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<!DOCTYPE html>
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<title>sklearn_glm</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="线性模型的概念">线性模型的概念<a class="anchor-link" href="#线性模型的概念">¶</a></h1>
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<h2 id="画一条直线">画一条直线<a class="anchor-link" href="#画一条直线">¶</a></h2>
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<div class=" highlight hl-ipython3"><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="c1"># 令x为-5到5之间，元素数为100的等差数列</span>
<span class="n">x</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">100</span><span class="p">)</span>
<span class="c1"># 输入直线方程</span>
<span class="n">y</span><span class="o">=</span><span class="mf">0.5</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">3</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="n">c</span><span class="o">=</span><span class="s2">"orange"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Straight line"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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bhnLfT4ERx/O9RvHDqV1EEqapEv2rMeiq+GFc9Hl32f+gq0LQydSuowFbXI59xh+XNQcg3s3w7H3wE9r9cQJQlORS0CsGsVFF0Gn70GbYdEQ5Ra9gydSgRQUUtd5xXw8cToDUMvh/4PQrerNERJYkVFLXXX9iXREKX170H7ETB4QnR7LJGYqbKozawR8D7QMPH4F9391lQHE0mZijJY9CDMvQXqNYTBT8LR/6vLvyW2qrOi3gsMd/dSM8sFPjCzN9x9aoqziSTfljnR5d+bi6Hz+VD4GDTpGDqVyCFVWdTu7kBp4tPcxD+eylAiSVe+NxqgNP8eaNAahr4AXb6hVbRkhGrtUZtZDjAD6AqMc/dplTxmFDAKID8/P5kZRQ7Phn9Gq+jtC6HgAhjwIDRsGzqVSLXVq86D3L3c3fsCnYFBZta7ksdMcPdCdy/My8tLckyRWthfGt39e/LJUFYKw16Hk36jkpaMU6OzPtx9q5lNAc4G5qUmkkgSrH0Hpo2Encvh2Cug7z2Q2zx0KpFaqXJFbWZ5ZtYq8XFj4ExgUYpzidTOvi0w9SJ498zotlhnvA8DH1VJS0arzor6S8DTiX3qesAL7v5aamOJ1MLKP0VDlPZugJ43QO9bNERJskJ1zvqYA/RLQxaR2tm9DmZcBSv+AK36wLDXoM2A0KlEkkZXJkrmcodPfgslo6FsJ/S5KxpHWi83dDKRpFJRS2bauQKKLoE1b0K7E6OrC1v2CJ1KJCVU1JJZvAKWjIdZ1wMOAx6BbleAVetMU5GMpKKWzLF9cXTfwg0fQIczYdAEaFYQOpVIyqmoJf4q9sPCB2DubVC/CQx5Co76H13+LXWGilribfPM6PLvLTOhy9eh8FFo3CF0KpG0UlFLPJXvgXk/hQU/h4btYOiLkP/10KlEglBRS/xs+EdiiNJiOPoH0O8BaNgmdCqRYFTUEh/7d8DssfDROGiaD6e/BV86K3QqkeBU1BIPn70FRaNg18ronoV97oLcZqFTicSCilrC2rsZSn4InzwNLbrDmX+HvJNDpxKJFRW1hLPij1B8BezdBL1ugt4/gZxGoVOJxI6KWtJv9xoovhJWvgSt+8Ppb0LrvqFTicSWilrSxx2WPRVtdZTvhr4/g+5joJ7+MxQ5FP0JkfQoXR69Wbh2MuSdAoMnQYtuoVOJZAQVtaSWV0Sn282+ETAoHAfHXqohSiI1oKKW1Nm2KLpwZeOH8KWzYdAT0fnRIlIjKmpJvor9sPA+mHs71G8GJ/4GCr6nIUoitaSiluTaXAJTL4StsyH/v6N50Y3bh04lktFU1JIcZbth3u2w8H5omAenvAxdvhY6lUhWUFHL4Vv/fjTQf8cSOOYi6HcfNGgdOpVI1lBRS+3t3wGzboAlj0HTo2D4ZOhwRuhUIllHRS2189kb0c1ld62C466JhijVbxo6lUhWUlFLzezZCCXXwvJnoGVPOOtDaDckdCqRrKailupxhxV/iGZ07NsCvW+OBinlNAydTCTrqailars+g+LLYdUr0KYQhr8DrU8InUqkzlBRy8G5w7JfQckYqNgbnc1x3GgNURJJM/2Jk8qVLoNpo2DdX+GIU2HQJGhxbOhUInWSilr+XUU5fPRLmH0TWA4MHA9dR2qIkkhAKmr5l20LYOpFsGkqdDwXBo2HJp1DpxKp86pcJplZFzObYmYLzGy+mV2TjmCSRuX7YO5P4Y2+ULoETnoWTvuzSlokJqqzoi4Dxrh7iZk1B2aY2WR3X5DibJIOm6ZHo0i3zoUjvxUNUWqUFzqViBygyqJ29zXAmsTHO8xsIdAJUFFnsrJdMPc2WPQANOoAp74Cnb8aOpWIVKJGe9RmVgD0A6alJI2kx7r3oiFKpR9D11HQ915o0DJ0KhE5iGoXtZk1A/4IjHb37ZV8fxQwCiA/X3fxiKV922DW9fDxE9DsGBjxLrQ/PXQqEalCtc65MrNcopJ+1t1fquwx7j7B3QvdvTAvT3ucsbP6L/CXXrB0YnTn7y/PUUmLZIgqV9RmZsCTwEJ3/0XqI0lS7dkAM0bDp89By15wykvQblDoVCJSA9XZ+jgZuACYa2azEl8b6+6vpyyVHD53+PR5mHEV7N8GvW+FXmMhp0HoZCJSQ9U56+MDQHclzSS7VsP0y2D1n6HtIBj8JLTqHTqViNSSrkzMJu6wdBLMvC66E3i/B6Kh/vVyQicTkcOgos4WO5ZC0UhYNyV6k3DQRGh+TOhUIpIEKupMV1EOix+GOT+Berkw6Ak4ZiSYdqtEsoWKOpNtnRdd/r2pCDp9BQY+Dk06hU4lIkmmos5E5ftg/t2w4G7IbQUn/x7y/1uraJEspaLONBunRavobfOh4LvQ/yFo1C50KhFJIRV1pijbCbNvhsUPQeOOcNpr0Onc0KlEJA1U1Jlg7bvRGR2ly6DrpdDv55DbInQqEUkTFXWc7dsKM38UnRvdrCuM+Bu0Py1wKBFJNxV1XK16Nbq6cM9a6PFjOP42qN84dCoRCUBFHTd71kPx1bDieWh1fDTQv21h6FQiEpCKOi7cYfmzMOMaKCuFE34araQ1REmkzlNRx8HOFVB0Kax5A9oOgSFPQsueoVOJSEyoqEPyiuhuKzN/HH3c/yHodqWGKInIv1FRh7J9CRRdDOvfh/YjYPBEaHZU6FQiEkMq6nSrKINFv4C5t0K9htGs6KP/V5d/i8hBqajTactsmHohbCmBzl+DwnHQpGPoVCIScyrqdCjfC/PuhAU/g4ZtYOgfoMvXtYoWkWpRUafahn9GQ5S2L4SCC2DAg9CwbehUIpJBVNSpsr80Gua/+BFo0gWGvQEdzw6dSkQykIo