
f60cb5f8ef
bspeice.github.io/predicting-santander-customer-happiness.html
Bradlee Speice f60cb5f8ef New blog post on Kaggle competition
2016-03-05 11:58:46 -05:00

1063 lines
70 KiB
HTML
Raw Blame History

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="description" content="My first Kaggle competition¶It&#39;s time! After embarking on a Machine Learning class this semester, and with a Saturday in which I don&#39;t have much planned, I wanted to put this class and training to ...">
<meta name="keywords" content="data science, kaggle, machine learning">
<link rel="icon" href="https://bspeice.github.io/favicon.ico">
<title>Predicting Santander Customer Happiness - Bradlee Speice</title>
<!-- Stylesheets -->
<link href="https://bspeice.github.io/theme/css/bootstrap.min.css" rel="stylesheet">
<link href="https://bspeice.github.io/theme/css/fonts.css" rel="stylesheet">
<link href="https://bspeice.github.io/theme/css/nest.css" rel="stylesheet">
<link href="https://bspeice.github.io/theme/css/pygment.css" rel="stylesheet">
<!-- /Stylesheets -->
<!-- RSS Feeds -->
<link href="https://bspeice.github.io/feeds/all.atom.xml" type="application/atom+xml" rel="alternate" title="Bradlee Speice Full Atom Feed" />
<link href="https://bspeice.github.io/feeds/blog.atom.xml" type="application/atom+xml" rel="alternate" title="Bradlee Speice Categories Atom Feed" />
<!-- /RSS Feeds -->
<!-- HTML5 shim and Respond.js for IE8 support of HTML5 elements and media queries -->
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
<!-- Google Analytics -->
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-74711362-1', 'auto');
ga('send', 'pageview');
</script>
<!-- /Google Analytics -->
</head>
<body>
<!-- Header -->
<div class="header-container gradient">
<!-- Static navbar -->
<div class="container">
<div class="header-nav">
<div class="header-logo">
<a class="pull-left" href="https://bspeice.github.io/"><img class="mr20" src="https://bspeice.github.io/images/logo.svg" alt="logo">Bradlee Speice</a>
</div>
<div class="nav pull-right">
</div>
</div>
</div>
<!-- /Static navbar -->
<!-- Header -->
<!-- Header -->
<div class="container header-wrapper">
<div class="row">
<div class="col-lg-12">
<div class="header-content">
<h1 class="header-title">Predicting Santander Customer Happiness</h1>
<p class="header-date"> <a href="https://bspeice.github.io/author/bradlee-speice.html">Bradlee Speice</a>, Sat 05 March 2016, <a href="https://bspeice.github.io/category/blog.html">Blog</a></p>
<div class="header-underline"></div>
<div class="clearfix"></div>
<p class="pull-right header-tags">
<span class="glyphicon glyphicon-tags mr5" aria-hidden="true"></span>
<a href="https://bspeice.github.io/tag/data-science.html">data science</a>, <a href="https://bspeice.github.io/tag/kaggle.html">kaggle</a>, <a href="https://bspeice.github.io/tag/machine-learning.html">machine learning</a> </p>
</div>
</div>
</div>
</div>
<!-- /Header -->
<!-- /Header -->
</div>
<!-- /Header -->
<!-- Content -->
<div class="container content">
<p>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="My-first-Kaggle-competition">My first Kaggle competition<a class="anchor-link" href="#My-first-Kaggle-competition">&#182;</a></h3><p>It's time! After embarking on a Machine Learning class this semester, and with a Saturday in which I don't have much planned, I wanted to put this class and training to work. It's my first competition submission. I want to walk you guys through how I'm approaching this problem, because I thought it would be really neat. The competition is Banco Santander's <a href="https://www.kaggle.com/c/santander-customer-satisfaction">Santander Customer Satisfaction</a> competition. It seemed like an easy enough problem I could actually make decent progress on it.</p>
<h1 id="Data-Exploration">Data Exploration<a class="anchor-link" href="#Data-Exploration">&#182;</a></h1><p>First up: we need to load our data and do some exploratory work. Because we're going to be using this data for model selection prior to testing, we need to make a further split. I've already gone ahead and done this work, please see the code in the <a href="#Appendix">appendix below</a>.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[1]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="c1"># Record how long it takes to run the notebook - I&#39;m curious.</span>
<span class="kn">from</span> <span class="nn">datetime</span> <span class="k">import</span> <span class="n">datetime</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">datetime</span><span class="o">.</span><span class="n">now</span><span class="p">()</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">&#39;split_train.csv&#39;</span><span class="p">)</span>
<span class="n">dataset</span><span class="o">.</span><span class="n">index</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">ID</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">drop</span><span class="p">([</span><span class="s1">&#39;TARGET&#39;</span><span class="p">,</span> <span class="s1">&#39;ID&#39;</span><span class="p">,</span> <span class="s1">&#39;ID.1&#39;</span><span class="p">],</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">TARGET</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[2]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">y</span><span class="o">.</span><span class="n">unique</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[2]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>array([0, 1], dtype=int64)</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[3]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">columns</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[3]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>369</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Okay, so there are only <a href="https://www.kaggle.com/c/santander-customer-satisfaction/data">two classes we're predicting</a>: 1 for unsatisfied customers, 0 for satisfied customers. I would have preferred this to be something more like a regression, or predicting multiple classes: maybe the customer isn't the most happy, but is nowhere near closing their accounts. For now though, that's just the data we're working with.</p>
