Universität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen. Language Models. Tobias Scheffer

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1 Universität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen Language Models Tobias Scheffer

2 Stochastic Language Models A stochastic language model is a probability distribution over words. Given a string of words, w 1,, w m, a language model assigns a probability p(w 1,, w m ). Words w 1,, w m can be words, letters, keystrokes. Useful for many (most) NLP tasks. Speech recognition, Spell checking, auto-corrrect, auto-complete, Machine translation, Text classification, Many non-standard NLP problems. 2

3 Language Models: Why? Speech recognition Acoustic model + language model. Acoustic model Most likely words Language model P I saw a tree = P Eyes awe entry = 3

4 Language Models: Why? Hand-written text recognition: Pattern-recognition model + language model Pattern recognition model Language model P I saw a tree P 1 saw a free = = 4

5 Language Models: Why? Machine translation Translation model + language model Translation model Language model P I saw a tree = P I saw one tree = 5

6 Language Models: Why? Auto-correct, auto-complete Keyboard model + language model Keyboard model Language model P I saw a tree P O saq a trew = = 6

7 The n-gram Model Basic tool for language modeling. Based on the Markov assumption of order n 1: p X t X t 1,, X 1 = p X t X t 1,, X t n+1 n-gram model: p X 1,, X T = p X 1 p X T X T 1,, X T n+1 T = P X 1 p X n 1 X n 2,, X 1 p X t X t 1,, X t n+1 t=n Categorical distributions 7

8 The n-gram Model See lecture on basic models. Inference: determine p(w 1,, w T ). Parameter estimation: Determine θ x1,,x m by counting occurances. Laplace smooting for regularization. Laplace smooting assigns positive probability to unseen n-grams. 8

9 Implementing the n-gram Model Probabilities of word sequences decrease exponentially in T. Fall below floating-point precision quickly. Instead of θ x1,,x m, use parameters θ xm x 1,,x m. