{ "source_file": "0930", "source_platform": "Medium", "author": "Shashank Kapadia", "title_listed": "Language Models: N-Gram", "keywords": "", "domain": "文本处理", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/introduction-to-language-models-n-gram-e323081503d9/", "publish_date": "2019-03-26", "corpus_stage": "", "notes": "", "id": "56db6c9f7883", "collected_at": "2026-10-02T10:07:29", "title": "Language Models: N-Gram | Towards Data Science", "body_markdown": "![Revisit consent button](../images/body-df29beacd7496220cc94.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. By clicking \"Accept All\", you consent to our use of cookies.\nCustomise Reject All Accept All\nCustomise Consent Preferences ![](../images/body-2159bb67f3de8ad870eb.svg)\nWe use cookies to help you navigate efficiently and perform certain functions. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\n# Language Models: N-Gram\nA step into statistical language modeling\n[Shashank Kapadia](https://towardsdatascience.com/author/shashank%20kapadia/)\nMarch 26, 20194 min read\n![Containers on display \\(N-Gram concept\\)](../images/000.jpg)\nPhoto by Erik Eastman on Unsplash\n## Introduction\nStatistical language models, in its essence, are the type of models that assign probabilities to the sequences of words. In this article, we’ll understand the simplest model that assigns probabilities to sentences and sequences of words, the _**n-gram**_.\nYou can think of an N-gram as the sequence of N words, by that notion, a 2-gram (or bigram) is a two-word sequence of words like “please turn,” “turn your,” or ”your homework,” and a 3-gram (or trigram) is a three-word sequence of words like, “please turn your,” or “turn your homework.”\n## Intuitive formulation\nLet’s start with equation P(w|h), the probability of word _w_ , given some history, _h_. For example,\nLearn this step by step with the interactive [Machine Learning](https://roadmap.sh/machine-learning) roadmap.\n![](../images/001.png)\n> Here, \n> w = The \n> h = its water is so transparent that\nAnd, one way to estimate the above probability function is through the relative frequency count approach, where you would take a substantially large corpus, count the number of times you see _**its water is so transparent that**_ , and then count the number of times it is followed by _**the**_. In other words, you are answering the question:\n> Out of the times you saw the history h, how many times did the word w follow it?\n![](../images/002.png)\nNow, you can imagine it is not feasible to perform this over an entire corpus, especially if it is of a significant size.\nThis shortcoming and ways to decompose the probability function using the chain rule serve as the base intuition of the N-gram model. Here, you, instead of computing probability using the entire corpus, would approximate it by just a few historical words.\n## The bigram model\nAs the name suggests, the bigram model approximates the probability of a word given all the previous words by using only the conditional probability of one preceding word. In other words, you approximate it with the probability: P(the | that).\nAnd so, when you use a bigram model to predict the conditional probability of the next word, you are thus making the following approximation:\n![](../images/003.png)\n> This assumption that the probability of a word depends only on the previous word is also known as **Markov** assumption.\n> Markov models are the class of probabilisitic models that assume that we can predict the probability of some future unit without looking too far in the past.\nYou can further generalize the bigram model to the **trigram model** which looks two words into the past and can thus be further generalized to the **N-gram model**.\n## Probability estimation\nNow that we understand the underlying base for N-gram models, you’d think, how can we estimate the probability function? One of the most straightforward and intuitive ways to do so is **Maximum Likelihood Estimation (MLE)**.\nFor example, to compute a particular bigram probability of a word _**y**_ given a previous word _**x**_ , you can determine the count of the bigram C(xy) and normalize it by the sum of all the bigrams that share the same first-word _**x**_.\n## Challenges\nThere are, of course, challenges, as with every modeling approach and estimation method. Let’s look at the key ones affecting the N-gram model, as well as the use of MLE\n**Sensitivity to the training corpus**\nThe N-gram model, like many statistical models, is significantly dependent on the training corpus. As a result**,** the probabilities often encode particular facts about a given training corpus. Besides, the performance of the N-gram model varies with the change in the value of N.\nMoreover, you may have a language task in which you know all the words that can occur, and hence, we know the vocabulary size V in advance. The closed vocabulary assumption assumes there are no unknown words, which is unlikely in practical scenarios.\n**Smoothing**\nA notable problem with the MLE approach is sparse data. Meaning any N-gram that appeared a sufficient number of times might have a reasonable estimate for its probability. But because any corpus is limited, some perfectly acceptable English word sequences are bound to be missing from it.\nAs a result, the N-gram matrix for any training corpus is bound to have a substantial number of cases of putative “zero probability N-grams.”\n## Sources:\n1. CHAPTER DRAFT — | Stanford Lagunita. \n2. Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech\nThanks for reading. If you have any feedback, please feel free to reach out by messaging me on [LinkedIn](https://www.linkedin.com/in/shashankkapadia/) or shooting me an email (shmkapadia[at]gmail.com).\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Machine Learning](https://towardsdatascience.com/category/artificial-intelligence/machine-learning/)\n# Language Models: N-Gram\nA step into statistical language modeling\n[Shashank Kapadia](https://towardsdatascience.com/author/shashank%20kapadia/)\nMarch 26, 20194 min read\n![Containers on display \\(N-Gram concept\\)](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/N-Gram-scaled.jpg)\nPhoto by Erik Eastman on Unsplash\n## Introduction\nStatistical language models, in its essence, are the type of models that assign probabilities to the sequences of words. In this article, we’ll understand the simplest model that assigns probabilities to sentences and sequences of words, the _**n-gram**_.\nYou can think of an N-gram as the sequence of N words, by that notion, a 2-gram (or bigram) is a two-word sequence of words like “please turn,” “turn your,” or ”your homework,” and a 3-gram (or trigram) is a three-word sequence of words like, “please turn your,” or “turn your homework.”\n## Intuitive formulation\nLet’s start with equation P(w|h), the probability of word _w_ , given some history, _h_. For example,\nLearn this step by step with the interactive [Machine Learning](https://roadmap.sh/machine-learning) roadmap.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/N-Gram-1.png)\n> Here, \n> w = The \n> h = its water is so transparent that\nAnd, one way to estimate the above probability function is through the relative frequency count approach, where you would take a substantially large corpus, count the number of times you see _**its water is so transparent that**_ , and then count the number of times it is followed by _**the**_. In other words, you are answering the question:\n> Out of the times you saw the history h, how many times did the word w follow it?\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/N-Gram-2-1024x35.png)\nNow, you can imagine it is not feasible to perform this over an entire corpus, especially if it is of a significant size.\nThis shortcoming and ways to decompose the probability function using the chain rule serve as the base intuition of the N-gram model. Here, you, instead of computing probability using the entire corpus, would approximate it by just a few historical words.\n## The bigram model\nAs the name suggests, the bigram model approximates the probability of a word given all the previous words by using only the conditional probability of one preceding word. In other words, you approximate it with the probability: P(the | that).\nAnd so, when you use a bigram model to predict the conditional probability of the next word, you are thus making the following approximation:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2025/03/N-Gram-3.png)\n> This assumption that the probability of a word depends only on the previous word is also known as **Markov** assumption.\n> Markov models are the class of probabilisitic models that assume that we can predict the probability of some future unit without looking too far in the past.\nYou can further generalize the bigram model to the **trigram model** which looks two words into the past and can thus be further generalized to the **N-gram model**.\n## Probability estimation\nNow that we understand the underlying base for N-gram models, you’d think, how can we estimate the probability function? One of the most straightforward and intuitive ways to do so is **Maximum Likelihood Estimation (MLE)**.\nFor example, to compute a particular bigram probability of a word _**y**_ given a previous word _**x**_ , you can determine the count of the bigram C(xy) and normalize it by the sum of all the bigrams that share the same first-word _**x**_.\n## Challenges\nThere are, of course, challenges, as with every modeling approach and estimation method. Let’s look at the key ones affecting the N-gram model, as well as the use of MLE\n**Sensitivity to the training corpus**\nThe N-gram model, like many statistical models, is significantly dependent on the training corpus. As a result**,** the probabilities often encode particular facts about a given training corpus. Besides, the performance of the N-gram model varies with the change in the value of N.\nMoreover, you may have a language task in which you know all the words that can occur, and hence, we know the vocabulary size V in advance. The closed vocabulary assumption assumes there are no unknown words, which is unlikely in practical scenarios.\n**Smoothing**\nA notable problem with the MLE approach is sparse data. Meaning any N-gram that appeared a sufficient number of times might have a reasonable estimate for its probability. But because any corpus is limited, some perfectly acceptable English word sequences are bound to be missing from it.\nAs a result, the N-gram matrix for any training corpus is bound to have a substantial number of cases of putative “zero probability N-grams.”\n## Sources:\n1. CHAPTER DRAFT — | Stanford Lagunita. \n2. Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech\nThanks for reading. If you have any feedback, please feel free to reach out by messaging me on [LinkedIn](https://www.linkedin.com/in/shashankkapadia/) or shooting me an email (shmkapadia[at]gmail.com).\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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