<p>Now, I'd like to make a scatter matrix of everything going on. Unfortunately as noted above, we have 369 different features. There's no way I can graphically make sense of that much data to start with.</p>
<p>We're also not told what the data actually represents: Are these survey results? Average time between contact with a customer care person? Frequency of contacting a customer care person? The idea is that I need to reduce the number of dimensions we're predicting across.</p>
<h2 id="Dimensionality-Reduction-pt.-1---Binary-Classifiers">Dimensionality Reduction pt. 1 - Binary Classifiers<a class="anchor-link" href="#Dimensionality-Reduction-pt.-1---Binary-Classifiers">&#182;</a></h2><p>My first attempt to reduce the data dimensionality is to find all the binary classifiers in the dataset (i.e. 0 or 1 values) and see if any of those are good (or anti-good) predictors of the final data.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[4]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">cols</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">columns</span>
<span class="n">b_class</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cols</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">unique</span><span class="p">())</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="n">b_class</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="nb">len</span><span class="p">(</span><span class="n">b_class</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[4]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>111</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>So there are 111 features in the dataset that are a binary label. Let's see if any of them are good at predicting the users satisfaction!</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[5]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># First we need to `binarize` the data to 0-1; some of the labels are {0, 1},</span>
<span class="c1"># some are {0, 3}, etc.</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="k">import</span> <span class="n">binarize</span>
<span class="n">X_bin</span> <span class="o">=</span> <span class="n">binarize</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">b_class</span><span class="p">])</span>
<span class="n">accuracy</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">X_bin</span><span class="p">[:,</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">y</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">b_class</span><span class="p">))]</span>
<span class="n">acc_df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">({</span><span class="s2">&quot;Accuracy&quot;</span><span class="p">:</span> <span class="n">accuracy</span><span class="p">},</span> <span class="n">index</span><span class="o">=</span><span class="n">b_class</span><span class="p">)</span>
<span class="n">acc_df</span><span class="o">.</span><span class="n">describe</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[5]:</div>
<div class="output_html rendered_html output_subarea output_execute_result">
<div>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>Accuracy</th>
</tr>
</thead>
<tbody>
<tr>
<th>count</th>
<td>111.000000</td>
</tr>
<tr>
<th>mean</th>
<td>0.905159</td>
</tr>
<tr>
<th>std</th>
<td>0.180602</td>
</tr>
<tr>
<th>min</th>
<td>0.043598</td>
</tr>
<tr>
<th>25%</th>
<td>0.937329</td>
</tr>
<tr>
<th>50%</th>
<td>0.959372</td>
</tr>
<tr>
<th>75%</th>
<td>0.960837</td>
</tr>
<tr>
<th>max</th>
<td>0.960837</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Wow! Looks like we've got some incredibly predictive features! So much so that we should be a bit concerned. My initial guess for what's happening is that we have a sparsity issue: so many of the values are 0, and these likely happen to line up with satisfied customers.</p>
<p>So the question we must now answer, which I likely should have asked long before now: What exactly is the distribution of un/satisfied customers?</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[6]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">unsat</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">count</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Satisfied customers: </span><span class="si">{}</span><span class="s2">; Unsatisfied customers: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">-</span> <span class="n">unsat</span><span class="p">,</span> <span class="n">unsat</span><span class="p">))</span>
<span class="n">naive_guess</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Naive guess accuracy: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">naive_guess</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>Satisfied customers: 51131; Unsatisfied customers: 2083
Naive guess accuracy: 0.9608561656706882
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>This is a bit discouraging. A naive guess of "always satisfied" performs as well as our best individual binary classifier. What this tells me then, is that these data columns aren't incredibly helpful in prediction. I'd be interested in a polynomial expansion of this data-set, but for now, that's more computation than I want to take on.</p>
