{"id":934853,"date":"2024-12-26T18:42:05","date_gmt":"2024-12-26T10:42:05","guid":{"rendered":""},"modified":"2024-12-26T18:42:07","modified_gmt":"2024-12-26T10:42:07","slug":"python%e5%a6%82%e4%bd%95mse%e4%bd%9c%e5%9b%be","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/934853.html","title":{"rendered":"python\u5982\u4f55mse\u4f5c\u56fe"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25071700\/ca000807-8e17-4b33-99cd-ed710c10d28a.webp\" alt=\"python\u5982\u4f55mse\u4f5c\u56fe\" \/><\/p>\n<p><p> <strong>\u8981\u4f7f\u7528Python\u8fdb\u884c\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u4f5c\u56fe\uff0c\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u5f0f\u5b9e\u73b0\uff0c\u5982\u4f7f\u7528Matplotlib\u3001Seaborn\u6216\u5176\u4ed6\u53ef\u89c6\u5316\u5e93\u3002\u901a\u5e38\uff0c\u6211\u4eec\u9700\u8981\u9996\u5148\u8ba1\u7b97MSE\uff0c\u7136\u540e\u4f7f\u7528\u8fd9\u4e9b\u5e93\u8fdb\u884c\u53ef\u89c6\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u5c06\u8be6\u7ec6\u63cf\u8ff0\u5982\u4f55\u4f7f\u7528Matplotlib\u8fdb\u884cMSE\u4f5c\u56fe\u3001\u4f7f\u7528\u5e93\u6765\u8ba1\u7b97\u8bef\u5dee\u3001\u901a\u8fc7\u56fe\u5f62\u5c55\u793a\u8bef\u5dee\u53d8\u5316\u8d8b\u52bf\u3002<\/strong><\/p>\n<\/p>\n<p><p>\u4e00\u3001\u8ba1\u7b97MSE\u5e76\u4f7f\u7528Matplotlib\u4f5c\u56fe<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u8ba1\u7b97\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09<\/strong><br \/>\u5747\u65b9\u8bef\u5dee\u662f\u4e00\u79cd\u8861\u91cf\u9884\u6d4b\u503c\u4e0e\u5b9e\u9645\u503c\u4e4b\u95f4\u5dee\u5f02\u7684\u6307\u6807\u3002\u5b83\u901a\u8fc7\u5bf9\u9884\u6d4b\u8bef\u5dee\u7684\u5e73\u65b9\u8fdb\u884c\u5e73\u5747\u6765\u8ba1\u7b97\u3002\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p><p>[<\/p>\n<p>\\text{MSE} = \\frac{1}{n} \\sum_{i=1}^{n} (y_i &#8211; \\hat{y}_i)^2<\/p>\n<p>]<\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff0c(y_i) \u662f\u5b9e\u9645\u503c\uff0c(\\hat{y}_i) \u662f\u9884\u6d4b\u503c\uff0c(n) \u662f\u6837\u672c\u6570\u91cf\u3002<\/p>\n<\/p>\n<p><p>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u6765\u8ba1\u7b97MSE\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>def calculate_mse(actual, predicted):<\/p>\n<p>    return np.mean((np.array(actual) - np.array(predicted))  2)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u4f7f\u7528Matplotlib\u4f5c\u56fe<\/strong><br \/>Matplotlib\u662fPython\u4e2d\u6700\u5e38\u7528\u7684\u7ed8\u56fe\u5e93\u4e4b\u4e00\uff0c\u53ef\u4ee5\u7528\u6765\u7ed8\u5236MSE\u968f\u65f6\u95f4\u53d8\u5316\u7684\u56fe\u8868\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import matplotlib.pyplot as plt<\/p>\n<p>def plot_mse(mse_values, title=&#39;MSE Over Time&#39;):<\/p>\n<p>    plt.figure(figsize=(10, 5))<\/p>\n<p>    plt.plot(mse_values, marker=&#39;o&#39;, linestyle=&#39;-&#39;)<\/p>\n<p>    plt.title(title)<\/p>\n<p>    plt.xlabel(&#39;Iterations&#39;)<\/p>\n<p>    plt.ylabel(&#39;MSE&#39;)<\/p>\n<p>    plt.grid(True)<\/p>\n<p>    plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u5c06MSE\u503c\u5217\u8868\u4f20\u9012\u7ed9<code>plot_mse<\/code>\u51fd\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230MSE\u7684\u53d8\u5316\u8d8b\u52bf\u56fe\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u4e8c\u3001\u5728<a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u6a21\u578b\u4e2d\u8ba1\u7b97\u548c\u4f5c\u56feMSE<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u6a21\u578b\u8bad\u7ec3\u4e2d\u7684MSE\u8ba1\u7b97<\/strong><br \/>\u5728\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u8ba1\u7b97\u8bad\u7ec3\u96c6\u548c\u9a8c\u8bc1\u96c6\u7684MSE\uff0c\u4ee5\u8bc4\u4f30\u6a21\u578b\u7684\u6027\u80fd\u3002\u4ee5\u7ebf\u6027\u56de\u5f52\u4e3a\u4f8b\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from sklearn.model_selection import tr<a href=\"https:\/\/docs.pingcode.com\/blog\/59162.html\" target=\"_blank\">AI<\/a>n_test_split<\/p>\n<p>from sklearn.linear_model import LinearRegression<\/p>\n<p>from sklearn.metrics import mean_squared_error<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e9b\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n<p>X = np.random.rand(100, 1) * 10<\/p>\n<p>y = 2.5 * X + np.random.randn(100, 1)<\/p>\n<h2><strong>\u5c06\u6570\u636e\u5206\u4e3a\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6<\/strong><\/h2>\n<p>X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)<\/p>\n<h2><strong>\u521b\u5efa\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5e76\u8fdb\u884c\u8bad\u7ec3<\/strong><\/h2>\n<p>model = LinearRegression()<\/p>\n<p>model.fit(X_train, y_train)<\/p>\n<h2><strong>\u9884\u6d4b\u5e76\u8ba1\u7b97MSE<\/strong><\/h2>\n<p>y_train_pred = model.predict(X_train)<\/p>\n<p>y_test_pred = model.predict(X_test)<\/p>\n<p>mse_train = mean_squared_error(y_train, y_train_pred)<\/p>\n<p>mse_test = mean_squared_error(y_test, y_test_pred)<\/p>\n<p>print(f&#39;Train MSE: {mse_train}, Test MSE: {mse_test}&#39;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u4e0a\u8ff0\u4ee3\u7801\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u7684MSE\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u4f5c\u56fe<\/strong><br \/>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u4ee5\u8bb0\u5f55\u6bcf\u6b21\u8fed\u4ee3\u7684MSE\uff0c\u5e76\u5728\u8bad\u7ec3\u7ed3\u675f\u540e\u8fdb\u884c\u53ef\u89c6\u5316\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">mse_values = []<\/p>\n<h2><strong>\u6a21\u62df\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684MSE\u53d8\u5316<\/strong><\/h2>\n<p>for i in range(100):<\/p>\n<p>    # \u5047\u8bbe\u6bcf\u6b21\u8fed\u4ee3\u540e\u5f97\u5230\u65b0\u7684\u9884\u6d4b\u503c\u5e76\u8ba1\u7b97MSE<\/p>\n<p>    mse_values.append(calculate_mse(y_train, y_train_pred - (i * 0.01)))<\/p>\n<h2><strong>\u4f5c\u56fe<\/strong><\/h2>\n<p>plot_mse(mse_values, title=&#39;Training MSE Over Iterations&#39;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u8fd9\u6837\u7684\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u89c2\u5730\u89c2\u5bdfMSE\u7684\u53d8\u5316\u8d8b\u52bf\uff0c\u4ece\u800c\u5e2e\u52a9\u6211\u4eec\u5224\u65ad\u6a21\u578b\u7684\u6536\u655b\u6027\u548c\u6027\u80fd\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u4e09\u3001\u4f7f\u7528Seaborn\u8fdb\u884cMSE\u4f5c\u56fe<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>Seaborn\u7b80\u4ecb<\/strong><br \/>Seaborn\u662f\u4e00\u4e2a\u57fa\u4e8eMatplotlib\u4e4b\u4e0a\u7684Python\u53ef\u89c6\u5316\u5e93\uff0c\u5b83\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7ea7\u7684\u63a5\u53e3\u7528\u4e8e\u7ed8\u5236\u7edf\u8ba1\u56fe\u5f62\u3002\u76f8\u6bd4\u4e8eMatplotlib\uff0cSeaborn\u53ef\u4ee5\u66f4\u8f7b\u677e\u5730\u5904\u7406\u6570\u636e\u6846\uff0c\u5e76\u751f\u6210\u66f4\u7f8e\u89c2\u7684\u56fe\u5f62\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u4f7f\u7528Seaborn\u4f5c\u56fe<\/strong><br \/>\u5728\u4f7f\u7528Seaborn\u7ed8\u5236MSE\u56fe\u65f6\uff0c\u901a\u5e38\u9700\u8981\u5c06\u6570\u636e\u6574\u7406\u6210DataFrame\u683c\u5f0f\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import seaborn as sns<\/p>\n<p>import pandas as pd<\/p>\n<h2><strong>\u521b\u5efa\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n<p>data = {<\/p>\n<p>    &#39;Iteration&#39;: range(1, 101),<\/p>\n<p>    &#39;MSE&#39;: mse_values<\/p>\n<p>}<\/p>\n<p>df = pd.DataFrame(data)<\/p>\n<h2><strong>\u4f7f\u7528Seaborn\u4f5c\u56fe<\/strong><\/h2>\n<p>sns.set(style=&#39;whitegrid&#39;)<\/p>\n<p>plt.figure(figsize=(10, 5))<\/p>\n<p>sns.lineplot(x=&#39;Iteration&#39;, y=&#39;MSE&#39;, data=df, marker=&#39;o&#39;)<\/p>\n<p>plt.title(&#39;MSE Over Iterations&#39;)<\/p>\n<p>plt.xlabel(&#39;Iterations&#39;)<\/p>\n<p>plt.ylabel(&#39;MSE&#39;)<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528Seaborn\u7684\u5f3a\u5927\u529f\u80fd\u548c\u7f8e\u89c2\u7684\u98ce\u683c\u6765\u7ed8\u5236MSE\u56fe\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u56db\u3001\u4f7f\u7528Plotly\u8fdb\u884c\u4ea4\u4e92\u5f0fMSE\u4f5c\u56fe<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>Plotly\u7b80\u4ecb<\/strong><br \/>Plotly\u662f\u4e00\u4e2a\u7528\u4e8e\u521b\u5efa\u4ea4\u4e92\u5f0f\u56fe\u8868\u7684\u5f00\u6e90\u5e93\u3002\u4e0eMatplotlib\u548cSeaborn\u4e0d\u540c\uff0cPlotly\u751f\u6210\u7684\u56fe\u8868\u53ef\u4ee5\u5728\u7f51\u9875\u4e2d\u8fdb\u884c\u4ea4\u4e92\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u4f7f\u7528Plotly\u4f5c\u56fe<\/strong><br \/>Plotly\u7684\u4f18\u52bf\u5728\u4e8e\u5176\u4ea4\u4e92\u6027\uff0c\u9002\u5408\u9700\u8981\u52a8\u6001\u5c55\u793a\u6570\u636e\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import plotly.graph_objects as go<\/p>\n<p>def plot_mse_interactive(mse_values):<\/p>\n<p>    fig = go.Figure()<\/p>\n<p>    fig.add_trace(go.Scatter(<\/p>\n<p>        x=list(range(1, len(mse_values) + 1)),<\/p>\n<p>        y=mse_values,<\/p>\n<p>        mode=&#39;lines+markers&#39;,<\/p>\n<p>        name=&#39;MSE&#39;<\/p>\n<p>    ))<\/p>\n<p>    fig.update_layout(<\/p>\n<p>        title=&#39;MSE Over Iterations&#39;,<\/p>\n<p>        xaxis_title=&#39;Iterations&#39;,<\/p>\n<p>        yaxis_title=&#39;MSE&#39;,<\/p>\n<p>        template=&#39;plotly_white&#39;<\/p>\n<p>    )<\/p>\n<p>    fig.show()<\/p>\n<h2><strong>\u7ed8\u5236\u4ea4\u4e92\u5f0f\u56fe\u8868<\/strong><\/h2>\n<p>plot_mse_interactive(mse_values)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4f7f\u7528Plotly\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6d4f\u89c8\u5668\u4e2d\u67e5\u770b\u5e76\u4ea4\u4e92\u5f0f\u5730\u63a2\u7d22MSE\u7684\u53d8\u5316\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u4e94\u3001\u603b\u7ed3\u4e0e\u7ecf\u9a8c<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u9009\u62e9\u5408\u9002\u7684\u5e93<\/strong><br \/>\u5728\u9009\u62e9\u7528\u4e8e\u4f5c\u56fe\u7684\u5e93\u65f6\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u9700\u6c42\u8fdb\u884c\u9009\u62e9\u3002Matplotlib\u9002\u5408\u9700\u8981\u7cbe\u7ec6\u63a7\u5236\u7684\u9759\u6001\u56fe\uff0cSeaborn\u9002\u5408\u5feb\u901f\u751f\u6210\u7f8e\u89c2\u7684\u7edf\u8ba1\u56fe\uff0cPlotly\u5219\u9002\u5408\u9700\u8981\u4ea4\u4e92\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u6ce8\u610f\u6570\u636e\u7684\u5c3a\u5ea6\u548c\u8303\u56f4<\/strong><br 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