6FdZMhqJRsHM5HHsF9L0HcpuHTiUiGUpFnUz7tkDJGFj2a2hxHJzxdzhiaOhUIpLhVNTJsvJlmH457N0APW+E42+BnEahU4lIFlBRH67d66D4Slj5IrTuC8P+Am36h04lIllERV1b7vDJb6FkNJTtgj53Q4/rojuBi4gkkYq6NnZ+CkWXwJq3oN1J0dWFLbuHTiUiWUpFXRNeAUseh1k3AA4DHoFuV4DVC51MRLKYirq6ti+GaRfDhg+gw1kweAI0PTJ0KhGpA1TUVanYDwsfgLm3Qf0mMOTXcNT3dfm3iKSNivpQNs+MLv/eMjOazVH4KDTuEDqViNQxKurKlO+BuXfAwnuhYTsY+iLkfz10KhGpo6osajP7FXAesN7de6c+UmAb/pEYorQ4mhPd/wFo0Dp0KhGpw6pzusJTQPZPE9q/A4qvgsmnRCvq09+CIb9SSYtIcFWuqN39fTMrSEOWcD57C6ZfEt1ktttV0OcuyG0WOpWICJDEPWozGwWMAsjPz0/WYVNr72Yo+SF88jS06A5nfgB5J4VOJSLyb5J2pYa7T3D3QncvzMvLS9ZhU2fFi/CXHrD8Geh1E5wzUyUtIrFU98762L0mMUTpJWjdL9qLbt03dCoRkYOqO0XtDsueirY6yndDn3sSQ5Tqzi+BiGSmKrc+zOx3wD+B48xslZldlPpYSVa6HKb8F0y7EFr1hi/Phl43qKRFJCNU56yPb6cjSEpUlMOScTB7LGBQOA6OvVRDlEQko2TvknLbwmiI0sYP4UvnwKDx0DRDzkYRETlA9hV1xX5YcC/MuyO6oeyJv4WC72qIkohkrOwq6s0lMPVC2Dob8r8JhY9AoyNCpxIROSzZUdRlu2He7bDw/qiYT/0TdD4/dCoRkaTI/KJe/360F71jCRx9IfS/X/M5RCSrZG5R798Os26EJY9B06Ng+DvQYUToVCIiSZeZRb36dZh+KexaBceNhj53Qv2moVOJiKREZhX1no1Qcm00n6NlTzjrQ2g3JHQqEZGUyoyidocVL0Tzovdtgd63QK+xkNMwdDIRkZSLf1Hv+gyKL4dVr0CbwmgvuvUJoVOJiKRNfIvaHZY+CTOvg4q90Pde6H6t5nOISJ0Tz9YrXQbTRsK6d+GI02DwJGjeNXQqEZEg4lXUFeXw0SMw+yaw+jBwPHQdqSFKIlKnxaeo922BKefApmnQ8TwY9Dg06Rw6lYhIcPEp6txW0OwYOO5qOPLbGqIkIpIQn6I2g5OfDZ1CRCR2tPkrIhJzKmoRkZhTUYuIxJyKWkQk5lTUIiIxp6IWEYk5FbWISMypqEVEYs7cPfkHNdsAfJr0A6dWO2Bj6BBpptdcN+g1Z4Yj3T2vsm+kpKgzkZkVu3th6BzppNdcN+g1Zz5tfYiIxJyKWkQk5lTU/zIhdIAA9JrrBr3mDKc9ahGRmNOKWkQk5lTUIiIxp6KuhJmNMTM3s3ahs6Samd1nZovMbI6ZvWxmrUJnSgUzO9vMFpvZx2Z2Q+g8qWZmXcxsipktMLP5ZnZN6EzpYmY5ZjbTzF4LnSVZVNRfYGZdgLOAFaGzpMlkoLe7nwB8BNwYOE/SmVkOMA44B+gJfNvMeoZNlXJlwBh37wkMAa6oA6/5c9cAC0OHSCYV9X96EPgxUCfeZXX3t929LPHpVCAb7yg8CPjY3Ze5+z7g98D5gTOllLuvcfeSxMc7iIqrU9hUqWdmnYFzgUmhsySTivoAZnY+sNrdZ4fOEsiFwBuhQ6RAJ2DlAZ+vog6U1ufMrADoB0wLHCUdHiJaaFUEzpFU8bm5bZqY2TtAh0q+dRMwlmjbI6sc6jW7+yuJx9xE9Ndl3WE4i5hZM+CPwGh33x46TyqZ2XnAenefYWbDAsdJqjpX1O5+RmVfN7PjgaOA2WYG0RZAiZkNcve1aYyYdAd7zZ8zsx8A5wEjPDtPrF8NdDng886Jr2U1M8slKuln3f2l0HnS4GTgq2b2ZaAR0MLMnnH37wXOddh0wctBmNlyoNDdM20CV42Y2dnAL4DT3H1D6DypYGb1id4oHUFU0NOB77j7/KDBUsii1cbTwGZ3Hx04TtolVtTXuft5gaMkhfao5VGgOTDZzGaZ2fjQgZIt8WbplcBbRG+qvZDNJZ1wMnABMDzx+zorsdKUDKQVtYhIzGlFLSIScypqEZGYU1GLiMScilpEJOZU1CIiMaeiFhGJORW1iEjM/T+R5w6YSsXPiAAAAABJRU5ErkJggg==
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<h2 id="通过2点确定一条直线">通过2点确定一条直线<a class="anchor-link" href="#通过2点确定一条直线">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 2点(1,3) (4,5) 确定一条直线</span>
<span class="c1"># 导入线性回归模型</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">LinearRegression</span>
<span class="c1"># 输入2个点的横坐标</span>
<span class="n">X</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">]]</span>
<span class="c1"># 输入2个点的纵坐标</span>
<span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
<span class="c1"># 用线性模型拟合这2个点</span>
<span class="n">lr</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span><span class="o">.</span><span class="n">fit</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"># 画出2个点和直线</span>
<span class="n">z</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</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="n">s</span><span class="o">=</span><span class="mi">80</span><span class="p">)</span> <span class="c1">#画2个点</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Straight line"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 输出该直线的方程</span>
<span class="n">w</span><span class="o">=</span><span class="n">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">b</span><span class="o">=</span><span class="n">lr</span><span class="o">.</span><span class="n">intercept_</span>
<span class="nb">print</span><span class="p">(</span> <span class="s2">"y = </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">w</span><span class="p">),</span> <span class="s2">"x"</span><span class="p">,</span> <span class="s2">" + </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="p">)</span>
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<pre>y = 0.667 x + 2.333
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">lr</span>
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<pre>LinearRegression()</pre>
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<h2 id="如果是3个点呢？">如果是3个点呢？<a class="anchor-link" href="#如果是3个点呢？">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 2点(1,3) (4,5) (3,3)确定一条直线</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">LinearRegression</span>
<span class="n">X</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">]]</span>
<span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="c1"># 拟合</span>
<span class="n">lr</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span><span class="o">.</span><span class="n">fit</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"># 画图</span>
<span class="n">z</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</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="n">s</span><span class="o">=</span><span class="mi">80</span><span class="p">)</span> <span class="c1">#画2个点</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Straight line"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 输出该直线的方程</span>
<span class="n">w</span><span class="o">=</span><span class="n">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">b</span><span class="o">=</span><span class="n">lr</span><span class="o">.</span><span class="n">intercept_</span>
<span class="nb">print</span><span class="p">(</span> <span class="s2">"y = </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">w</span><span class="p">),</span> <span class="s2">"x"</span><span class="p">,</span> <span class="s2">" + </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="p">)</span>
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<pre>y = 0.571 x + 2.143
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<h2 id="生成更多点，做线性拟合">生成更多点，做线性拟合<a class="anchor-link" href="#生成更多点，做线性拟合">¶</a></h2>
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<div class="prompt input_prompt">In [5]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <span class="n">make_regression</span>
<span class="c1">#生成用于回归分析的数据</span>
<span class="n">X</span><span class="p">,</span><span class="n">y</span><span class="o">=</span><span class="n">make_regression</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_informative</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># 线性拟合</span>
<span class="n">reg</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span>
<span class="n">reg</span><span class="o">.</span><span class="n">fit</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"># 生成等差数列z作为横轴，画线性模型的图形</span>
<span class="n">z</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</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="n">c</span><span class="o">=</span><span class="s1">'b'</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">60</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">z</span><span class="p">,</span> <span class="n">reg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">z</span><span class="p">),</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span> <span class="c1">#预测每个x对应的y</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Linear regression"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 输出该直线的方程</span>
<span class="n">w</span><span class="o">=</span><span class="n">reg</span><span class="o">.</span><span class="n">coef_</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">b</span><span class="o">=</span><span class="n">reg</span><span class="o">.</span><span class="n">intercept_</span>
<span class="nb">print</span><span class="p">(</span> <span class="s2">"y = </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">w</span><span class="p">),</span> <span class="s2">"x"</span><span class="p">,</span> <span class="s2">" + </span><span class="si">{:.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="p">)</span>
