fixed w38 4a error
This commit is contained in:
KarlHenrik
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
<li class="toctree-l1"><a class="reference internal" href="../../../../../../week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
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||||
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||||
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||||
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||||
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||||
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||||
<li class="toctree-l1"><a class="reference internal" href="../../../../../../../week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
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||||
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||||
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|
||||
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||||
@@ -290,7 +290,8 @@
|
||||
"$$\n",
|
||||
"\\mathrm{var}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\tilde{\\boldsymbol{y}}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right]=\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2.\n",
|
||||
"$$\n",
|
||||
"In order to arrive at the equation for the bias, we have to approximate the unknown function $f$ with the output/target values $y$."
|
||||
"\n",
|
||||
"In order to arrive at the equation for the bias, we have to approximate the unknown function $f$ with the output/target values $y$.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -321,7 +322,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"execution_count": null,
|
||||
"id": "b5bf581c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
@@ -332,7 +333,8 @@
|
||||
"bootstraps = 1000\n",
|
||||
"\n",
|
||||
"predictions = np.random.rand(bootstraps, n) * 10 + 10\n",
|
||||
"targets = np.random.rand(bootstraps, n)\n",
|
||||
"# The definition of targets has been updated, and was wrong earlier in the week.\n",
|
||||
"targets = np.random.rand(1, n)\n",
|
||||
"\n",
|
||||
"mse = ...\n",
|
||||
"bias = ...\n",
|
||||
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||||
<p><strong>b)</strong> Compute the mean square error for the line model and for the second degree polynomial model.</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></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="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||||
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|
||||
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|
||||
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@@ -520,7 +520,7 @@ document.write(`
|
||||
<p>Hopefully your model fit the data quite well, but to know how well the model actually generalizes to unseen data, which is most often what we care about, we need to split our data into training and testing data.</p>
|
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
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@@ -515,7 +515,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
|
||||
<p>We calculate the optimal intercept by including a feature with the constant value of 1 in our model, which is then multplied by some parameter <span class="math notranslate nohighlight">\(\theta_0\)</span> from the OLS method into the optimal intercept value (which will be <span class="math notranslate nohighlight">\(\theta_0\)</span>). In practice, we include the intercept in our model by adding a column of ones to the start of our feature matrix.</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
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|
||||
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|
||||
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|
||||
@@ -544,7 +544,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
|
||||
<p><strong>b)</strong> Use the expression from <strong>3d)</strong> to find the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\hat{\beta}_{OLS}}\)</span> for predicting spending based on these features. Create a function for this operation, as you are going to need to use it a lot.</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="o">...</span>
|
||||
|
||||
<span class="c1">#beta = OLS_parameters(X, y)</span>
|
||||
@@ -569,7 +569,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
|
||||
<p><strong>a)</strong> Create a feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> for the features <span class="math notranslate nohighlight">\(x, x^2, x^3, x^4, x^5\)</span>, including an intercept column of ones at the start. Make this into a function, as you will do this a lot over the next weeks.</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="n">X</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="n">n</span><span class="p">,</span> <span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
|
||||
<span class="c1">#X[:, 0] = ...</span>
|
||||
@@ -593,7 +593,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
|
||||
<p><strong>c)</strong> Like in exercise 4 last week, split your feature matrix and target data into a training split and test split.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
|
||||
<span class="c1">#X_train, X_test, y_train, y_test = ...</span>
|
||||
</pre></div>
|
||||
|
||||
@@ -28,7 +28,7 @@
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
|
||||
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
|
||||
@@ -467,10 +467,10 @@ defining a new cost function to be optimized, that is</p>
|
||||
<h2>Exercise 3 - Scaling data<a class="headerlink" href="#exercise-3-scaling-data" title="Link to this heading">#</a></h2>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></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="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -487,7 +487,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
<p><strong>a)</strong> Adapt your function from last week to only include the intercept column if the boolean argument <code class="docutils literal notranslate"><span class="pre">intercept</span></code> is set to true.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="n">X</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="n">n</span><span class="p">,</span> <span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
|
||||
<span class="c1">#X[:, 0] = ...</span>
|
||||
@@ -500,7 +500,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
</div>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="n">X</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="n">n</span><span class="p">,</span> <span class="n">p</span><span class="p">))</span>
|
||||
<span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:]</span>
|
||||
@@ -546,7 +546,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
<p><strong>a)</strong> Implement a function for computing the optimal Ridge parameters using the expression from <strong>2a)</strong>.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Ridge_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">Ridge_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||||
<span class="c1"># Assumes X is scaled and has no intercept column</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span>
|
||||
|
||||
|
||||
@@ -28,7 +28,7 @@
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
|
||||
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
|
||||
@@ -584,7 +584,7 @@ Then we compute the target values <span class="math notranslate nohighlight">\(y
|
||||
<p>Below is the code to generate the dataset:</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
|
||||
<span class="c1"># Set random seed for reproducibility</span>
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||||
|
||||
@@ -28,7 +28,7 @@
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
|
||||
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
|
||||
@@ -525,13 +525,14 @@ C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_
|
||||
<p><strong>a)</strong> Using the expression above, compute the mean squared error, bias and variance of the given data. Check that the sum of the bias and variance correctly gives (approximately) the mean squared error.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||||
<span class="n">bootstraps</span> <span class="o">=</span> <span class="mi">1000</span>
|
||||
|
||||
<span class="n">predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">bootstraps</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">*</span> <span class="mi">10</span> <span class="o">+</span> <span class="mi">10</span>
|
||||
<span class="n">targets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">bootstraps</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||||
<span class="c1"># The definition of targets has been updated, and was wrong earlier in the week.</span>
|
||||
<span class="n">targets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mse</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">bias</span> <span class="o">=</span> <span class="o">...</span>
|
||||
@@ -545,15 +546,15 @@ C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_
|
||||
<p><strong>d)</strong> Perform a bias-variance analysis of a polynomial OLS model fit to a one-dimensional function by computing and plotting the bias and variances values as a function of the polynomial degree of your model.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></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="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="p">(</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="p">(</span>
|
||||
<span class="n">PolynomialFeatures</span><span class="p">,</span>
|
||||
<span class="p">)</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">resample</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">resample</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -28,7 +28,7 @@
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
|
||||
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
|
||||
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
|
||||
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user