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\u5b9a\u5e94\u7528\u73af\u5883\u4e2d\u6709\u7528\u4e14\u53ef\u9760\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<h3>\u4e8c\u3001\u5408\u6210\u6570\u636e\u751f\u6210\u6280\u672f<\/h3>\n<p>\u4f7f\u7528\u6982\u7387\u6280\u672f\u751f\u6210\u5408\u6210\u6570\u636e\u662f\u57fa\u4e8e\u4f7f\u7528\u6570\u5b66\u5206\u5e03\u6765\u6a21\u62df\u5728\u771f\u5b9e\u6570\u636e\u96c6\u4e2d\u89c2\u5bdf\u5230\u7684\u53d8\u5f02\u6027\u3002\u8fd9\u79cd\u65b9\u6cd5\u5141\u8bb8\u60a8\u5efa\u6a21\u548c\u521b\u5efa\u9075\u5faa\u7279\u5b9a\u7edf\u8ba1\u5206\u5e03\uff08\u4f8b\u5982\u6b63\u6001\u5206\u5e03\u3001\u5747\u5300\u5206\u5e03\u6216\u4e8c\u9879\u5206\u5e03\uff09\u7684\u6570\u636e\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5c24\u5176\u9002\u7528\u4e8e\uff1a<\/p>\n<p>\u2022\u5728\u53d7\u63a7\u6761\u4ef6\u4e0b\u6d4b\u8bd5\u7b97\u6cd5\u3002<\/p>\n<p>\u2022\u4e3a\u771f\u5b9e\u6570\u636e\u6709\u9650\u6216\u4e0d\u53ef\u7528\u7684\u60c5\u51b5\u751f\u6210\u6570\u636e\u96c6\u3002<\/p>\n<p>\u2022\u6839\u636e\u5b9a\u4e49\u7684\u6982\u7387\u6a21\u578b\u6a21\u62df\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<h4>1.\u57fa\u672c\u5206\u5e03<\/h4>\n<p>\u6570\u5b66\u5206\u5e03\uff0c\u4f8b\u5982\u6b63\u6001\u5206\u5e03\uff08\u9ad8\u65af\u5206\u5e03\uff09\u3001\u5747\u5300\u5206\u5e03\u548c\u6cca\u677e\u5206\u5e03\uff0c\u662f\u751f\u6210\u5408\u6210\u6570\u636e\u7684\u57fa\u672c\u5de5\u5177\u3002\u4f7f\u7528 NumPy \u7b49 Python \u5e93\uff0c\u60a8\u53ef\u4ee5\u521b\u5efa\u4ee3\u8868\u7279\u5b9a\u573a\u666f\u7684\u6a21\u62df\u6570\u636e\u96c6\u3002<\/p>\n<p>\u793a\u4f8b\uff1a\u751f\u6210\u5177\u6709\u6b63\u6001\u5206\u5e03\u7684\u6570\u636e\u96c6<\/p>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"000000\" data-has-transparency=\"true\" style=\"--dominant-color: #000000;\" loading=\"lazy\" decoding=\"async\" class=\"has-transparency alignnone size-full wp-image-27562\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f6e6ce23920023ca86e0336c2229b15ee454b4.png\" width=\"259\" height=\"69\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f6e6ce23920023ca86e0336c2229b15ee454b4.png 259w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f6e6ce23920023ca86e0336c2229b15ee454b4-150x40.png 150w\" sizes=\"auto, (max-width: 259px) 100vw, 259px\" \/><\/p>\n<p>&nbsp;<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_0\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">import numpy as np \r\nimport matplotlib.pyplot as plt \r\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6570\u636emu, sigma = 0, 1 # \u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\r\ndata_normal = np.random.normal(mu, sigma, 1000) \r\n# \u53ef\u89c6\u5316\r\nplt.hist(data_normal, bins=30, alpha=0.7, color='blue', edgecolor='black') \r\nplt.title('\u6b63\u6001\u5206\u5e03') \r\nplt.xlabel('\u503c') \r\nplt.ylabel('\u9891\u7387') \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_0\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"cacaf5\" data-has-transparency=\"false\" style=\"--dominant-color: #cacaf5;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27563\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/27e90f1979df80818c3645c858762d47ab44ae.png\" width=\"805\" height=\"601\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/27e90f1979df80818c3645c858762d47ab44ae.png 805w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/27e90f1979df80818c3645c858762d47ab44ae-300x224.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/27e90f1979df80818c3645c858762d47ab44ae-150x112.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/27e90f1979df80818c3645c858762d47ab44ae-768x573.png 768w\" sizes=\"auto, (max-width: 805px) 100vw, 805px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h4>2.\u8499\u7279\u5361\u7f57\u91c7\u6837<\/h4>\n<p>\u8499\u7279\u5361\u6d1b\u91c7\u6837\u662f\u4e00\u79cd\u901a\u8fc7\u6a21\u62df\u66f4\u590d\u6742\u7684\u5206\u5e03\u6216\u7531\u4efb\u610f\u590d\u6742\u51fd\u6570\u5b9a\u4e49\u7684\u5206\u5e03\u6765\u751f\u6210\u6570\u636e\u7684\u6280\u672f\u3002\u5f53\u7b80\u5355\u5206\u5e03\u65e0\u6cd5\u6ee1\u8db3\u9700\u6c42\u65f6\uff0c\u5b83\u662f\u7406\u60f3\u7684\u9009\u62e9\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"000000\" data-has-transparency=\"true\" style=\"--dominant-color: #000000;\" loading=\"lazy\" decoding=\"async\" class=\"has-transparency alignnone size-full wp-image-27564\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/a61ebe126dd9cb4a3b8963b1c388bc2b511d17.png\" width=\"225\" height=\"86\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/a61ebe126dd9cb4a3b8963b1c388bc2b511d17.png 225w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/a61ebe126dd9cb4a3b8963b1c388bc2b511d17-150x57.png 150w\" sizes=\"auto, (max-width: 225px) 100vw, 225px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u793a\u4f8b\uff1a\u4f7f\u7528\u8499\u7279\u5361\u6d1b\u8fd1\u4f3c\u79ef\u5206\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_1\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">import numpy as np \r\nimport matplotlib.pyplot as plt \r\n# \u771f\u5b9e\u5206\u5e03\u7684\u53c2\u6570\uff08\u7b49\u5f85\u65f6\u95f4\uff09\r\nreal_mu = 10 # \u5e73\u5747\u503c\r\nreal_sigma = 2 # \u6807\u51c6\u5deen_real_samples = 10000 # \u771f\u5b9e\u6570\u636e\u6570\u91cf\uff08\u6837\u672c\uff09\r\n# \u771f\u5b9e\u6570\u636e\u751f\u6210\uff08\u89c2\u6d4b\u5206\u5e03\uff09\r\nreal_data = np.random.normal(real_mu, real_sigma, n_real_samples) \r\n# \u8499\u7279\u5361\u6d1b\uff1a\u7528\u4e8e\u8fd1\u4f3c\u771f\u5b9e\u5206\u5e03\u7684\u6e10\u8fdb\u6837\u672c\r\nn_monte_carlo_samples = 500 # \u8499\u7279\u5361\u6d1b\u6837\u672c\u7684\u6700\u5927\u6570\u91cf\r\nmonte_carlo_data = np.random.normal(real_mu, real_sigma, n_monte_carlo_samples) \r\n# \u521b\u5efa\u56fe\u8868\u6765\u6bd4\u8f83\u771f\u5b9e\u5206\u5e03\u548c\u8499\u7279\u5361\u6d1b\u6a21\u62df\r\nplt.figure(figsize=(12, 6)) \r\n# \u771f\u5b9e\u5206\u5e03\r\nplt.hist(real_data, bins=30, alpha=0.5, color='blue', label='\u771f\u5b9e\u5206\u5e03', density=True) \r\n# \u8499\u7279\u5361\u6d1b\u5206\u5e03\r\nplt.hist(monte_carlo_data, bins=30, alpha=0.5, color='orange', label='\u8499\u7279\u5361\u6d1b', density=True) \r\nplt.title(\"\u771f\u5b9e\u5206\u5e03\u4e0e\u8499\u7279\u5361\u6d1b\u6a21\u62df\u7684\u6bd4\u8f83\") \r\nplt.xlabel(\"\u7b49\u5f85\u65f6\u95f4\uff08\u5206\u949f\uff09\") \r\nplt.ylabel(\"\u5bc6\u5ea6\") \r\nplt.legend() \r\nplt.grid(True) \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_1\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<li>17.<\/li>\n<li>18.<\/li>\n<li>19.<\/li>\n<li>20.<\/li>\n<li>21.<\/li>\n<li>22.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"eae0de\" data-has-transparency=\"false\" style=\"--dominant-color: #eae0de;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27565\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/21e0d354331613cfa80589e3ba7afc689e5e34.png\" width=\"860\" height=\"460\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/21e0d354331613cfa80589e3ba7afc689e5e34.png 860w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/21e0d354331613cfa80589e3ba7afc689e5e34-300x160.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/21e0d354331613cfa80589e3ba7afc689e5e34-150x80.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/21e0d354331613cfa80589e3ba7afc689e5e34-768x411.png 768w\" sizes=\"auto, (max-width: 860px) 100vw, 860px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h4>3.\u6761\u4ef6\u5206\u5e03<\/h4>\n<p>\u6761\u4ef6\u5206\u5e03\u5141\u8bb8\u4f60\u6a21\u62df\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u76f8\u5173\u6027\u7684\u6570\u636e\u96c6\u3002\u8fd9\u5bf9\u4e8e\u751f\u6210\u7ef4\u6301\u6570\u636e\u96c6\u7ef4\u5ea6\u4e4b\u95f4\u6709\u610f\u4e49\u5173\u7cfb\u7684\u5408\u6210\u6570\u636e\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<p>\u793a\u4f8b\uff1a\u591a\u5143\u6b63\u6001\u5206\u5e03<\/p>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"000000\" data-has-transparency=\"true\" style=\"--dominant-color: #000000;\" loading=\"lazy\" decoding=\"async\" class=\"has-transparency alignnone size-full wp-image-27566\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b7ff121917cfca5925a128ec867d845a5e3cda.png\" width=\"647\" height=\"74\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b7ff121917cfca5925a128ec867d845a5e3cda.png 647w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b7ff121917cfca5925a128ec867d845a5e3cda-300x34.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b7ff121917cfca5925a128ec867d845a5e3cda-150x17.png 150w\" sizes=\"auto, (max-width: 647px) 100vw, 647px\" \/><\/p>\n<p>&nbsp;<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_2\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">mean = [0, 0] # X \u548c Y \u7684\u5e73\u5747\u503c\r\ncovariance = [[1, 0.8], [0.8, 1]] # \u534f\u65b9\u5dee\u77e9\u9635\r\ndata_multivariate = np.random.multivariate_normal(mean, covariance, 500) \r\n# \u53ef\u89c6\u5316\r\nplt.scatter(data_multivariate[:, 0], data_multivariate[:, 1], alpha=0.6) \r\nplt.title('\u591a\u5143\u6b63\u6001\u5206\u5e03') \r\nplt.xlabel('X') \r\nplt.ylabel('Y') \r\nplt.axis('equal') \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_2\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"eaf1f6\" data-has-transparency=\"false\" style=\"--dominant-color: #eaf1f6;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27567\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/83077f2004ed3ac6f86501a02a8aa45d14dfd8.png\" width=\"800\" height=\"625\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/83077f2004ed3ac6f86501a02a8aa45d14dfd8.png 800w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/83077f2004ed3ac6f86501a02a8aa45d14dfd8-300x234.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/83077f2004ed3ac6f86501a02a8aa45d14dfd8-150x117.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/83077f2004ed3ac6f86501a02a8aa45d14dfd8-768x600.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u57fa\u4e8e\u7edf\u8ba1\u5206\u5e03\u7684\u6570\u636e\u751f\u6210\u65b9\u6cd5\u5177\u6709\u8bf8\u591a\u4f18\u52bf\u3002\u5b83\u4eec\u5141\u8bb8\u5b8c\u5168\u63a7\u5236\uff0c\u80fd\u591f\u5b9a\u4e49\u7279\u5b9a\u53c2\u6570\uff0c\u786e\u4fdd\u6570\u636e\u6309\u7167\u5b9a\u4e49\u660e\u786e\u7684\u7edf\u8ba1\u6a21\u578b\u751f\u6210\u3002\u6b64\u5916\uff0c\u5b83\u4eec\u8fd8\u5177\u6709\u7075\u6d3b\u6027\uff0c\u80fd\u591f\u8f7b\u677e\u9002\u5e94\u4e0d\u540c\u60c5\u51b5\uff0c\u4f8b\u5982\u9700\u8981\u5355\u5cf0\u6216\u591a\u5cf0\u5206\u5e03\u7684\u60c5\u51b5\u3002\u4ece\u64cd\u4f5c\u89d2\u5ea6\u6765\u770b\uff0c\u5b83\u4eec\u88ab\u8bc1\u660e\u7279\u522b\u9ad8\u6548\uff0c\u56e0\u4e3a\u5373\u4f7f\u5bf9\u4e8e\u5927\u578b\u6570\u636e\u96c6\uff0c\u6570\u636e\u751f\u6210\u4e5f\u5feb\u901f\u4e14\u5145\u5206\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5b83\u4eec\u4e5f\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002\u8fd9\u4e9b\u65b9\u6cd5\u6700\u9002\u7528\u4e8e\u7edf\u8ba1\u7ed3\u6784\u7b80\u5355\u6e05\u6670\u7684\u6570\u636e\u96c6\uff0c\u4f46\u5728\u8868\u793a\u590d\u6742\u6216\u975e\u7ebf\u6027\u5173\u7cfb\u65b9\u9762\u6548\u679c\u8f83\u5dee\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u83b7\u5f97\u6709\u7528\u7684\u7ed3\u679c\uff0c\u5fc5\u987b\u6df1\u5165\u4e86\u89e3\u5206\u5e03\u53ca\u5176\u53c2\u6570\uff0c\u8fd9\u8981\u6c42\u4f7f\u7528\u65b9\u6cd5\u7684\u4eba\u5177\u5907\u4e00\u5b9a\u7684\u6280\u672f\u4e13\u4e1a\u77e5\u8bc6\u3002<\/p>\n<p>\u5b8c\u6574\u793a\u4f8b\uff1a\u5177\u6709\u7279\u5b9a\u5173\u7cfb\u7684\u6570\u636e\u751f\u6210<\/p>\n<p>\u8ba9\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u5408\u6210\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u566a\u58f0\u7ebf\u6027\u5173\u7cfb\uff0c\u4f8b\u5982\u8eab\u9ad8\u548c\u4f53\u91cd\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_3\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\"># \u53c2\u6570\r\nnp.random.seed(42) \r\nn_samples = 1000 \r\nslope = 2.5 # \u7ebf\u6027\u5173\u7cfb\u7684\u659c\u7387\r\nintercept = 50 # \u622a\u8ddd\r\nnoise_level = 5 # \u566a\u58f0\u6c34\u5e73\r\n# \u6570\u636e\u751f\u6210\r\nheights = np.random.normal(170, 10, n_samples) # \u6b63\u6001\u5206\u5e03\u7684\u8eab\u9ad8\r\nweights = slope * heights + intercept + np.random.normal(0, noise_level, n_samples) \r\n# \u53ef\u89c6\u5316\r\nplt.scatter(heights, weights, alpha=0.6) \r\nplt.title('\u7efc\u5408\u7ebf\u6027\u5173\u7cfb (\u8eab\u9ad8 vs \u4f53\u91cd)') \r\nplt.xlabel('\u8eab\u9ad8 (cm)') \r\nplt.ylabel('\u4f53\u91cd (kg)') \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_3\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"f0f4f7\" data-has-transparency=\"false\" style=\"--dominant-color: #f0f4f7;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27568\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/07b0d24960d7ec5466f261dfe86e0ecc1370d0.png\" width=\"638\" height=\"472\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/07b0d24960d7ec5466f261dfe86e0ecc1370d0.png 638w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/07b0d24960d7ec5466f261dfe86e0ecc1370d0-300x222.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/07b0d24960d7ec5466f261dfe86e0ecc1370d0-150x111.png 150w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h4>4.\u4f7f\u7528\u4f20\u7edf\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u751f\u6210\u6570\u636e<\/h4>\n<p>\u4f7f\u7528\u4f20\u7edf\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u751f\u6210\u5408\u6210\u6570\u636e\u662f\u4e00\u79cd\u5e7f\u6cdb\u4f7f\u7528\u7684\u6280\u672f\uff0c\u7528\u4e8e\u6269\u5c55\u73b0\u6709\u6570\u636e\u96c6\u6216\u521b\u5efa\u65b0\u6570\u636e\u96c6\uff0c\u540c\u65f6\u4fdd\u6301\u5408\u7406\u7684\u7ed3\u6784\u548c\u5206\u5e03\u3002\u4e0e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7b49\u9ad8\u7ea7\u65b9\u6cd5\u4e0d\u540c\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u6613\u4e8e\u5b9e\u73b0\uff0c\u5e76\u4e14\u53ef\u4ee5\u76f4\u63a5\u63a7\u5236\u751f\u6210\u6570\u636e\u7684\u7279\u5f81\u3002<\/p>\n<p><strong>\uff081\uff09\u9ad8\u65af\u6df7\u5408\u6a21\u578b<\/strong><\/p>\n<p>\u9ad8\u65af\u6df7\u5408\u6a21\u578b (GMM) \u662f\u4e00\u79cd\u6982\u7387\u6a21\u578b\uff0c\u5b83\u5c06\u6570\u636e\u96c6\u8868\u793a\u4e3a\u591a\u4e2a\u9ad8\u65af\u5206\u5e03\u7684\u7ec4\u5408\u3002GMM \u4e2d\u7684\u6bcf\u4e2a\u805a\u7c7b\u90fd\u5bf9\u5e94\u4e00\u4e2a\u9ad8\u65af\u5206\u91cf\u3002\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u751f\u6210\u6a21\u62df\u591a\u7c7b\u6570\u636e\u96c6\u7684\u6570\u636e\u7279\u522b\u6709\u7528\u3002<\/p>\n<p>\u793a\u4f8b\uff1a\u4f7f\u7528 GMM \u6839\u636e\u6837\u672c\u6570\u636e\u751f\u6210\u5408\u6210\u6570\u636e\u96c6<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_4\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">import numpy as np \r\nimport matplotlib.pyplot as plt \r\nfrom sklearn.mixture import GaussianMixture \r\n# \u539f\u59cb\u6570\u636e\uff1a\u4e24\u4e2a\u4e3b\u8981\u805a\u7c7b\r\nnp.random.seed(42) \r\ndata_original = np.concatenate([ \r\n    np.random.normal(loc=0, scale=1, size=(100, 2)), \r\n    np.random.normal(loc=5, scale=1.5, size=(100, 2)) \r\n]) \r\n# \u521b\u5efa GMM \u6a21\u578b\r\ngmm = GaussianMixture(n_compnotallow=2, random_state=42) \r\ngmm.fit(data_original) \r\n# \u751f\u6210\u65b0\u7684\u5408\u6210\u6570\u636e\r\ndata_sintetici = gmm.sample(200)[0] \r\n# \u5e76\u6392\u53ef\u89c6\u5316\r\nfig, axes = plt.subplots(1, 2, figsize=(12, 6), sharex=True, sharey=True) \r\n# \u539f\u59cb\u6570\u636e\u56fe\r\naxes[0].scatter(data_original[:, 0], data_original[:, 1], alpha=0.6, label=\"Original Data\") \r\naxes[0].legend() \r\naxes[0].set_title(\"Original Data\") \r\naxes[0].grid(True) \r\n# \u5408\u6210\u6570\u636e\u56fe\r\naxes[1].scatter(data_sintetici[:, 0], data_sintetici[:, 1], color='r', alpha=0.6, label=\"Dati Sintetici\") \r\naxes[1].legend() \r\naxes[1].set_title(\"Synthetic Data Generated with GMM\") \r\naxes[1].grid(True) \r\nplt.tight_layout() \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_4\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<li>17.<\/li>\n<li>18.<\/li>\n<li>19.<\/li>\n<li>20.<\/li>\n<li>21.<\/li>\n<li>22.<\/li>\n<li>23.<\/li>\n<li>24.<\/li>\n<li>25.<\/li>\n<li>26.<\/li>\n<li>27.<\/li>\n<li>28.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"f6f4f5\" data-has-transparency=\"false\" style=\"--dominant-color: #f6f4f5;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27569\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/266a029856a6c850763061781d88f5f2098157.png\" width=\"875\" height=\"439\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/266a029856a6c850763061781d88f5f2098157.png 875w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/266a029856a6c850763061781d88f5f2098157-300x151.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/266a029856a6c850763061781d88f5f2098157-150x75.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/266a029856a6c850763061781d88f5f2098157-768x385.png 768w\" sizes=\"auto, (max-width: 875px) 100vw, 875px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u4e3b\u8981\u4f18\u70b9\u4e4b\u4e00\u662f\u80fd\u591f\u76f4\u63a5\u63a7\u5236\u805a\u7c7b\u6570\u91cf\u548c\u65b9\u5dee\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u6709\u9488\u5bf9\u6027\u548c\u4e2a\u6027\u5316\u7684\u5206\u6790\u3002\u6b64\u5916\uff0c\u5b83\u5bf9\u4e8e\u5177\u6709\u591a\u5cf0\u5206\u5e03\u7684\u6570\u636e\u7279\u522b\u6709\u6548\uff0c\u80fd\u591f\u5f88\u597d\u5730\u8fd1\u4f3c\u5176\u7ed3\u6784\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8be5\u65b9\u6cd5\u4e5f\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002\u8be5\u65b9\u6cd5\u4ec5\u9002\u7528\u4e8e\u80fd\u591f\u7528\u9ad8\u65af\u5206\u5e03\u5efa\u6a21\u7684\u6570\u636e\u96c6\uff0c\u8fd9\u9650\u5236\u4e86\u5176\u5e94\u7528\u8303\u56f4\u3002\u6b64\u5916\uff0c\u5b83\u9700\u8981\u9884\u5148\u786e\u5b9a\u6700\u4f73\u7ec4\u4ef6\u6570\u91cf\uff0c\u8fd9\u5728\u66f4\u590d\u6742\u7684\u73af\u5883\u4e2d\u53ef\u80fd\u662f\u4e00\u4e2a\u6311\u6218\u3002<\/p>\n<p><strong>\uff082\uff09\u751f\u6210\u51b3\u7b56\u6811<\/strong><\/p>\n<p>\u751f\u6210\u51b3\u7b56\u6811\u5728\u53d8\u91cf\u4e4b\u95f4\u5efa\u7acb\u6761\u4ef6\u5173\u7cfb\u3002\u5b83\u4eec\u53ef\u7528\u4e8e\u751f\u6210\u9075\u5faa\u590d\u6742\u6a21\u5f0f\u7684\u6570\u636e\uff0c\u4f8b\u5982\u903b\u8f91\u7ea6\u675f\u6216\u53d8\u91cf\u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u3002<\/p>\n<p>\u793a\u4f8b\uff1a\u6839\u636e\u6761\u4ef6\u89c4\u5219\u751f\u6210\u5408\u6210\u6570\u636e\u96c6\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"051109\" data-has-transparency=\"false\" style=\"--dominant-color: #051109;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27570\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193.png\" width=\"303\" height=\"154\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193.png 303w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193-300x152.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193-150x76.png 150w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>&nbsp;<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_5\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">import numpy as np \r\nimport matplotlib.pyplot as plt \r\nfrom sklearn.mixture import GaussianMixture \r\nfrom sklearn.tree import DecisionTreeClassifier \r\nimport pandas as pd \r\n# \u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u6570\u636e\u96c6\r\nnp.random.seed(42) \r\ndata_original = pd.DataFrame({ \r\n    'Feature1': np.random.choice([0, 1], size=100), \r\n    'Feature2': np.random.choice([0, 1], size=100), \r\n    'Label': np.random.choice([0, 1], size=100) \r\n}) \r\n# \u6784\u5efa\u51b3\u7b56\u6811\r\nX = data_original[['Feature1', 'Feature2']] \r\ny = data_original['Label'] \r\ntree = DecisionTreeClassifier(max_depth=3, random_state=42) \r\ntree.fit(X, y) \r\n# \u751f\u6210\u65b0\u6570\u636e\r\nsyntetic_data = pd.DataFrame({     'Feature1': np.random.choice([0, 1], size=100), \r\n    'Feature2': np.random.choice([0, 1], size=100) \r\n}) \r\nsynthesized_data['Label'] = tree.predict(synthetic_data) \r\nprint(\"\u751f\u6210\u7684\u5408\u6210\u6570\u636e:\\n\", synthesized_data.head())<\/code><\/pre>\n<ul id=\"code_id_5\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<li>17.<\/li>\n<li>18.<\/li>\n<li>19.<\/li>\n<li>20.<\/li>\n<li>21.<\/li>\n<li>22.<\/li>\n<li>23.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"051109\" data-has-transparency=\"false\" style=\"--dominant-color: #051109;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27570\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193.png\" width=\"303\" height=\"154\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193.png 303w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193-300x152.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/f1e287f212f05228090151364d4ce9b2fc9193-150x76.png 150w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u4e3b\u8981\u4f18\u70b9\u4e4b\u4e00\u662f\u5176\u7075\u6d3b\u6027\uff0c\u751a\u81f3\u53ef\u4ee5\u5bf9\u590d\u6742\u7684\u89c4\u5219\u8fdb\u884c\u5efa\u6a21\u3002\u5f53\u60a8\u60f3\u8981\u590d\u5236\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u6761\u4ef6\u5173\u7cfb\u7684\u6570\u636e\u96c6\u65f6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5c24\u5176\u6709\u7528\uff0c\u53ef\u4ee5\u786e\u4fdd\u6570\u636e\u7ed3\u6784\u7684\u4e00\u81f4\u6027\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8be5\u65b9\u6cd5\u4e5f\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002\u5b83\u53ef\u80fd\u4f1a\u5bfc\u81f4\u539f\u59cb\u6570\u636e\u8fc7\u5ea6\u62df\u5408\uff0c\u4ece\u800c\u964d\u4f4e\u5176\u6cdb\u5316\u80fd\u529b\u3002\u6b64\u5916\uff0c\u5b83\u5e76\u975e\u751f\u6210\u9ad8\u53d8\u5f02\u6027\u6570\u636e\u96c6\u7684\u6700\u4f73\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u4e3a\u5728\u9ad8\u53d8\u5f02\u6027\u6570\u636e\u96c6\u4e2d\uff0c\u4fdd\u6301\u6570\u636e\u7684\u4ee3\u8868\u6027\u66f4\u52a0\u56f0\u96be\u3002<\/p>\n<h4>5.\u4f7f\u7528 LLM\uff08\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff09\u751f\u6210\u5408\u6210\u6570\u636e<\/h4>\n<p>\u5927\u578b\u8bed\u8a00\u6a21\u578b (LLM) \u4ee3\u8868\u4e86\u751f\u6210\u5408\u6210\u6570\u636e\u7684\u6700\u5148\u8fdb\u6280\u672f\u4e4b\u4e00\u3002\u5b83\u4eec\u5c06\u81ea\u7136\u8bed\u8a00\u7406\u89e3\u548c\u751f\u6210\u529f\u80fd\u4e0e\u6df1\u5ea6\u5b66\u4e60\u7684\u5f3a\u5927\u529f\u80fd\u76f8\u7ed3\u5408\uff0c\u4f7f\u5176\u6210\u4e3a\u521b\u5efa\u7ed3\u6784\u5316\u3001\u8fde\u8d2f\u4e14\u4e2a\u6027\u5316\u6570\u636e\u96c6\u7684\u7406\u60f3\u5de5\u5177\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u7d22\u5982\u4f55\u4f7f\u7528 LLM \u751f\u6210\u5408\u6210\u6570\u636e\uff0c\u5e76\u901a\u8fc7\u5b9e\u9645\u793a\u4f8b\u548c Python \u4ee3\u7801\u6765\u6f14\u793a\u5176\u5e94\u7528\u3002<\/p>\n<p>\u50cf GPT \u6216 BERT \u8fd9\u6837\u7684 LLM \u53ef\u4ee5\u901a\u8fc7\u8bad\u7ec3\u6216\u8c03\u6574\u6765\u521b\u5efa\u5408\u6210\u6570\u636e\uff0c\u8fd9\u5f97\u76ca\u4e8e\u5b83\u4eec\u5177\u6709\u4ee5\u4e0b\u80fd\u529b\uff1a<\/p>\n<p>\u2022\u7406\u89e3\u80cc\u666f\uff1a\u4ed6\u4eec\u53ef\u4ee5\u5206\u6790\u548c\u751f\u6210\u5177\u6709\u590d\u6742\u5173\u7cfb\u7684\u6570\u636e\uff0c\u4ee5\u9002\u5e94\u7279\u5b9a\u7684\u80cc\u666f\u3002<\/p>\n<p>\u2022\u4e2a\u6027\u5316\uff1a\u5b83\u4eec\u63d0\u4f9b\u751f\u6210\u7b26\u5408\u7528\u6237\u5b9a\u4e49\u7684\u89c4\u5219\u6216\u6a21\u5f0f\u7684\u6570\u636e\u7684\u80fd\u529b\u3002<\/p>\n<p>\u2022\u5bf9\u975e\u7ed3\u6784\u5316\u6570\u636e\u7684\u6709\u6548\u6027\uff1a\u5b83\u4eec\u5bf9\u4e8e\u751f\u6210\u6587\u672c\u548c\u8868\u683c\u6570\u636e\u7279\u522b\u5f3a\u5927\u3002<\/p>\n<p>\u793a\u4f8b\uff1a\u521b\u5efa\u8868\u683c\u6570\u636e\u96c6<\/p>\n<p>\u8ba9\u6211\u4eec\u8003\u8651\u8fd9\u6837\u4e00\u79cd\u60c5\u51b5\uff1a\u6211\u4eec\u60f3\u8981\u4e3a\u8425\u9500\u5e94\u7528\u7a0b\u5e8f\u751f\u6210\u4e00\u4e2a\u8868\u683c\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u5ba2\u6237\u4fe1\u606f\uff0c\u4f8b\u5982\u5e74\u9f84\u3001\u57ce\u5e02\u548c\u5e74\u6536\u5165\u3002<\/p>\n<p><strong>\u6b65\u9aa4 1\uff1a\u5b9a\u4e49\u63d0\u793a<\/strong><\/p>\n<p>\u6709\u6548\u7684\u63d0\u793a\u80fd\u591f\u5f15\u5bfc\u5927\u578b\u8bed\u8a00\u6a21\u578b\u00a0(LLM) \u64b0\u5199\u8fde\u8d2f\u7684\u6570\u636e\u3002\u4ee5\u4e0b\u662f\u793a\u4f8b\u63d0\u793a\uff1a<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_6\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">\u751f\u6210\u4e00\u4e2a\u5305\u542b 10 \u884c 4 \u5217\u7684\u6570\u636e\u96c6\uff1a\\n\u201c \r\nJob\u201d\uff08\u8868\u793a\u4eba\u5458\u804c\u4e1a\u7684\u5b57\u7b26\u4e32\uff09\u3001\u201c \r\nAge\u201d\uff0818 \u5230 75 \u4e4b\u95f4\u7684\u6574\u6570\uff09\u3001\u201c \r\nCountry\u201d\uff08\u8868\u793a\u56fd\u5bb6\u540d\u79f0\u7684\u5b57\u7b26\u4e32\uff09\r\n\u548c\u201cScore\u201d\uff080 \u5230 100 \u4e4b\u95f4\u7684\u6d6e\u70b9\u6570\uff09\u3002\\n\\n\u201c \r\n\u201cJob | Age | Country | Score\\n\u201d \r\n\u201c---------------------------------\\n\u201d \u201cTeacher | 30 | USA | 88.5\\n\u201d \r\n\u201cEngineer | 45 | UK | 92.3\\n\u201d \r\n\u201cNurse | 28 | Canada | 75.4\\n\u201d \r\n\u201cArtist | 33 | France | 68.9\\n\u201d \r\n\u201cDoctor | 50 | Germany | 85.1\\n\u201d<\/code><\/pre>\n<ul id=\"code_id_6\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><strong>\u6b65\u9aa42\uff1a\u4f7f\u7528Python\u751f\u6210\u6570\u636e<\/strong><\/p>\n<p>\u501f\u52a9\u201ctransformers\u201d\u4e4b\u7c7b\u7684\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u4e0e\u9884\u5148\u8bad\u7ec3\u7684\u6a21\u578b\u4ea4\u4e92\u6765\u751f\u6210\u6570\u636e\u96c6\uff1a<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_7\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">from transformers import GPTNeoForCausalLM, GPT2Tokenizer \r\nimport torch \r\nimport re \r\n# \u52a0\u8f7d tokenizer \u548c hugging face \u6a21\u578b\r\nmodel_name = \"EleutherAI\/gpt-neo-1.3B\" \r\ntokenizer = GPT2Tokenizer.from_pretrained(model_name) \r\ntokenizer.pad_token = tokenizer.eos_token \r\nmodel = GPTNeoForCausalLM.from_pretrained(model_name) \r\nmodel.config.pad_token_id = tokenizer.eos_token_id \r\ndevice = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\") \r\nmodel.to(device) \r\nmodel.eval() \r\nprompt = ( \r\n    \"\u751f\u6210\u4e00\u4e2a\u5305\u542b 10 \u884c 4 \u5217\u7684\u6570\u636e\u96c6\uff1a\\n\" \r\n    \"Job\uff08\u8868\u793a\u4eba\u5458\u804c\u4e1a\u7684\u5b57\u7b26\u4e32\uff09\u3001\" \r\n    \"Age\uff0818 \u5230 75 \u4e4b\u95f4\u7684\u6574\u6570\uff09\u3001\" \r\n    \"Country\uff08\u8868\u793a\u56fd\u5bb6\u540d\u79f0\u7684\u5b57\u7b26\u4e32\uff09\u3001\" \r\n    \"and Score\uff08\u6d6e\u70b9\u6570\uff09\u4ecb\u4e8e 0 \u548c 100 \u4e4b\u95f4\uff09\u3002\\n\\n\" \r\n    \"\u5de5\u4f5c | \u5e74\u9f84 | \u56fd\u5bb6 | \u5e74\u6536\u5165\\n\" \r\n    \"---------------------------------\\n\" \r\n    \"\u6559\u5e08 | 30 | \u7f8e\u56fd | 88.5\\n\" \r\n    \"\u5de5\u7a0b\u5e08 | 45 | \u82f1\u56fd | 92.3\\n\" \r\n    \"\u62a4\u58eb | 28 | \u52a0\u62ff\u5927 | 75.4\\n\" \r\n    \"\u827a\u672f\u5bb6 | 33 | \u6cd5\u56fd | 68.9\\n\" \r\n    \"\u533b\u751f | 50 | \u5fb7\u56fd | 85.1\\n\" \r\n) \r\n# \u5bf9\u63d0\u793a\u8fdb\u884c\u7f16\u7801\r\ninputs = tokenizer(prompt, return_tensors=\"pt\", padding=True).to(device) \r\ninput_ids = inputs['input_ids'] \r\nattention_mask = inputs['attention_mask'] \r\n# \u751f\u6210\u6587\u672c\r\noutput = model.generate( \r\n    input_ids=input_ids,     attention_mask=attention_mask, \r\n    max_length=input_ids.shape[1] + 200, \r\n    num_return_sequences=1, \r\n    no_repeat_ngram_size=2, \r\n    do_sample=False, \r\n    temperature=0.7, \r\n    pad_token_id=tokenizer.eos_token_id \r\n) \r\n# \u89e3\u7801\u8f93\u51fa\r\ngenerated_text = tokenizer.decode(output[0], skip_special_tokens=True) \r\nprint(generated_text) \r\n# \u63d0\u53d6\u9605\u8bfb\u6a21\u5f0f\r\ndata_pattern = re.compile( \r\n    r\"([A-Za-z\\s]+)\\s*\\|\\s*(\\d{1,2})\\s*\\|\\s*([A-Za-z\\s]+)\\s*\\|\\s*(\\d{1,3}\\.\\d+)\" \r\n) \r\nmatches = data_pattern.findall(generated_text) \r\nprint(\"\\nExtracted Data:\") \r\nfor match in matches: \r\n    print(f\"Job: {match[0].strip()}, Age: {match[1]}, \u56fd\u5bb6: {match[2].strip()}, \u6536\u5165: {match[3]}\")<\/code><\/pre>\n<ul id=\"code_id_7\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<li>17.<\/li>\n<li>18.<\/li>\n<li>19.<\/li>\n<li>20.<\/li>\n<li>21.<\/li>\n<li>22.<\/li>\n<li>23.<\/li>\n<li>24.<\/li>\n<li>25.<\/li>\n<li>26.<\/li>\n<li>27.<\/li>\n<li>28.<\/li>\n<li>29.<\/li>\n<li>30.<\/li>\n<li>31.<\/li>\n<li>32.<\/li>\n<li>33.<\/li>\n<li>34.<\/li>\n<li>35.<\/li>\n<li>36.<\/li>\n<li>37.<\/li>\n<li>38.<\/li>\n<li>39.<\/li>\n<li>40.<\/li>\n<li>41.<\/li>\n<li>42.<\/li>\n<li>43.<\/li>\n<li>44.<\/li>\n<li>45.<\/li>\n<li>46.<\/li>\n<li>47.<\/li>\n<li>48.<\/li>\n<li>49.<\/li>\n<li>50.<\/li>\n<li>51.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u63d0\u53d6\u7684\u6570\u636e\uff1a<br \/>\n\u5de5\u4f5c\uff1a\u6559\u5e08\uff0c\u5e74\u9f84\uff1a30\uff0c\u56fd\u5bb6\uff1a\u7f8e\u56fd\uff0c\u6536\u5165\uff1a88.5<br \/>\n\u5de5\u4f5c\uff1a\u5de5\u7a0b\u5e08\uff0c\u5e74\u9f84\uff1a45\uff0c\u56fd\u5bb6\uff1a\u82f1\u56fd\uff0c\u6536\u5165\uff1a92.3<br \/>\n\u5de5\u4f5c\uff1a\u62a4\u58eb\uff0c\u5e74\u9f84\uff1a28\uff0c\u56fd\u5bb6\uff1a\u52a0\u62ff\u5927\uff0c\u6536\u5165\uff1a75.4<br \/>\n\u5de5\u4f5c\uff1a\u827a\u672f\u5bb6\uff0c\u5e74\u9f84\uff1a33\uff0c\u56fd\u5bb6\uff1a\u6cd5\u56fd\uff0c\u6536\u5165\uff1a68.9<br \/>\n\u5de5\u4f5c\uff1a\u533b\u751f\uff0c\u5e74\u9f84\uff1a50\uff0c\u56fd\u5bb6\uff1a\u5fb7\u56fd\uff0c\u6536\u5165\uff1a85.1<br \/>\n\u5de5\u4f5c\uff1a\u7ecf\u7406\uff0c\u5e74\u9f84\uff1a25\uff0c\u56fd\u5bb6\uff1a\u897f\u73ed\u7259\uff0c\u6536\u5165\uff1a77.8<br \/>\n\u5de5\u4f5c\uff1a\u9500\u552e\u5458\uff0c\u5e74\u9f84\uff1a35\uff0c\u56fd\u5bb6\uff1a\u65e5\u672c\uff0c\u6536\u5165\uff1a73.6<br \/>\n\u5de5\u4f5c\uff1a\u53f8\u673a\uff0c\u5e74\u9f84\uff1a20\uff0c\u56fd\u5bb6\uff1a\u6fb3\u5927\u5229\u4e9a\uff0c\u6536\u5165\uff1a71.2<br \/>\n\u5de5\u4f5c\uff1a\u529e\u4e8b\u5458\uff0c\u5e74\u9f84\uff1a40\uff0c\u56fd\u5bb6\uff1a\u5370\u5ea6\uff0c\u6536\u5165\uff1a70.7<br \/>\n\u5de5\u4f5c\uff1a\u5b66\u751f\uff0c\u5e74\u9f84\uff1a24\uff0c\u56fd\u5bb6\uff1a\u4e2d\u56fd\uff0c\u6536\u5165\uff1a69.0<br \/>\n\u5de5\u4f5c\uff1a\u9762\u5305\u5e08\uff0c\u5e74\u9f84\uff1a22\uff0c\u56fd\u5bb6\uff1a\u5df4\u897f\uff0c\u6536\u5165\uff1a66.75<br \/>\n\u5de5\u4f5c\uff1a\u5973\u4f63\uff0c\u5e74\u9f84\uff1a 23\uff0c\u56fd\u5bb6\uff1a\u610f\u5927\u5229\uff0c\u6536\u5165\uff1a65.25<br \/>\n\u804c\u4e1a\uff1a\u53a8\u5e08\uff0c\u5e74\u9f84\uff1a21\uff0c\u56fd\u5bb6\uff1a\u5e0c\u814a\uff0c\u6536\u5165\uff1a64.15<br \/>\n\u804c\u4e1a\uff1a\u5bb6\u5ead\u4e3b\u5987\uff0c\u5e74\u9f84\uff1a26\uff0c\u56fd\u5bb6\uff1a\u571f\u8033\u5176\uff0c\u6536\u5165\uff1a63.85<br \/>\n\u804c\u4e1a\uff1a\u6e14\u592b\uff0c\u5e74\u9f84\uff1a29\uff0c\u56fd\u5bb6\uff1a\u4fc4\u7f57\u65af\uff0c\u6536\u5165\uff1a62.65<br \/>\n\u804c\u4e1a\uff1a\u642c\u8fd0\u5de5\uff0c\u5e74\u9f84\uff1a27\uff0c\u56fd\u5bb6\uff1a\u5357\u975e\uff0c\u6536\u5165\uff1a61.45<br \/>\n\u804c\u4e1a\uff1a\u6c34\u624b\uff0c\u5e74\u9f84\uff1a32\uff0c\u56fd\u5bb6\uff1a\u7f8e\u56fd\uff0c\u6536\u5165\uff1a60.35<br \/>\n\u804c\u4e1a\uff1a\u58eb\u5175\uff0c\u5e74\u9f84\uff1a31\uff0c\u56fd\u5bb6\uff1a\u745e\u5178\uff0c\u6536\u5165\uff1a59.05<br \/>\n\u804c\u4e1a\uff1a\u8b66\u5bdf\uff0c\u5e74\u9f84\uff1a34\uff0c\u56fd\u5bb6\uff1a\u8377\u5170\uff0c\u6536\u5165\uff1a58.95<br \/>\n\u804c\u4e1a\uff1a\u62a4\u7406\u4eba\u5458\uff0c\u5e74\u9f84\uff1a36\uff0c\u56fd\u5bb6\uff1a\u6bd4\u5229\u65f6\uff0c\u6536\u5165\uff1a57.55<br \/>\n\u804c\u4e1a\uff1a\u5efa\u7b51\u5de5\u4eba\uff0c\u5e74\u9f84\uff1a37\uff0c\u56fd\u5bb6\uff1a\u4e39\u9ea6\uff0c\u6536\u5165\uff1a56.40\u804c\u4e1a\uff1a\u7535\u5de5\uff0c\u5e74\u9f84\uff1a38\uff0c\u56fd\u5bb6\uff1a\u632a\u5a01\uff0c\u6536\u5165\uff1a 55.10<\/p>\n<p>LLM\uff08\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff09\u62e5\u6709\u4f17\u591a\u4f18\u52bf\uff0c\u4f7f\u5176\u6210\u4e3a\u7528\u9014\u6781\u4e3a\u5e7f\u6cdb\u7684\u5de5\u5177\u3002\u9996\u5148\uff0c\u5b83\u4eec\u5177\u6709\u6781\u5927\u7684\u7075\u6d3b\u6027\uff1a\u80fd\u591f\u751f\u6210\u7ed3\u6784\u5316\u548c\u975e\u7ed3\u6784\u5316\u6570\u636e\uff0c\u4ece\u800c\u9002\u5e94\u591a\u79cd\u9700\u6c42\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u4f7f\u7528 API \u548c Python \u5e93\uff0c\u5b83\u4eec\u53ef\u4ee5\u7b80\u5316\u4e0e\u5de5\u4f5c\u6d41\u7a0b\u7684\u96c6\u6210\uff0c\u4ece\u800c\u5b9e\u73b0\u5feb\u901f\u6709\u6548\u7684\u5b9e\u65bd\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u79ef\u6781\u7684\u65b9\u9762\u662f\u5b9a\u5236\u7684\u53ef\u80fd\u6027\uff1a\u53ef\u4ee5\u8f7b\u677e\u4fee\u6539\u63d0\u793a\u4ee5\u6ee1\u8db3\u7279\u5b9a\u9700\u6c42\uff0c\u4ece\u800c\u4f7f\u8fd9\u4e9b\u6a21\u578b\u5728\u76ee\u6807\u73af\u5883\u4e2d\u66f4\u6709\u7528\u3002<\/p>\n<p>\u7136\u800c\uff0c\u9700\u8981\u8003\u8651\u4e00\u4e9b\u9650\u5236\u548c\u5173\u952e\u65b9\u9762\u3002\u4f8b\u5982\uff0c\u751f\u6210\u6570\u636e\u7684\u8d28\u91cf\u5f88\u5927\u7a0b\u5ea6\u4e0a\u53d6\u51b3\u4e8e\u6240\u4f7f\u7528\u7684\u516c\u5f0f\u548c\u6a21\u578b\u7684\u8bbe\u7f6e\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u9700\u8981\u6ce8\u610f\u7684\u56e0\u7d20\u662f\u504f\u5dee\u7684\u5b58\u5728\uff1a\u7531\u4e8e\u6a21\u578b\u662f\u4ece\u8bad\u7ec3\u6570\u636e\u4e2d\u5b66\u4e60\u7684\uff0c\u56e0\u6b64\u5b83\u4eec\u53ef\u80fd\u4f1a\u91cd\u73b0\u6570\u636e\u4e2d\u5df2\u7ecf\u5b58\u5728\u7684\u504f\u5dee\u6216\u626d\u66f2\u3002\u6700\u540e\uff0c\u6210\u672c\u4e5f\u662f\u4e00\u4e2a\u91cd\u8981\u56e0\u7d20\uff0c\u5c24\u5176\u662f\u5728\u751f\u4ea7\u73af\u5883\u4e2d\uff0c\u5927\u91cf\u4f7f\u7528LLM\u53ef\u80fd\u4f1a\u5bfc\u81f4\u5de8\u989d\u6210\u672c\u3002<\/p>\n<h4>6.\u5177\u6709\u7279\u5b9a\u7ed3\u6784\u548c\u5173\u7cfb\u7684\u6570\u636e\u751f\u6210<\/h4>\n<p>\u751f\u6210\u5177\u6709\u7279\u5b9a\u7ed3\u6784\u548c\u5173\u7cfb\u7684\u5408\u6210\u6570\u636e\u662f\u4e00\u9879\u9ad8\u7ea7\u5b9e\u8df5\uff0c\u9700\u8981\u8fd0\u7528\u6280\u672f\u5728\u9075\u5faa\u590d\u6742\u7ea6\u675f\u7684\u540c\u65f6\u521b\u5efa\u4eba\u5de5\u6570\u636e\u96c6\u3002\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u6a21\u62df\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u5408\u6210\u6570\u636e\u5fc5\u987b\u4ee3\u8868\u771f\u5b9e\u573a\u666f\u6216\u8865\u5145\u73b0\u6709\u6570\u636e\u96c6\uff0c\u4e14\u4e0d\u635f\u5bb3\u5176\u5b8c\u6574\u6027\u3002<\/p>\n<p>\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u751f\u6210\u5177\u6709\u660e\u786e\u7ed3\u6784\u7684\u6570\u636e\u90fd\u975e\u5e38\u6709\u7528\u3002\u4f8b\u5982\uff0c\u5728\u91d1\u878d\u6a21\u62df\u4e2d\uff0c\u751f\u6210\u9075\u5faa\u53d8\u91cf\u95f4\u7279\u5b9a\u76f8\u5173\u6027\u7684\u65f6\u95f4\u5e8f\u5217\u975e\u5e38\u91cd\u8981\u3002\u5728\u7269\u7406\u5b66\u9886\u57df\uff0c\u521b\u5efa\u9075\u5faa\u7279\u5b9a\u65b9\u7a0b\u6216\u81ea\u7136\u6cd5\u5219\u7684\u6570\u636e\u81f3\u5173\u91cd\u8981\u3002\u7136\u800c\uff0c\u5728\u751f\u7269\u4fe1\u606f\u5b66\u4e2d\uff0c\u6784\u5efa\u8003\u8651\u7279\u5b9a\u7814\u7a76\u80cc\u666f\u4e2d\u7684\u751f\u7269\u6216\u5316\u5b66\u7ea6\u675f\u7684\u6570\u636e\u96c6\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<p>\u4e3b\u8981\u76ee\u6807\u662f\u521b\u5efa\u4e0d\u4ec5\u5177\u6709\u7edf\u8ba1\u4ee3\u8868\u6027\u800c\u4e14\u7b26\u5408\u5176\u6240\u6307\u5e94\u7528\u9886\u57df\u7684\u89c4\u5219\u548c\u5173\u7cfb\u7279\u5f81\u7684\u5408\u6210\u6570\u636e\u3002<\/p>\n<p><strong>\uff081\uff09\u5904\u7406\u590d\u6742\u7684\u5173\u7cfb<\/strong><\/p>\n<p><strong>\u793a\u4f8b\uff1a\u56fa\u5b9a\u603b\u548c\u6570\u636e\u751f\u6210<\/strong><\/p>\n<p>\u4e00\u4e2a\u5e38\u89c1\u7684\u60c5\u51b5\u662f\u751f\u6210\u9075\u5b88\u603b\u548c\u7ea6\u675f\u7684\u53d8\u91cf\uff0c\u4f8b\u5982\u4e0d\u540c\u90e8\u95e8\u4e4b\u95f4\u7684\u9884\u7b97\u5206\u914d\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_8\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">import numpy as np \r\nimport pandas as pd \r\n# \u89c2\u5bdf\u503c\u548c\u7c7b\u522b\u7684\u6570\u91cf\r\nn_observations = 100 \r\nn_categories = 3 \r\n# \u6bcf\u4e2a\u89c2\u5bdf\u503c\u7684\u603b\u548c\r\ntotal_sum = 100 \r\n# \u751f\u6210\u968f\u673a\u6570\u636e\r\ndata = np.random.dirichlet(np.ones(n_categories), size=n_observations) * total_sum \r\n# \u521b\u5efa DataFrame \r\ndf = pd.DataFrame(data, columns=[f\"Category_{i+1}\" for i in range(n_categories)]) \r\ndf[\"Total\"] = df.sum(axis=1) \r\nprint(\"\u4f7f\u7528\u56fa\u5b9a\u548c\u751f\u6210\u7684\u6570\u636e\u96c6\u793a\u4f8b\uff1a\") \r\nprint(df.head()) &gt;&gt;&gt;<\/code><\/pre>\n<ul id=\"code_id_8\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u4f7f\u7528\u56fa\u5b9a\u548c\u751f\u6210\u7684\u6570\u636e\u96c6\u793a\u4f8b\uff1a<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_9\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">Category_1 Category_2 Category_3 Total \r\n0 58.673361 34.972747 6.353891 100.0 \r\n1 16.882673 14.145658 68.971669 100.0 \r\n2 71.446625 10.170256 18.383118 100.0 \r\n3 57.066341 37.334702 5.598957 100.0 \r\n4 15.686990 3.622839 80.690171 100.0<\/code><\/pre>\n<ul id=\"code_id_9\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u72c4\u5229\u514b\u96f7\u5206\u5e03\u7528\u4e8e\u751f\u6210\u968f\u673a\u6bd4\u4f8b\uff0c\u6bcf\u4e2a\u6bd4\u4f8b\u4ee3\u8868\u603b\u6570\u7684\u4e00\u90e8\u5206\u3002\u8fd9\u4e9b\u6bd4\u4f8b\u4e00\u65e6\u8ba1\u7b97\u51fa\u6765\uff0c\u5c31\u4f1a\u8fdb\u884c\u7f29\u653e\uff0c\u4f7f\u5176\u603b\u548c\u7b49\u4e8e\u5b9a\u4e49\u4e3a total_sum \u7684\u7279\u5b9a\u503c\u3002\u8fd9\u6837\uff0c\u8be5\u51fd\u6570\u751f\u6210\u7684\u6570\u636e\u5c31\u9075\u5faa\u4e86\u57fa\u672c\u7ea6\u675f\uff0c\u5373\u6240\u6709\u6bd4\u4f8b\u7684\u603b\u548c\u6070\u597d\u7b49\u4e8e\u6307\u5b9a\u7684\u76ee\u6807\u503c\u3002<\/p>\n<p><strong>\u793a\u4f8b\uff1a\u5177\u6709\u9884\u5b9a\u4e49\u76f8\u5173\u6027\u7684\u6570\u636e<\/strong><\/p>\n<p>\u53e6\u4e00\u4e2a\u5e38\u89c1\u7684\u9700\u6c42\u662f\u751f\u6210\u5177\u6709\u53d8\u91cf\u4e4b\u95f4\u7279\u5b9a\u76f8\u5173\u6027\u7684\u5408\u6210\u6570\u636e\u3002<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_10\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">from