{"id":364,"date":"2026-02-03T22:34:00","date_gmt":"2026-02-03T14:34:00","guid":{"rendered":"https:\/\/mitongxue.cn\/?p=364"},"modified":"2026-06-12T22:42:09","modified_gmt":"2026-06-12T14:42:09","slug":"n-gram%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/mitongxue.cn\/index.php\/2026\/02\/03\/n-gram%e6%a8%a1%e5%9e%8b\/","title":{"rendered":"N-Gram\u6a21\u578b"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u4ece 1970 \u5e74\u4ee5\u540e\u4eba\u4eec\u610f\u8bc6\u5230\u4e0d\u80fd\u57fa\u4e8e\u89c4\u5219\uff0c\u5f97\u57fa\u4e8e\u7edf\u8ba1\u8fd9\u4e2a\u65f6\u95f4\u8282\u70b9\u5f00\u59cb\uff0c\u5c31\u51fa\u73b0\u4e86\u5f88\u591a\u8bed\u8a00\u6a21\u578b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u57fa\u672c\u4ecb\u7ecd<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N-Gram\u6a21\u578b\u8bde\u751f\u4e8e 1950s\u20131960s\uff0c\u6700\u65e9\u7531\u9999\u519c\uff08Claude Shannon\uff09\u5728\u4fe1\u606f\u8bba\u4e2d\u63d0\u51fa\uff0c\u7528\u4e8e\u8bed\u8a00\u7684\u6982\u7387\u5efa\u6a21\uff0c\u9999\u519c\u5728 1951 \u5e74\u7684\u8bba\u6587\u4e2d\u63d0\u51fa\uff0c\u4f7f\u7528 1-gram\u30012-gram \u7b49\u65b9\u6cd5\u4f30\u8ba1\u82f1\u6587\u6587\u672c\u7684\u6982\u7387\u3002\u524d\u9762\u7684 N \u662f\u4e00\u4e2a\u6570\u5b57\uff0c\u8868\u793a\u4f60\u6bcf\u6b21\u8981\u770b\u51e0\u4e2a\u8bcd\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1-Gram\uff08Unigram\uff09\uff1a\u53ea\u770b\u4e00\u4e2a\u8bcd\uff08\u4e0d\u770b\u524d\u9762\u7684\u8bcd\uff09\u3002<\/li>\n\n\n\n<li>2-Gram\uff08Bigram\uff09\uff1a\u4f1a\u770b\u524d\u9762\u7684\u4e00\u4e2a\u8bcd\u3002<\/li>\n\n\n\n<li>3-Gram\uff08Trigram\uff09\uff1a\u4f1a\u770b\u524d\u9762\u4e24\u4e2a\u8bcd\u3002<\/li>\n\n\n\n<li>\u4ee5\u6b64\u7c7b\u63a8\u2026<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u6a21\u578b\u57fa\u4e8e\u9a6c\u5c14\u53ef\u592b\u5047\u8bbe\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9a6c\u5c14\u53ef\u592b\u5047\u8bbe\uff1a\u4e00\u4e2a\u8bcd\u51fa\u73b0\u7684\u6982\u7387\uff0c\u4f9d\u8d56\u4e8e\u5b83\u524d\u9762\u7684 N-1 \u4e2a\u8bcd\uff0c\u800c\u4e0d\u662f\u6574\u4e2a\u53e5\u5b50\u5386\u53f2\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\uff08\u53a8\u623f\uff09\u5988\u5988\u8bf4\uff1a\u201c\u5e2e\u6211\u62ff\u4e00\u4e0b\u51b0\u7bb1\u91cc\u9762\u7684....\u201d<\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9e21\u86cb<\/li>\n\n\n\n<li>\u725b\u8111<\/li>\n\n\n\n<li>\u82f9\u679c<\/li>\n\n\n\n<li>&#8230;.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u4f60\u7684\u5927\u8111\u4e2d\uff0c\u5c31\u4f1a\u81ea\u52a8\u7684\u53bb\u9884\u6d4b\u4e0b\u4e00\u4e2a\u8bcd\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u4f1a\u5f39\u51fa\u4e0b\u9762\u7684\u8bcd\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u98de\u673a<\/li>\n\n\n\n<li>\u6c7d\u8f66<\/li>\n\n\n\n<li>\u7535\u8111<\/li>\n\n\n\n<li>&#8230;.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5de5\u4f5c\u539f\u7406<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u6211\u4eec\u4ee5 Bigram\uff082-Gram\uff09\uff1a\u4f1a\u770b\u524d\u9762\u7684\u4e00\u4e2a\u8bcd\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6211\u4eec\u6709\u8fd9\u6837\u4e00\u4e2a\u201c\u8bed\u6599\u5e93\u201d\uff0c\u6211\u4eec\u7528\u8fd9\u4e9b\u6570\u636e\u6765\u8bad\u7ec3\u6a21\u578b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u201c\u6211 \u7231 \u5403 \u82f9\u679c\u201d<br>\u201c\u6211 \u7231 \u5403 \u9999\u8549\u201d<br>\u201c\u6211 \u559c\u6b22 \u5403 \u82f9\u679c\u201d<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Bigram \u6a21\u578b\u4f1a<strong>\u6839\u636e\u4e00\u4e2a\u8bcd\u7edf\u8ba1\u4e0b\u4e00\u4e2a\u8bcd\u51fa\u73b0\u7684\u6982\u7387<\/strong>\uff0c\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u6570\u4e00\u6570\u6240\u6709\u8bcd\u5bf9\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u524d\u4e00\u4e2a\u8bcd<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u4e0b\u4e00\u4e2a\u8bcd<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u6b21\u6570<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u6211<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u7231<\/td><td class=\"has-text-align-left\" data-align=\"left\">2 \u6b21<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u6211<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u559c\u6b22<\/td><td class=\"has-text-align-left\" data-align=\"left\">1 \u6b21<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u7231<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5403<\/td><td class=\"has-text-align-left\" data-align=\"left\">2 \u6b21<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u559c\u6b22<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u5403<\/td><td class=\"has-text-align-left\" data-align=\"left\">1 \u6b21<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u5403<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u82f9\u679c<\/td><td class=\"has-text-align-left\" data-align=\"left\">2 \u6b21<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u5403<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u9999\u8549<\/td><td class=\"has-text-align-left\" data-align=\"left\">1 \u6b21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6839\u636e\u8fd9\u4e2a\u8bcd\u7684\u7ec4\u5408\uff0c\u5c31\u53ef\u4ee5\u53bb\u9884\u6d4b\u4e00\u4e2a\u8bcd\u7684\u4e0b\u4e00\u4e2a\u8bcd\uff0c\u6bd4\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6211<\/strong>\u540e\u9762\u51fa\u73b0\u201c\u7231\u201d\u7684\u6982\u7387\u662f 2\/3\uff0c\u51fa\u73b0\u201c\u559c\u6b22\u201d\u7684\u6982\u7387\u662f 1\/3\u3002<\/li>\n\n\n\n<li><strong>\u5403<\/strong>\u540e\u9762\u51fa\u73b0\u201c\u82f9\u679c\u201d\u7684\u6982\u7387\u662f 2\/3\uff0c\u51fa\u73b0\u201c\u9999\u8549\u201d\u7684\u6982\u7387\u662f 1\/3\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4f60\u770b\u5230\u201c<strong>\u6211 \u7231 \u5403<\/strong>\u201d\uff0c\u90a3\u4e0b\u4e00\u4e2a\u8bcd\u5927\u6982\u7387\u662f\u201c\u82f9\u679c\u201d\uff01<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4ee3\u7801\u5b9e\u8df5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">jieba \u662f python \u91cc\u9762\u7528\u4e8e\u5bf9\u4e2d\u6587\u5206\u8bcd\u7684\u4e00\u4e2a\u5e93\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201c\u6211\u559c\u6b22\u5403\u82f9\u679c\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u3001\u559c\u6b22\u3001\u5403\u3001\u82f9\u679c<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import jieba  # \u5bfc\u5165 jieba \u4e2d\u6587\u5206\u8bcd\u5e93<br># \u5bfc\u5165 defaultdict \u548c Counter\uff0c\u7528\u4e8e\u6784\u5efa\u9891\u7387\u7edf\u8ba1\u8868<br>from collections import defaultdict, Counter<br>\u200b<br># \u793a\u4f8b\u8bed\u6599\u5e93\uff08\u6ce8\u610f\uff1a\u8fd9\u4e9b\u662f\u8fde\u7eed\u7684\u4e2d\u6587\u53e5\u5b50\uff0c\u6ca1\u6709\u7a7a\u683c\uff09<br>corpus = &#91;<br> &nbsp;  \"\u6211\u559c\u6b22\u5403\u82f9\u679c\",<br> &nbsp;  \"\u6211\u559c\u6b22\u5403\u9999\u8549\",<br> &nbsp;  \"\u5979\u559c\u6b22\u5403\u8461\u8404\",<br> &nbsp;  \"\u4ed6\u4e0d\u559c\u6b22\u5403\u9999\u8549\",<br> &nbsp;  \"\u4ed6\u559c\u6b22\u5403\u82f9\u679c\",<br> &nbsp;  \"\u5979\u559c\u6b22\u5403\u8349\u8393\"<br>]<br>\u200b<br># 1. \u6784\u5efa Bigram \u7edf\u8ba1\u8868\uff0c\u683c\u5f0f\u4e3a bigrams&#91;\u524d\u4e00\u4e2a\u8bcd]&#91;\u4e0b\u4e00\u4e2a\u8bcd] = \u51fa\u73b0\u6b21\u6570<br>bigrams = defaultdict(Counter)  # \u81ea\u52a8\u521d\u59cb\u5316\u5d4c\u5957\u7ed3\u6784\uff0c\u907f\u514d\u624b\u52a8\u5224\u65ad\u952e\u662f\u5426\u5b58\u5728<br>\u200b<br># \u904d\u5386\u6bcf\u4e00\u53e5\u8bdd<br>for sentence in corpus:<br> &nbsp;  words = list(jieba.cut(sentence))  # \u4f7f\u7528 jieba \u5bf9\u53e5\u5b50\u8fdb\u884c\u5206\u8bcd\uff0c\u8fd4\u56de\u8bcd\u5217\u8868<br> &nbsp;  # \u6784\u5efa\u4e8c\u5143\u7ec4\uff08Bigram\uff09\uff1a\u6bcf\u4e24\u4e2a\u8fde\u7eed\u8bcd\u4e4b\u95f4\u7684\u642d\u914d<br> &nbsp;  for i in range(len(words) - 1):<br> &nbsp; &nbsp; &nbsp;  w1, w2 = words&#91;i], words&#91;i + 1]  # \u5f53\u524d\u8bcd\u548c\u4e0b\u4e00\u4e2a\u8bcd<br> &nbsp; &nbsp; &nbsp;  bigrams&#91;w1]&#91;w2] += 1  # \u51fa\u73b0\u4e00\u6b21\u5c31 +1<br>\u200b<br># 2. \u5c06\u9891\u7387\u8f6c\u6362\u6210\u6982\u7387\uff0c\u6784\u5efa Bigram \u6982\u7387\u6a21\u578b<br>bigram_probs = {}  # \u6700\u7ec8\u4fdd\u5b58\u7684\u662f P(w2 | w1) \u7684\u6982\u7387\u8868<br>\u200b<br># \u904d\u5386\u6240\u6709\u524d\u8bcd\uff08w1\uff09<br>for w1 in bigrams:<br> &nbsp;  total = sum(bigrams&#91;w1].values())  # w1 \u540e\u9762\u51fa\u73b0\u6240\u6709\u8bcd\u7684\u603b\u6b21\u6570<br> &nbsp;  # \u8ba1\u7b97\u6bcf\u4e00\u4e2a w2 \u7684\u6761\u4ef6\u6982\u7387\uff1aP(w2 | w1) = \u9891\u7387 \/ \u603b\u6570<br> &nbsp;  bigram_probs&#91;w1] = {<br> &nbsp; &nbsp; &nbsp;  w2: count \/ total for w2, count in bigrams&#91;w1].items()<br> &nbsp;  }<br>\u200b<br># 3. \u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\uff1a\u8f93\u5165\u4e00\u4e2a\u8bcd\uff0c\u9884\u6d4b\u5b83\u540e\u9762\u6700\u53ef\u80fd\u51fa\u73b0\u7684\u8bcd\uff08\u6309\u6982\u7387\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\uff09<br>\u200b<br>\u200b<br>def predict_next_word(word):<br> &nbsp;  if word not in bigram_probs:<br> &nbsp; &nbsp; &nbsp;  return \"\u672a\u77e5\uff08\u6ca1\u6709\u6570\u636e\uff09\"  # \u5982\u679c\u8fd9\u4e2a\u8bcd\u4ece\u672a\u51fa\u73b0\u5728\u8bad\u7ec3\u8bed\u6599\u4e2d<br> &nbsp;  # \u6309\u7167\u6982\u7387\u4ece\u9ad8\u5230\u4f4e\u6392\u5e8f\u8fd4\u56de<br> &nbsp;  sorted_probs = sorted(<br> &nbsp; &nbsp; &nbsp;  bigram_probs&#91;word].items(), key=lambda x: x&#91;1], reverse=True<br> &nbsp;  )<br> &nbsp;  return sorted_probs<br>\u200b<br>\u200b<br># 4. \u6253\u5370\u6240\u6709 Bigram \u7684\u6761\u4ef6\u6982\u7387<br>print(\"=== Bigram \u6982\u7387 ===\")<br>for w1 in bigram_probs:<br> &nbsp;  for w2 in bigram_probs&#91;w1]:<br> &nbsp; &nbsp; &nbsp;  prob = bigram_probs&#91;w1]&#91;w2]<br> &nbsp; &nbsp; &nbsp;  print(f\"P({w2} | {w1}) = {prob:.2f}\")  # \u8f93\u51fa\u5f62\u5982\uff1aP(\u5403 | \u559c\u6b22) = 1.00<br>\u200b<br># 5. \u6d4b\u8bd5\u9884\u6d4b\u67d0\u4e9b\u8bcd\u540e\u9762\u6700\u53ef\u80fd\u51fa\u73b0\u7684\u8bcd<br>print(\"\\n=== \u9884\u6d4b\u793a\u4f8b ===\")<br>for test_word in &#91;\"\u6211\", \"\u5403\", \"\u559c\u6b22\", \"\u82f9\u679c\"]:<br> &nbsp;  print(f\"{test_word} \u2192 {predict_next_word(test_word)}\")<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">N-Gram \u867d\u7136\u6bd4\u8f83\u7b80\u964b\uff0c\u4f46\u662f\u5b83\u786e\u786e\u5b9e\u5b9e\u662f\u57fa\u4e8e\u7edf\u8ba1\u8bed\u8a00\u5efa\u6a21\u7684\u8d77\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>N-Gram\u6a21\u578b\u7f3a\u9677<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8bed\u5883\u77ed\u89c6\uff1a\u53ea\u770b\u524d N-1\u4e2a\u8bcd\uff0c\u65e0\u6cd5\u7406\u89e3\u957f\u8ddd\u79bb\u8bcd\u6027\u7684\u4f9d\u8d56\u3002\n<ul class=\"wp-block-list\">\n<li>\u201c\u6211\u6628\u5929\u89c1\u5230\u4e00\u4e2a\u670b\u53cb\uff0c\u4ed6\u8bf4\u4ed6\u975e\u5e38\u559c\u6b22\u7f16\u7a0b\u3002\u201d<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u65e0\u6cd5\u6cdb\u5316\uff1a\u53ea\u80fd\u8bb0\u4f4f\u89c1\u8fc7\u7684\u8bcd\u8bed\u7ec4\u5408\uff0c\u5bf9\u6ca1\u6709\u89c1\u8fc7\u7684\u7ec4\u5408\u65e0\u80fd\u4e3a\u529b\u3002\n<ul class=\"wp-block-list\">\n<li>\u8bed\u6599\u5e93\uff1a\u6211\u7231\u5403\u897f\u74dc\uff08\u6ca1\u6709\u8461\u8404\u8fd9\u4e2a\u8bcd\uff09<\/li>\n\n\n\n<li>\u6c38\u8fdc\u4e0d\u53ef\u80fd\u51fa\u73b0\uff1a\u6211\u7231\u5403\u8461\u8404 \u8fd9\u79cd\u7ec4\u5408<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4e0d\u5177\u5907\u8bed\u4e49\u7406\u89e3\u80fd\u529b\n<ul class=\"wp-block-list\">\n<li>\u65e0\u6cd5\u5224\u65ad\uff1a\u559c\u6b22 \u548c \u7231 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