<h1 id="Dimensionality-Reduction-pt.-2---LDA">Dimensionality Reduction pt. 2 - LDA<a class="anchor-link" href="#Dimensionality-Reduction-pt.-2---LDA">&#182;</a></h1><p>Knowing that our naive guess performs so well is a blessing and a curse:</p>
<ul>
<li>Curse: The threshold for performance is incredibly high: We can only "improve" over the naive guess by 4%</li>
<li>Blessing: All the binary classification features we just discovered are worthless on their own. We can throw them out and reduce the data dimensionality from 369 to 111.</li>
</ul>
<p>Now, in removing these features from the dataset, I'm not saying that there is no "information" contained within them. There might be. But the only way we'd know is through a polynomial expansion, and I'm not going to take that on within this post.</p>
<p>My initial thought for a "next guess" is to use the <a href="http://scikit-learn.org/stable/modules/lda_qda.html">LDA</a> model for dimensionality reduction. However, it can only reduce dimensions to $1 - p$, with $p$ being the number of classes. Since this is a binary classification, every LDA model that I try will have dimensionality one; when I actually try this, the predictor ends up being slightly less accurate than the naive guess.</p>
<p>Instead, let's take a different approach to dimensionality reduction: <a href="http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html">principle components analysis</a>. This allows us to perform the dimensionality reduction without worrying about the number of classes. Then, we'll use a <a href="http://scikit-learn.org/stable/modules/naive_bayes.html#gaussian-naive-bayes">Gaussian Naive Bayes</a> model to actually do the prediction. This model is chosen simply because it doesn't take a long time to fit and compute; because PCA will take so long, I just want a prediction at the end of this. We can worry about using a more sophisticated LDA/QDA/SVM model later.</p>
<p>Now into the actual process: We're going to test out PCA dimensionality reduction from 1 - 20 dimensions, and then predict using a Gaussian Naive Bayes model. The 20 dimensions upper limit was selected because the accuracy never improves after you get beyond that (I found out by running it myself). Hopefully, we'll find that we can create a model better than the naive guess.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[7]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="k">import</span> <span class="n">GaussianNB</span>
<span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="k">import</span> <span class="n">PCA</span>
<span class="n">X_no_bin</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="n">b_class</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">evaluate_gnb</span><span class="p">(</span><span class="n">dims</span><span class="p">):</span>
<span class="n">pca</span> <span class="o">=</span> <span class="n">PCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">dims</span><span class="p">)</span>
<span class="n">X_xform</span> <span class="o">=</span> <span class="n">pca</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X_no_bin</span><span class="p">)</span>
<span class="n">gnb</span> <span class="o">=</span> <span class="n">GaussianNB</span><span class="p">()</span>
<span class="n">gnb</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_xform</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="k">return</span> <span class="n">gnb</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_xform</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">dim_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">21</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">dim_range</span><span class="p">,</span> <span class="p">[</span><span class="n">evaluate_gnb</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span> <span class="k">for</span> <span class="n">dim</span> <span class="ow">in</span> <span class="n">dim_range</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Gaussian NB Accuracy&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="n">naive_guess</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Naive Guess&quot;</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">naive_guess</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Inverse Naive Guess&quot;</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">gcf</span><span class="p">()</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_png output_subarea ">
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAsYAAAFwCAYAAAC7E71AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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"
>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>**sigh...** After all the effort and computational power, we're still at square one: we have yet to beat out the naive guess threshold. With PCA in play we end up performing terribly, but not terribly enough that we can guess against ourselves.</p>
<p>Let's try one last-ditch attempt using the entire data set:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[8]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">evaluate_gnb_full</span><span class="p">(</span><span class="n">dims</span><span class="p">):</span>
<span class="n">pca</span> <span class="o">=</span> <span class="n">PCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">dims</span><span class="p">)</span>
<span class="n">X_xform</span> <span class="o">=</span> <span class="n">pca</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">gnb</span> <span class="o">=</span> <span class="n">GaussianNB</span><span class="p">()</span>
<span class="n">gnb</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_xform</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="k">return</span> <span class="n">gnb</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_xform</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">dim_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">21</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">dim_range</span><span class="p">,</span> <span class="p">[</span><span class="n">evaluate_gnb</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span> <span class="k">for</span> <span class="n">dim</span> <span class="ow">in</span> <span class="n">dim_range</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Gaussian NB Accuracy&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="n">naive_guess</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Naive Guess&quot;</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">naive_guess</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Inverse Naive Guess&quot;</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">gcf</span><span class="p">()</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_png output_subarea ">
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAsYAAAFwCAYAAAC7E71AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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"
>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Nothing. It is interesting to note that the graphs are almost exactly the same: This would imply again that the variables we removed earlier (all the binary classifiers) indeed have almost no predictive power. It seems this problem is high-dimensional, but with almost no data that can actually inform our decisions.</p>
<h1 id="Summary-for-Day-1">Summary for Day 1<a class="anchor-link" href="#Summary-for-Day-1">&#182;</a></h1><p>After spending a couple hours with this dataset, there seems to be a fundamental issue in play: We have very high-dimensional data, and it has no bearing on our ability to actually predict customer satisfaction. This can be a huge issue: it implies that <strong>no matter what model we use, we fundamentally can't perform well.</strong> I'm sure most of this is because I'm not an experienced data scientist. Even so, we have yet to develop a strategy that can actually beat out the village idiot; <strong>so far, the bank is best off just assuming all its customers are satisfied.</strong> Hopefully more to come soon.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[9]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">end</span> <span class="o">=</span> <span class="n">datetime</span><span class="o">.</span><span class="n">now</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Running time: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">end</span> <span class="o">-</span> <span class="n">start</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>Running time: 0:00:58.715714
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Appendix">Appendix<a class="anchor-link" href="#Appendix">&#182;</a></h1><p>Code used to split the initial training data:</p>
<div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">&#39;train.csv&#39;</span><span class="p">)</span>
<span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">ID</span>
<span class="n">data_train</span><span class="p">,</span> <span class="n">data_validate</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span>
<span class="n">data</span><span class="p">,</span> <span class="n">train_size</span><span class="o">=.</span><span class="mi">7</span><span class="p">)</span>
<span class="n">data_train</span><span class="o">.</span><span class="n">to_csv</span><span class="p">(</span><span class="s1">&#39;split_train.csv&#39;</span><span class="p">)</span>
<span class="n">data_validate</span><span class="o">.</span><span class="n">to_csv</span><span class="p">(</span><span class="s1">&#39;split_validate.csv&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div></p>
<script type="text/x-mathjax-config">
# MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\(','\)']]}});
MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$']]}});
</script>
<script async src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_CHTML'></script>
<div class="comments">
<div id="disqus_thread"></div>
<script type="text/javascript">
var disqus_shortname = 'bradleespeice';
var disqus_identifier = 'predicting-santander-customer-happiness.html';
var disqus_url = 'https://bspeice.github.io/predicting-santander-customer-happiness.html';
(function() {
var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
dsq.src = '//' + disqus_shortname + '.disqus.com/embed.js';
(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
})();
</script>
<noscript>Please enable JavaScript to view the comments.</noscript>
</div>
</div>
<!-- /Content -->
<!-- Footer -->
<div class="footer gradient-2">
<div class="container footer-container ">
<div class="row">
<div class="col-xs-4 col-sm-3 col-md-3 col-lg-3">
<div class="footer-title"></div>
<ul class="list-unstyled">
<li><a href="https://bspeice.github.io/feeds/all.atom.xml" type="application/atom+xml" rel="alternate"></a></li>
</ul>
</div>
<div class="col-xs-4 col-sm-3 col-md-3 col-lg-3">
<div class="footer-title"></div>
<ul class="list-unstyled">
<li><a href="https://github.com/bspeice" target="_blank">Github</a></li>
<li><a href="https://www.linkedin.com/in/bradleespeice" target="_blank">LinkedIn</a></li>
</ul>
</div>
<div class="col-xs-4 col-sm-3 col-md-3 col-lg-3">
</div>
<div class="col-xs-12 col-sm-3 col-md-3 col-lg-3">
<p class="pull-right text-right">
<small><em>Proudly powered by <a href="http://docs.getpelican.com/" target="_blank">pelican</a></em></small><br/>
<small><em>Theme and code by <a href="https://github.com/molivier" target="_blank">molivier</a></em></small><br/>
<small></small>
</p>
</div>
</div>
</div>
</div>
<!-- /Footer -->
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink