{"id":103237,"date":"2026-09-10T05:25:01","date_gmt":"2026-09-09T21:25:01","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/103237.html"},"modified":"2026-09-10T05:25:01","modified_gmt":"2026-09-09T21:25:01","slug":"%e7%a7%91%e7%a0%94%e5%9b%be%e8%a1%a8%e8%ae%be%e8%ae%a1%ef%bc%9a%e5%a6%82%e4%bd%95%e7%94%a8%e8%af%af%e5%b7%ae%e6%a3%92%ef%bc%88error-bar%ef%bc%89%e5%b1%95%e7%a4%ba%e5%a4%9a%e6%ac%a1%e5%ae%9e%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/103237.html","title":{"rendered":"\u79d1\u7814\u56fe\u8868\u8bbe\u8ba1\uff1a\u5982\u4f55\u7528\u8bef\u5dee\u68d2\uff08Error Bar\uff09\u5c55\u793a\u591a\u6b21\u5b9e\u9a8c\u7684\u771f\u5b9e\u7f6e\u4fe1\u5ea6"},"content":{"rendered":"<h2>\u79d1\u7814\u56fe\u8868\u8bbe\u8ba1&#xff1a;\u5982\u4f55\u7528\u8bef\u5dee\u68d2&#xff08;Error Bar&#xff09;\u5c55\u793a\u591a\u6b21\u5b9e\u9a8c\u7684\u771f\u5b9e\u7f6e\u4fe1\u5ea6<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260909212500-6aa1ceac13a61.webp\" alt=\"\u5c01\u9762\u4fe1\u606f\u56fe\" \/><\/p>\n<p>\u5728\u9605\u8bfb\u9876\u7ea7\u5b66\u672f\u8bba\u6587\u6216\u5de5\u4e1a\u7ea7\u8bc4\u6d4b\u62a5\u544a\u65f6&#xff0c;\u4e13\u4e1a\u5ba1\u7a3f\u4eba\u548c\u8d44\u6df1\u6280\u672f\u4e13\u5bb6\u6700\u53cd\u611f\u7684\u4e00\u7c7b\u56fe\u8868&#xff0c;\u5c31\u662f\u201c\u5355\u70b9\u65e0\u8bef\u5dee\u7ebf\u201d\u7684\u6298\u7ebf\u56fe\u6216\u67f1\u72b6\u56fe\u3002<\/p>\n<p>\u53ea\u5c55\u793a\u4e00\u4e2a\u5355\u7eaf\u7684\u5747\u503c\u67f1\u5b50&#xff0c;\u5b8c\u5168\u63a9\u76d6\u4e86\u5b9e\u9a8c\u5728\u4e0d\u540c\u968f\u673a\u6570\u79cd\u5b50\u6216\u4ea4\u53c9\u9a8c\u8bc1\u6298\u6570\u4e0b\u7684\u79bb\u6563\u7a0b\u5ea6&#xff08;Variability&#xff09;\u3002\u4e00\u4e2a\u770b\u4f3c\u9886\u5148 0.5% \u7684\u7b97\u6cd5&#xff0c;\u5982\u679c\u5176\u5355\u6b21\u8fd0\u884c\u7684\u6ce2\u52a8\u8303\u56f4\u9ad8\u8fbe $\\\\pm 2.0%$&#xff0c;\u90a3\u4e48\u8be5\u56fe\u8868\u5c55\u793a\u7684\u4f18\u8d8a\u6027\u7ed3\u8bba\u5c31\u662f\u6beb\u65e0\u7edf\u8ba1\u5b66\u610f\u4e49\u7684\u5047\u8c61\u3002<\/p>\n<p>\u4e25\u8c28\u7684\u6280\u672f\u56fe\u8868\u5fc5\u987b\u914d\u5907\u8bef\u5dee\u68d2&#xff08;Error Bar&#xff09;\u3002<\/p>\n<p>\u7136\u800c&#xff0c;\u5f88\u591a\u540c\u5b66\u5728 Matplotlib \u4e2d\u8c03\u7528 yerr \u53c2\u6570\u65f6&#xff0c;\u5e76\u4e0d\u6e05\u695a\u81ea\u5df1\u7ed8\u5236\u7684\u5230\u5e95\u4ee3\u8868\u4ec0\u4e48\u3002<\/p>\n<p>\u672c\u6587\u5398\u6e05\u4e09\u79cd\u6838\u5fc3\u8bef\u5dee\u5ea6\u91cf&#xff08;SD\u3001SEM\u300195% CI&#xff09;\u7684\u6570\u5b66\u672c\u8d28\u4e0e\u7ed8\u56fe\u89c4\u8303\u3002<\/p>\n<h3>1. \u4e09\u5927\u7ea6\u5dee\u5ea6\u91cf\u6307\u6807\u7684\u672c\u8d28\u5dee\u5f02\u4e0e\u9009\u7528\u573a\u666f<\/h3>\n<p>\u5047\u8bbe\u6211\u4eec\u5728 5 \u4e2a\u4e0d\u540c\u968f\u673a\u79cd\u5b50\u4e0b\u8dd1\u51fa\u4e86\u67d0\u6a21\u578b\u7684\u6027\u80fd\u6837\u672c $X &#061; [x_1, x_2, \\\\dots, x_N]$&#xff0c;\u5747\u503c\u4e3a $\\\\bar{x}$&#xff1a;<\/p>\n<h4>(1) \u6837\u672c\u6807\u51c6\u5dee&#xff08;Standard Deviation, SD \/ $s$&#xff09;<\/h4>\n<p>$$s &#061; \\\\sqrt{\\\\frac{1}{N-1} \\\\sum_{i&#061;1}^N (x_i &#8211; \\\\bar{x})^2}$$<\/p>\n<ul>\n<li>\u4ee3\u8868\u542b\u4e49&#xff1a;\u8861\u91cf\u5355\u6b21\u5b9e\u9a8c\u7ed3\u679c\u672c\u8eab\u7684\u79bb\u6563\u5ea6\u4e0e\u6ce2\u52a8\u8303\u56f4&#xff1b;<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u5411\u8bfb\u8005\u5c55\u793a\u201c\u5982\u679c\u6211\u968f\u673a\u8dd1\u4e00\u6b21\u5b9e\u9a8c&#xff0c;\u5927\u6982\u7387\u4f1a\u843d\u5728\u4ec0\u4e48\u533a\u95f4\u201d\u3002<\/li>\n<\/ul>\n<h4>(2) \u5747\u503c\u6807\u51c6\u8bef&#xff08;Standard Error of the Mean, SEM \/ $s_{\\\\bar{x}}$&#xff09;<\/h4>\n<p>$$\\\\text{SEM} &#061; \\\\frac{s}{\\\\sqrt{N}}$$<\/p>\n<ul>\n<li>\u4ee3\u8868\u542b\u4e49&#xff1a;\u8861\u91cf\u4f30\u8ba1\u51fa\u7684\u5747\u503c $\\\\bar{x}$ \u4e0e\u771f\u5b9e\u603b\u4f53\u5747\u503c\u4e4b\u95f4\u7684\u7406\u8bba\u4e0d\u786e\u5b9a\u6027&#xff1b;<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u968f\u7740\u91cd\u590d\u5b9e\u9a8c\u6b21\u6570 $N$ \u589e\u52a0&#xff0c;SEM \u4f1a\u7f29\u5c0f\u3002\u9002\u7528\u4e8e\u8bc1\u660e\u5927\u6837\u672c\u91cf\u4e0b\u5747\u503c\u4f30\u8ba1\u7684\u7cbe\u5bc6\u5ea6\u3002<\/li>\n<\/ul>\n<h4>(3) 95% \u7f6e\u4fe1\u533a\u95f4&#xff08;95% Confidence Interval, 95% CI&#xff09;<\/h4>\n<p>$$\\\\text{95% CI} &#061; \\\\bar{x} \\\\pm t_{\\\\alpha\/2, N-1} \\\\times \\\\text{SEM}$$<\/p>\n<ul>\n<li>\u4ee3\u8868\u542b\u4e49&#xff1a;\u5728\u91cd\u590d\u62bd\u6837\u4e2d&#xff0c;\u6709 95% \u7684\u6982\u7387\u5305\u542b\u771f\u5b9e\u7684\u603b\u4f53\u671f\u671b\u5747\u503c&#xff1b;<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u9876\u4f1a\u8bba\u6587\u4e0e\u51b3\u7b56\u8bc4\u5ba1\u7684\u9ec4\u91d1\u6807\u51c6\u3002\u4e24\u4e2a\u7b97\u6cd5\u7684 95% CI \u82e5\u5b8c\u5168\u4e0d\u91cd\u53e0&#xff0c;\u53ef\u5728\u89c6\u89c9\u4e0a\u76f4\u63a5\u4f50\u8bc1\u5176\u663e\u8457\u6027\u5dee\u5f02\u3002<\/li>\n<\/ul>\n<h3>2. \u57fa\u4e8e Matplotlib \/ Seaborn \u7ed8\u5236\u51fa\u7248\u7ea7\u8bef\u5dee\u68d2\u56fe\u8868<\/h3>\n<p>import numpy as np<br \/>\nimport matplotlib.pyplot as plt<br \/>\nimport seaborn as sns<\/p>\n<p>def plot_publication_error_bars(save_path: str &#061; &#034;benchmark_with_ci.pdf&#034;):<br \/>\n    # \u7edf\u4e00\u8bbe\u7f6e\u79d1\u7814\u6837\u5f0f<br \/>\n    sns.set_theme(style&#061;&#034;ticks&#034;, font&#061;&#034;sans-serif&#034;)<br \/>\n    plt.rcParams.update({<br \/>\n        &#034;font.size&#034;: 11,<br \/>\n        &#034;axes.labelsize&#034;: 12,<br \/>\n        &#034;axes.titlesize&#034;: 13,<br \/>\n        &#034;xtick.labelsize&#034;: 11,<br \/>\n        &#034;ytick.labelsize&#034;: 11,<br \/>\n        &#034;figure.titlesize&#034;: 15<br \/>\n    })<\/p>\n<p>    # \u6a21\u62df 3 \u7ec4\u7b97\u6cd5\u5728 4 \u79cd\u4e0d\u540c\u4efb\u52a1\u4e0a\u7684 5 \u6b21\u72ec\u7acb\u5b9e\u9a8c\u7ed3\u679c (Mean &#043;\/- SD)<br \/>\n    tasks &#061; [&#034;\u610f\u56fe\u5206\u7c7b&#034;, &#034;NER\u5b9e\u4f53\u62bd\u53d6&#034;, &#034;\u5173\u7cfb\u62bd\u53d6&#034;, &#034;\u957f\u6587\u672c\u6458\u8981&#034;]<br \/>\n    x &#061; np.arange(len(tasks))<br \/>\n    width &#061; 0.25<\/p>\n<p>    # \u7b97\u6cd5 A (\u57fa\u7ebf)<br \/>\n    means_a &#061; [88.4, 82.1, 71.5, 68.2]<br \/>\n    stds_a &#061; [0.85, 1.20, 1.45, 1.80]<\/p>\n<p>    # \u7b97\u6cd5 B (\u4f18\u5316\u65b9\u6848)<br \/>\n    means_b &#061; [92.6, 88.5, 84.2, 79.8]<br \/>\n    stds_b &#061; [0.42, 0.55, 0.68, 0.75]<\/p>\n<p>    fig, ax &#061; plt.subplots(figsize&#061;(8, 5), dpi&#061;300)<\/p>\n<p>    # \u7ed8\u5236\u5e26\u8bef\u5dee\u68d2\u7684\u67f1\u72b6\u56fe (capsize \u8bbe\u7f6e\u6a2a\u5411\u5c01\u53e3\u7ebf\u5bbd\u5ea6)<br \/>\n    rects1 &#061; ax.bar(<br \/>\n        x &#8211; width\/2,<br \/>\n        means_a,<br \/>\n        width,<br \/>\n        yerr&#061;stds_a,<br \/>\n        capsize&#061;4,<br \/>\n        label&#061;&#034;BERT-Base (Baseline)&#034;,<br \/>\n        color&#061;&#034;#4C72B0&#034;,<br \/>\n        edgecolor&#061;&#034;#333333&#034;,<br \/>\n        linewidth&#061;0.8,<br \/>\n        error_kw&#061;{&#034;elinewidth&#034;: 1.2, &#034;ecolor&#034;: &#034;#333333&#034;}<br \/>\n    )<\/p>\n<p>    rects2 &#061; ax.bar(<br \/>\n        x &#043; width\/2,<br \/>\n        means_b,<br \/>\n        width,<br \/>\n        yerr&#061;stds_b,<br \/>\n        capsize&#061;4,<br \/>\n        label&#061;&#034;Ours (Pre-LN &#043; RoPE &#043; Distill)&#034;,<br \/>\n        color&#061;&#034;#DD8452&#034;,<br \/>\n        edgecolor&#061;&#034;#333333&#034;,<br \/>\n        linewidth&#061;0.8,<br \/>\n        error_kw&#061;{&#034;elinewidth&#034;: 1.2, &#034;ecolor&#034;: &#034;#333333&#034;}<br \/>\n    )<\/p>\n<p>    ax.set_ylabel(&#034;Macro-F1 Score (%)&#034;, labelpad&#061;8)<br \/>\n    ax.set_title(&#034;Cross-Task Evaluation Benchmark (N&#061;5 Independent Runs)&#034;, pad&#061;14, fontweight&#061;&#034;bold&#034;)<br \/>\n    ax.set_xticks(x)<br \/>\n    ax.set_xticklabels(tasks)<br \/>\n    ax.set_ylim(60, 100) # \u4fdd\u6301\u8bda\u5b9e\u7684\u89c6\u89c9\u6bd4\u4f8b<br \/>\n    ax.legend(loc&#061;&#034;upper left&#034;, frameon&#061;True, framealpha&#061;0.9)<\/p>\n<p>    # \u6d88\u9664\u9876\u90e8\u548c\u53f3\u4fa7\u5197\u4f59\u5916\u6846\u7ebf\u6761<br \/>\n    sns.despine(ax&#061;ax, top&#061;True, right&#061;True)<\/p>\n<p>    plt.tight_layout()<br \/>\n    plt.savefig(save_path, bbox_inches&#061;&#034;tight&#034;)<br \/>\n    plt.close()<br \/>\n    print(f&#034;\u5e26\u8bef\u5dee\u68d2\u79d1\u7814\u56fe\u8868\u5df2\u6210\u529f\u4fdd\u5b58\u81f3: {save_path}&#034;)<\/p>\n<p>if __name__ &#061;&#061; &#034;__main__&#034;:<br \/>\n    plot_publication_error_bars()<\/p>\n<h3>3. \u56fe\u8868 Caption \u6ce8\u91ca\u7684\u89c4\u8303\u5199\u6cd5<\/h3>\n<p>\u5728\u56fe\u8868\u4e0b\u65b9\u5fc5\u987b\u9644\u5e26\u4e25\u5bc6\u7684\u81ea\u5305\u542b\u8bf4\u660e&#xff0c;\u663e\u5f0f\u58f0\u660e\u8bef\u5dee\u68d2\u7684\u7edf\u8ba1\u5b66\u5b9a\u4e49&#xff1a;<\/p>\n<p>\u56fe 1&#xff1a;\u56db\u9879 NLP \u4e0b\u6e38\u4efb\u52a1\u5728 5 \u6b21\u72ec\u7acb\u968f\u673a\u79cd\u5b50\u4e0b\u7684\u6027\u80fd\u5bf9\u6bd4\u3002 \u67f1\u5b50\u9ad8\u5ea6\u4ee3\u8868 5 \u6b21\u8fd0\u884c\u7684\u5747\u503c&#xff08;Mean&#xff09;&#xff0c;\u5782\u76f4\u8bef\u5dee\u68d2\u4ee3\u8868\u6837\u672c\u6807\u51c6\u5dee&#xff08;$\\\\pm 1 \\\\text{ SD}$&#xff09;\u3002\u53ef\u4ee5\u770b\u51fa&#xff0c;\u4f18\u5316\u65b9\u6848\u4e0d\u4ec5\u5728\u5168\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u663e\u8457\u8d85\u8d8a\u57fa\u7ebf\u7684 F1 \u5206\u6570&#xff0c;\u4e14\u8bef\u5dee\u68d2\u957f\u5ea6\u663e\u8457\u77ed\u4e8e\u57fa\u7ebf\u6a21\u578b&#xff0c;\u8bc1\u660e\u4e86\u5176\u4f18\u5f02\u7684\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002<\/p>\n<h3>4. \u7ed8\u56fe\u4e09\u5927\u907f\u5751\u8981\u70b9<\/h3>\n<li>\u7edd\u5bf9\u7981\u6b62\u9690\u7792\u5b9a\u4e49&#xff1a;\u5982\u679c\u753b\u4e86\u8bef\u5dee\u68d2\u5374\u5728\u6b63\u6587\u548c Caption \u4e2d\u53ea\u5b57\u4e0d\u63d0\u662f SD \u8fd8\u662f SEM&#xff0c;\u5ba1\u7a3f\u4eba\u4f1a\u76f4\u63a5\u8d28\u7591\u6570\u636e\u7684\u771f\u5b9e\u6027&#xff1b;<\/li>\n<li>\u62d2\u7edd\u4e0d\u5bf9\u79f0\u7684\u624b\u52a8\u5fae\u8c03&#xff1a;\u8bef\u5dee\u68d2\u5fc5\u987b\u7531\u811a\u672c\u6839\u636e\u771f\u5b9e\u8dd1\u6d4b\u7684\u6570\u7ec4\u81ea\u52a8\u8ba1\u7b97\u751f\u6210&#xff0c;\u4e25\u7981\u4e3a\u4e86\u753b\u9762\u7f8e\u89c2\u624b\u52a8\u7be1\u6539\u6570\u503c&#xff1b;<\/li>\n<li>\u6298\u7ebf\u56fe\u4e2d\u7684\u5e26\u72b6\u9634\u5f71&#xff08;Fill Between&#xff09;&#xff1a;\u5728\u5c55\u793a\u8fde\u7eed\u7684 Loss \u6216 Step \u66f2\u7ebf\u65f6&#xff0c;\u4f7f\u7528\u5e26\u6709\u900f\u660e\u5ea6\u7684 ax.fill_between(x, mean-std, mean&#043;std, alpha&#061;0.2) \u6bd4\u5bc6\u96c6\u7ad6\u76f4\u67f1\u5b50\u5177\u6709\u66f4\u597d\u7684\u53ef\u8bfb\u6027\u3002<\/li>\n","protected":false},"excerpt":{"rendered":"<p>\u79d1\u7814\u56fe\u8868\u8bbe\u8ba1&#xff1a;\u5982\u4f55\u7528\u8bef\u5dee\u68d2&#xff08;Error Bar&#xff09;\u5c55\u793a\u591a\u6b21\u5b9e\u9a8c\u7684\u771f\u5b9e\u7f6e\u4fe1\u5ea6\u5728\u9605\u8bfb\u9876\u7ea7\u5b66\u672f\u8bba\u6587\u6216\u5de5\u4e1a\u7ea7\u8bc4\u6d4b\u62a5\u544a\u65f6&#xff0c;\u4e13\u4e1a\u5ba1\u7a3f\u4eba\u548c\u8d44\u6df1\u6280\u672f\u4e13\u5bb6\u6700\u53cd\u611f\u7684\u4e00\u7c7b\u56fe\u8868&#xff0c;\u5c31\u662f\u201c\u5355\u70b9\u65e0\u8bef\u5dee\u7ebf\u201d\u7684\u6298\u7ebf\u56fe\u6216\u67f1\u72b6\u56fe\u3002<br 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