scipy.stats import norm \r\n# \u6570\u636e\u96c6\u7684\u7ef4\u5ea6\r\nn_samples = 1000 \r\n# \u6240\u9700\u7684\u76f8\u5173\u77e9\u9635\r\ncorrelation_matrix = np.array([[1.0, 0.8, 0.5], [0.8, 1.0, 0.3],[0.5, 0.3, 1.0]]) \r\n# \u521b\u5efa\u76f8\u5173\u6570\u636e\r\nmean = [0, 0, 0] \r\ndata = np.random.multivariate_normal(mean, correlation_matrix, size=n_samples) \r\n# \u8f6c\u6362\u4e3a DataFrame \r\ndf_corr = pd.DataFrame(data, columns=[\"Variable_1\", \"Variable_2\", \"Variable_3\"]) \r\nprint(df_corr.corr()) \r\n&gt;&gt;&gt; \r\nVariable_1 Variable_2 Variable_3 \r\nVariable_1 1.000000 0.784861 0.490152 \r\nVariable_2 0.784861 1.000000 0.263210\r\n\u53d8\u91cf_3 0.490152 0.263210 1.000000<\/code><\/pre>\n<ul id=\"code_id_10\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<li>13.<\/li>\n<li>14.<\/li>\n<li>15.<\/li>\n<li>16.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>multivariate_normal \u51fd\u6570\u5141\u8bb8\u60a8\u751f\u6210\u9075\u5faa\u591a\u5143\u5206\u5e03\u7684\u6570\u636e\uff0c\u5c0a\u91cd\u4f5c\u4e3a\u8f93\u5165\u63d0\u4f9b\u7684\u76f8\u5173\u77e9\u9635\u5efa\u7acb\u7684\u76f8\u5173\u6027\u3002<\/p>\n<p><strong>\uff082\uff09\u57fa\u4e8e\u56fe\u7684\u6a21\u578b<\/strong><\/p>\n<p>\u57fa\u4e8e\u56fe\u7684\u6a21\u578b\u5bf9\u4e8e\u6a21\u62df\u793e\u4ea4\u7f51\u7edc\u3001\u4ea4\u6613\u6216\u4fe1\u606f\u6d41\u5f88\u6709\u7528\u3002<\/p>\n<p>\u5bfc\u5165 networkx \u4f5c\u4e3a nx<br \/>\n\u5bfc\u5165 pandas \u4f5c\u4e3a pd<br \/>\n\u5bfc\u5165 matplotlib.pyplot \u4f5c\u4e3a plt\u00a0# \u521b\u5efa\u56e0\u679c\u56fe<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_11\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">n_nodes = 10 \r\np_connection = 0.3 \r\ngraph = nx.erdos_renyi_graph(n_nodes, p_connection) \r\n# \u8f6c\u6362\u4e3a DataFrame \r\nedges = nx.to_pandas_edgelist(graph) \r\nprint(\"\u8fde\u63a5\u5217\u8868\uff08\u5f27\uff09\uff1a\") \r\nprint(edges) \r\n# \u56fe\u5f62\u53ef\u89c6\u5316\r\nplt.figure(figsize=(8, 6)) \r\nnx.draw(graph, with_labels=True, node_color='lightblue', edge_color='gray', node_size=700, font_size=10) \r\nplt.title(\"\u56e0\u679c\u56fe\u7684\u8868\u793a\") \r\nplt.show()<\/code><\/pre>\n<ul id=\"code_id_11\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"020703\" data-has-transparency=\"false\" style=\"--dominant-color: #020703;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27572\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/81644e18482f8dd8da185066019c98c3f0e1cf.png\" width=\"255\" height=\"338\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/81644e18482f8dd8da185066019c98c3f0e1cf.png 255w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/81644e18482f8dd8da185066019c98c3f0e1cf-226x300.png 226w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/81644e18482f8dd8da185066019c98c3f0e1cf-113x150.png 113w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"fbfcfc\" data-has-transparency=\"false\" style=\"--dominant-color: #fbfcfc;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27573\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/d8f727d624a5e29e4d75143edc1fae53a19d14.png\" width=\"685\" height=\"505\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/d8f727d624a5e29e4d75143edc1fae53a19d14.png 685w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/d8f727d624a5e29e4d75143edc1fae53a19d14-300x221.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/d8f727d624a5e29e4d75143edc1fae53a19d14-150x111.png 150w\" sizes=\"auto, (max-width: 685px) 100vw, 685px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u8fd9\u4e00\u80cc\u666f\u4e0b\u7684\u4e3b\u8981\u5e94\u7528\u5305\u62ec\uff1a\u4e00\u65b9\u9762\uff0c\u793e\u4ea4\u7f51\u7edc\u7684\u6a21\u62df\uff0c\u5b83\u53ef\u4ee5\u5206\u6790\u548c\u9884\u6d4b\u865a\u62df\u6216\u73b0\u5b9e\u793e\u533a\u4e2d\u7684\u4e92\u52a8\u52a8\u6001\u548c\u96c6\u4f53\u884c\u4e3a\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u53d1\u73b0\u5206\u5e03\u5f0f\u7cfb\u7edf\u4e2d\u7684\u6570\u636e\u6d41\u5efa\u6a21\u662f\u7406\u89e3\u3001\u4f18\u5316\u548c\u7ba1\u7406\u590d\u6742\u4e14\u4e92\u8054\u7684\u6280\u672f\u73af\u5883\u4e2d\u4fe1\u606f\u4f20\u8f93\u7684\u5173\u952e\u6d3b\u52a8\u3002<\/p>\n<p><strong>\uff083\uff09\u65f6\u95f4\u5e8f\u5217\u7684\u81ea\u56de\u5f52\u6a21\u578b<\/strong><\/p>\n<p>\u81ea\u56de\u5f52\u65f6\u95f4\u5e8f\u5217\u7528\u4e8e\u6a21\u62df\u5177\u6709\u65f6\u95f4\u4f9d\u8d56\u6027\u7684\u6570\u636e\u3002<\/p>\n<p>\u5bfc\u5165 numpy \u4f5c\u4e3a np<br \/>\n\u5bfc\u5165 networkx \u4f5c\u4e3a nx<br \/>\n\u5bfc\u5165 pandas \u4f5c\u4e3a pd<br \/>\n\u5bfc\u5165 matplotlib.pyplot \u4f5c\u4e3a plt<\/p>\n<div>\n<div class=\"hljs-cto\">\n<div class=\"hljs-cto\"><button class=\"copy_btn disable\" data-clipboard-target=\"#code_id_12\">\u590d\u5236<\/button><\/p>\n<div class=\"code-toolbar\">\n<pre class=\"has-pre-numbering language-typescript\" tabindex=\"0\"><code class=\"language-typescript\">\u4ece statsmodels.tsa.arima_process \u5bfc\u5165 ArmaProcess \r\n# \u5b9a\u4e49 AR \u548c MA \u53c2\u6570\r\nar_params = np.array([1, -0.5]) \r\nma_params = np.array([1, 0.4]) \r\nmodel = ArmaProcess(ar=ar_params, ma=ma_params) \r\n# \u751f\u6210\u65f6\u95f4\u5e8f\u5217\r\nn_points = 200 \r\ntime_series = model.generate_sample(nsample=n_points) \r\n# \u53ef\u89c6\u5316\r\n\u5bfc\u5165 matplotlib.pyplot \u4f5c\u4e3a plt \r\nplt.plot(time_series) \r\nplt.title(\"\u81ea\u56de\u5f52\u65f6\u95f4\u5e8f\u5217\") plt.show()<\/code><\/pre>\n<ul id=\"code_id_12\" class=\"pre-numbering\">\n<li>1.<\/li>\n<li>2.<\/li>\n<li>3.<\/li>\n<li>4.<\/li>\n<li>5.<\/li>\n<li>6.<\/li>\n<li>7.<\/li>\n<li>8.<\/li>\n<li>9.<\/li>\n<li>10.<\/li>\n<li>11.<\/li>\n<li>12.<\/li>\n<\/ul>\n<div class=\"toolbar\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><img data-dominant-color=\"edf3f7\" data-has-transparency=\"false\" style=\"--dominant-color: #edf3f7;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-27574\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b6f765c87f6b0f7e554959f115bf72bc3c595c.png\" width=\"683\" height=\"526\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b6f765c87f6b0f7e554959f115bf72bc3c595c.png 683w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b6f765c87f6b0f7e554959f115bf72bc3c595c-300x231.