</pre></div>
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<pre>y = 79.525 x + 10.922
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<h1 id="最基本的线性模型---线性回归">最基本的线性模型 - 线性回归<a class="anchor-link" href="#最基本的线性模型---线性回归">¶</a></h1>
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<h2 id="无噪音模拟数据">无噪音模拟数据<a class="anchor-link" href="#无噪音模拟数据">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <span class="n">make_regression</span>
<span class="c1"># 导入数据集拆分工具</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">LinearRegression</span>
<span class="n">X</span><span class="p">,</span><span class="n">y</span><span class="o">=</span><span class="n">make_regression</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">n_informative</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">38</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</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="n">random_state</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
<span class="n">lr</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="c1"># 打印出模型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"coef:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">[:])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"intercept:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span>
<span class="c1"># y=w1*x1 +w2*x2 + b</span>
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<pre>coef: [70.38592453 7.43213621]
intercept: -7.105427357601002e-15
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 打分</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"training set:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"tesing set:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="c1"># 完全对的原因，是因为没有添加noise！真实世界的数据，噪音是很大的。</span>
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<pre>training set: 1.0
tesing set: 1.0
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<h2 id="载入真实数据---糖尿病数据">载入真实数据 - 糖尿病数据<a class="anchor-link" href="#载入真实数据---糖尿病数据">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 导入数据集拆分工具</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">LinearRegression</span>
<span class="c1"># 载入数据</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <span class="n">load_diabetes</span>
<span class="n">X</span><span class="p">,</span><span class="n">y</span><span class="o">=</span><span class="n">load_diabetes</span><span class="p">()</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">load_diabetes</span><span class="p">()</span><span class="o">.</span><span class="n">target</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</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="n">random_state</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
<span class="n">lr</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="c1"># 打印出模型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"coef:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">[:])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"intercept:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span>
<span class="c1"># y=w1*x1 +w2*x2 + b</span>
<span class="c1"># 打分</span>
<span class="nb">print</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"training set:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"tesing set:"</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="c1"># 分别是0.53 和0.46，打分降低了很多！</span>
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<pre>coef: [ 11.5106203 -282.51347161 534.20455671 401.73142674
-1043.89718398 634.92464089 186.43262636 204.93373199
762.47149733 91.9460394 ]
intercept: 152.5624877455247
training set: 0.5303814759709331
tesing set: 0.4593440496691642
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<h1 id="使用L2正则化的线性模型---岭回归">使用L2正则化的线性模型 - 岭回归<a class="anchor-link" href="#使用L2正则化的线性模型---岭回归">¶</a></h1>
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<p>保留全部特征变量，只是降低特征变量的系数来避免过拟合的方法，称为L2正则化。</p>
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<h2 id="糖尿病数据集---岭回归">糖尿病数据集 - 岭回归<a class="anchor-link" href="#糖尿病数据集---岭回归">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 导入数据集拆分工具</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <span class="n">train_test_split</span>
<span class="c1"># 载入数据</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <span class="n">load_diabetes</span>
<span class="n">X</span><span class="p">,</span><span class="n">y</span><span class="o">=</span><span class="n">load_diabetes</span><span class="p">()</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">load_diabetes</span><span class="p">()</span><span class="o">.</span><span class="n">target</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</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="n">random_state</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
<span class="c1"># 导入岭回归</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">Ridge</span>
<span class="c1"># 使用岭回归对数据进行拟合</span>
<span class="n">ridge</span><span class="o">=</span><span class="n">Ridge</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="c1"># 打印出模型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"coef:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">coef_</span><span class="p">[:])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"intercept:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span>
<span class="c1"># y=w1*x1 +w2*x2 + b</span>
<span class="c1"># 打分</span>
<span class="nb">print</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"training set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"tesing set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="c1"># 分别是 0.43 和 0.43，打分接近</span>
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<pre>coef: [ 36.8262072 -75.80823733 282.42652716 207.39314972 -1.46580263
-27.81750835 -134.3740951 98.97724793 222.67543268 117.97255343]
intercept: 152.553545058867
training set: 0.4326376676137663
tesing set: 0.4325217769068186
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<p>可以说，复杂度越低的模型，在训练集上表现越差，但是其泛化能力会更好。</p>
<p>如果在意泛化能力，则应该选择岭回归，而不是线性回归模型</p>
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<h2 id="岭回归的参数调节">岭回归的参数调节<a class="anchor-link" href="#岭回归的参数调节">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">Ridge</span>
<span class="c1"># 使用岭回归对数据进行拟合，设置 alpha=10</span>
<span class="n">ridge</span><span class="o">=</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="c1"># 打印出模型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"coef:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">coef_</span><span class="p">[:])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"intercept:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span>
<span class="c1"># y=w1*x1 +w2*x2 + b</span>
<span class="c1"># 打分</span>
<span class="nb">print</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"training set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"tesing set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="c1"># 分别是 0.15 和 0.16，测试集打分超过训练集了</span>
<span class="c1"># 也就是说，如果模型过拟合，可以通过提高 alpha 值来降低过拟合现象。</span>
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<pre>coef: [ 15.08676646 -1.9586191 60.69903425 47.11843221 14.72337546
9.87779644 -35.56015266 35.74603575 54.27193163 37.42095846]
intercept: 152.7585777843719
training set: 0.15119962367011153
tesing set: 0.16202013428866247
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<p>降低 alpha 值会让系数的限制变得不那么严格。当alpha很小时，限制可以忽略不计，非常接近线性回归。</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">Ridge</span>
<span class="c1"># 使用岭回归对数据进行拟合，设置 alpha=0.1</span>
<span class="n">ridge</span><span class="o">=</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="c1"># 打印出模型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"coef:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">coef_</span><span class="p">[:])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"intercept:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span>
<span class="c1"># y=w1*x1 +w2*x2 + b</span>
<span class="c1"># 打分</span>
<span class="nb">print</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"training set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"tesing set:"</span><span class="p">,</span> <span class="n">ridge</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span>
<span class="c1"># 分别是 0.52 和 0.47</span>
<span class="c1"># 相比线性模型，alpha很小时，训练集打分略降低，而测试集打分略提高。</span>
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<pre>coef: [ 24.77802114 -228.33364296 495.54594378 361.21481169 -109.82542594
-78.3286822 -190.69780344 108.24040795 383.72269392 107.42593373]
intercept: 152.48093836963517
training set: 0.521564605524134
tesing set: 0.4734019500945309
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<h2 id="alpha值对模型的影响">alpha值对模型的影响<a class="anchor-link" href="#alpha值对模型的影响">¶</a></h2>
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<ul>
<li>画图展示 不同 alpha 值对应的模型的 coef_ 属性。</li>
<li>较高的 alpha 值表示模型的限制更加严格。</li>
<li>所以我们认为，alpha值越高，coef<em>属性的数值会更小，反之 coef</em> 属性的值更大。</li>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="c1"># alpha=0.1 时的模型系数</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Ridge alpha=0.1"</span><span class="p">)</span>
<span class="c1"># alpha=1 时的模型系数</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="s1">'s'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Ridge alpha=1"</span><span class="p">)</span>
<span class="c1"># alpha=10 时的模型系数</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="s1">'^'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Ridge alpha=10"</span><span class="p">)</span>
<span class="c1"># 绘制线性回归的系数作为对比</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="k">import</span> <span class="n">LinearRegression</span>
<span class="n">lr</span><span class="o">=</span><span class="n">LinearRegression</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</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">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="s2">"o"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"linear regression"</span><span class="p">)</span>
<span class="c1">#</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"coefficient index"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"coefficent magnitude"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hlines</span><span class="p">(</span><span class="mi">0</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">lr</span><span class="o">.</span><span class="n">coef_</span><span class="p">))</span> <span class="c1">#水平直线，过原点</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<h2 id="数据集大小对岭回归的影响---学习曲线">数据集大小对岭回归的影响 - 学习曲线<a class="anchor-link" href="#数据集大小对岭回归的影响---学习曲线">¶</a></h2>
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<p>另一个理解正则化对模型影响的方法，就是固定alpha值，该不安训练集的数据量。</p>
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<div class=" highlight hl-ipython3"><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">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <span class="n">learning_curve</span><span class="p">,</span> <span class="n">KFold</span>
<span class="c1"># 定义一个绘制学习曲线的函数</span>
<span class="k">def</span> <span class="nf">plot_learning_curve</span><span class="p">(</span><span class="n">est</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"># 对数据进行20次拆分用来对模型进行评分</span>
<span class="n">training_set_size</span><span class="p">,</span> <span class="n">train_scores</span><span class="p">,</span> <span class="n">test_scores</span><span class="o">=</span><span class="n">learning_curve</span><span class="p">(</span>
<span class="n">est</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="n">train_sizes</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">),</span> <span class="n">cv</span><span class="o">=</span><span class="n">KFold</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span>
<span class="n">estimator_name</span><span class="o">=</span><span class="n">est</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span>
<span class="n">line</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">training_set_size</span><span class="p">,</span> <span class="n">train_scores</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="s1">'--'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"training "</span><span class="o">+</span><span class="n">estimator_name</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">training_set_size</span><span class="p">,</span> <span class="n">test_scores</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="s1">'-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"test "</span><span class="o">+</span><span class="n">estimator_name</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="n">line</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">get_color</span><span class="p">())</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Training set size"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Score"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">)</span>
<span class="n">plot_learning_curve</span><span class="p">(</span><span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mi">1</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="n">plot_learning_curve</span><span class="p">(</span><span class="n">LinearRegression</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="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">),</span> <span class="n">ncol</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
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<pre><matplotlib.legend.Legend at 0x7f5c2bec9630></pre>
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<li>可见，数据量小的时候，岭回归的训练集和测试集表现差不多，而普通线性回归则差异很大。</li>
<li>当数据量很大时，正则化就没那么重要了，两者表现一致。</li>
<li>随着数据量的增大，线性回归在训练集上的得分是下降的；说明数据量越大，线性回归越不容易过拟合，或者越难记住已知数据。</li>
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<h2 id="岭迹图-x=alpha,-y=coef">岭迹图 x=alpha, y=coef<a class="anchor-link" href="#岭迹图-x=alpha,-y=coef">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
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<pre>array([1.e-10, 1.e-06, 1.e-02, 1.e+02])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 创建 alpha 集合</span>
<span class="n">alphas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span> <span class="c1"># -3 到 2 取100份</span>
<span class="c1"># 计算对应的 coef</span>
<span class="n">coefs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">alpha</span> <span class="ow">in</span> <span class="n">alphas</span><span class="p">:</span>
<span class="c1"># 获取模型 设置参数</span>
<span class="c1"># 通过修改Ridge(fit_intercept=False)，来让岭回归模型来关闭差值，不让差值调整结果值，这样我们获得的斜率就不是0了。</span>
<span class="n">rr</span> <span class="o">=</span> <span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">,</span> <span class="n">fit_intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">rr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">coefs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">rr</span><span class="o">.</span><span class="n">coef_</span><span class="p">)</span>
<span class="c1"># 绘图</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">alphas</span><span class="p">,</span><span class="n">coefs</span><span class="p">)</span>
<span class="c1"># 设置坐标轴 不是以均匀的方式展示 设置x轴线 而是 以10的倍数来显示</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xscale</span><span class="p">(</span><span class="s1">'log'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Alpha"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Coef"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<h1 id="使用-L1-正则化的线性模型---套索回归-lasso">使用 L1 正则化的线性模型 - 套索回归 lasso<a class="anchor-link" href="#使用-L1-正则化的线性模型---套索回归-lasso">¶</a></h1>
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