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/10\/b6f765c87f6b0f7e554959f115bf72bc3c595c-150x116.png 150w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h3>\u4e09\u3001\u5408\u6210\u6570\u636e\u751f\u6210\u4e2d\u7684\u4f26\u7406\u8003\u8651\u548c\u9650\u5236<\/h3>\n<p>\u5408\u6210\u6570\u636e\u7684\u751f\u6210\u63d0\u4f9b\u4e86\u4e00\u79cd\u521b\u65b0\u800c\u7075\u6d3b\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u53ef\u4ee5\u514b\u670d\u4e0e\u771f\u5b9e\u6570\u636e\u7684\u53ef\u7528\u6027\u3001\u8d28\u91cf\u548c\u4fdd\u62a4\u76f8\u5173\u7684\u6311\u6218\uff0c\u4f46\u5b83\u4e5f\u5f15\u53d1\u4e86\u9700\u8981\u4ed4\u7ec6\u8bc4\u4f30\u7684\u91cd\u5927\u9053\u5fb7\u548c\u64cd\u4f5c\u95ee\u9898\u3002<\/p>\n<p>\u4e00\u4e2a\u95ee\u9898\u6d89\u53ca\u4e0e\u771f\u5b9e\u6570\u636e\u8fc7\u5ea6\u76f8\u4f3c\u7684\u98ce\u9669\u3002\u5982\u679c\u5408\u6210\u6570\u636e\u8fc7\u4e8e\u5fe0\u5b9e\u4e8e\u539f\u59cb\u6765\u6e90\uff0c\u5219\u53ef\u80fd\u4f1a\u6cc4\u9732\u4e2a\u4eba\u654f\u611f\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u5c06\u8fd9\u4e9b\u6570\u636e\u4e0e\u5176\u4ed6\u6570\u636e\u96c6\u76f8\u7ed3\u5408\uff0c\u6709\u52a9\u4e8e\u8bc6\u522b\u5176\u4e2d\u7684\u5173\u8054\u6027\uff0c\u4ece\u800c\u4fc3\u8fdb\u91cd\u65b0\u8bc6\u522b\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u5173\u952e\u95ee\u9898\u662f\u539f\u59cb\u6570\u636e\u4e2d\u5b58\u5728\u7684\u504f\u5dee\u53ef\u80fd\u4f1a\u88ab\u8f6c\u79fb\u6216\u653e\u5927\u3002\u5982\u679c\u5728\u751f\u6210\u8fc7\u7a0b\u4e2d\u6ca1\u6709\u8fdb\u884c\u4e25\u683c\u7684\u63a7\u5236\uff0c\u5408\u6210\u6570\u636e\u786e\u5b9e\u53ef\u80fd\u4f1a\u4f7f\u7c7b\u522b\u4e0d\u5e73\u8861\u6216\u5c5e\u6027\u6c38\u4e45\u5316\u3002\u6b64\u5916\uff0c\u5728\u521b\u5efa\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u80fd\u4f1a\u5f15\u5165\u65b0\u7684\u65e0\u610f\u504f\u5dee\uff0c\u4ece\u800c\u52a0\u5267\u95ee\u9898\u3002<\/p>\n<p>\u5408\u6210\u6570\u636e\u7684\u6709\u6548\u6027\u548c\u53ef\u7528\u6027\u662f\u53e6\u4e00\u4e2a\u6311\u6218\u3002\u4e3a\u4e86\u53d1\u6325\u4f5c\u7528\uff0c\u6570\u636e\u5fc5\u987b\u9075\u5faa\u73b0\u5b9e\u4e16\u754c\u6570\u636e\u56fa\u6709\u7684\u5173\u7cfb\u548c\u7ea6\u675f\uff0c\u4f8b\u5982\u6c42\u548c\u6216\u65f6\u95f4\u5e8f\u5217\u3002\u5982\u679c\u7f3a\u5c11\u8fd9\u4e9b\u7279\u5f81\uff0c\u5408\u6210\u6570\u636e\u53ef\u80fd\u65e0\u6cd5\u4f7f\u7528\u3002\u6b64\u5916\uff0c\u57fa\u4e8e\u5408\u6210\u6570\u636e\u8bad\u7ec3\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u53ef\u80fd\u65e0\u6cd5\u5145\u5206\u63a8\u5e7f\u5230\u73b0\u5b9e\u4e16\u754c\u3002<\/p>\n<p>\u4ece\u76d1\u7ba1\u548c\u9053\u5fb7\u89d2\u5ea6\u6765\u770b\uff0c\u5408\u6210\u6570\u636e\u7684\u751f\u6210\u5fc5\u987b\u7b26\u5408\u6570\u636e\u4fdd\u62a4\u6cd5\uff0c\u4f8b\u5982\u6b27\u6d32\u7684\u300a\u901a\u7528\u6570\u636e\u4fdd\u62a4\u6761\u4f8b\u300b\uff08GDPR\uff09\u6216\u7f8e\u56fd\u7684\u300a\u6d88\u8d39\u8005\u9690\u79c1\u6cd5\u6848\u300b\uff08CCPA\uff09\u3002\u8fd9\u610f\u5473\u7740\u5bf9\u539f\u59cb\u6570\u636e\u8fdb\u884c\u4e25\u683c\u7ba1\u7406\uff0c\u5e76\u5728\u6d41\u7a0b\u7684\u6bcf\u4e2a\u9636\u6bb5\u90fd\u9075\u5b88\u6cd5\u5f8b\u8981\u6c42\u3002<\/p>\n<h3>\u56db\u3001\u5c0f\u7ed3<\/h3>\n<p>\u5408\u6210\u6570\u636e\u751f\u6210\u6b63\u9010\u6e10\u6210\u4e3a\u6570\u636e\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5173\u952e\u8981\u7d20\uff0c\u5c24\u5176\u662f\u5728\u771f\u5b9e\u6570\u636e\u53ef\u7528\u6027\u53d7\u5230\u9690\u79c1\u9650\u5236\u3001\u504f\u89c1\u6216\u7f3a\u4e4f\u4ee3\u8868\u6027\u7b49\u56e0\u7d20\u9650\u5236\u7684\u60c5\u51b5\u4e0b\u3002\u7136\u800c\uff0c\u5176\u6709\u6548\u6027\u53d6\u51b3\u4e8e\u9009\u62e9\u6700\u5408\u9002\u7684\u6280\u672f\uff0c\u5e76\u610f\u8bc6\u5230\u5176\u5c40\u9650\u6027\u548c\u4f26\u7406\u5f71\u54cd\u3002<\/p>\n<p>\u5728\u73b0\u6709\u7684\u6280\u672f\u4e2d\uff0c\u6982\u7387\u6280\u672f\u88ab\u8bc1\u660e\u80fd\u591f\u7b80\u5355\u6709\u6548\u5730\u8868\u793a\u7ebf\u6027\u5206\u5e03\uff0c\u5c3d\u7ba1\u5b83\u4eec\u5728\u5904\u7406\u590d\u6742\u6570\u636e\u65f6\u5b58\u5728\u5c40\u9650\u6027\u3002\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5728\u7b80\u5355\u6027\u548c\u6355\u6349\u66f4\u590d\u6742\u7ed3\u6784\u7684\u80fd\u529b\u4e4b\u95f4\u53d6\u5f97\u4e86\u826f\u597d\u7684\u5e73\u8861\u3002\u9ad8\u7ea7\u8bed\u8a00\u6a21\u578b\uff08\u4f8b\u5982\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff09\u4ee5\u5176\u7075\u6d3b\u6027\u800c\u8457\u79f0\uff0c\u80fd\u591f\u751f\u6210\u9ad8\u5ea6\u771f\u5b9e\u4e14\u590d\u6742\u7684\u6570\u636e\uff0c\u975e\u5e38\u9002\u5408\u6a21\u62df\u3001\u8868\u683c\u5206\u6790\u548c\u6587\u672c\u7b49\u5e94\u7528\u573a\u666f\u3002<\/p>\n<p>\u4e3a\u4e86\u6700\u5927\u9650\u5ea6\u5730\u53d1\u6325\u5408\u6210\u6570\u636e\u7684\u4ef7\u503c\uff0c\u81f3\u5173\u91cd\u8981\u7684\u662f\u8981\u6839\u636e\u5177\u4f53\u9700\u6c42\u5b9a\u5236\u751f\u6210\u7b56\u7565\uff0c\u6301\u7eed\u76d1\u63a7\u6240\u751f\u6210\u6570\u636e\u7684\u8d28\u91cf\uff0c\u5e76\u5c06\u5176\u4e0e\u771f\u5b9e\u6570\u636e\u8fdb\u884c\u6bd4\u8f83\u3002\u6b64\u5916\uff0c\u8fd8\u9700\u8981\u6574\u5408\u63a7\u5236\u63aa\u65bd\u4ee5\u51cf\u8f7b\u504f\u89c1\u548c\u9690\u79c1\u4fb5\u72af\uff0c\u5e76\u53ca\u65f6\u4e86\u89e3\u8be5\u9886\u57df\u7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class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_27560\" class=\"pvc_stats total_only  \" data-element-id=\"27560\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" viewBox=\"0 0 502 315\" preserveAspectRatio=\"xMidYMid meet\"><g transform=\"translate(0,332) scale(0.1,-0.1)\" fill=\"\" stroke=\"none\"><path d=\"M2394 3279 l-29 -30 -3 -207 c-2 -182 0 -211 15 -242 39 -76 157 -76 196 0 15 31 17 60 15 243 l-3 209 -33 29 c-26 23 -41 29 -80 29 -41 0 -53 -5 -78 -31z\"\/><path d=\"M3085 3251 c-45 -19 -58 -50 -96 -229 -47 -217 -49 -260 -13 -295 52 -53 146 -42 177 20 16 31 87 366 87 410 0 70 -86 122 -155 94z\"\/><path d=\"M1751 3234 c-13 -9 -29 -31 -37 -50 -12 -29 -10 -49 21 -204 19 -94 39 -189 45 -210 14 -50 54 -80 110 -80 34 0 48 6 76 34 21 21 34 44 34 59 0 14 -18 113 -40 219 -37 178 -43 195 -70 221 -36 32 -101 37 -139 11z\"\/><path d=\"M1163 3073 c-36 -7 -73 -59 -73 -102 0 -56 133 -378 171 -413 34 -32 83 -37 129 -13 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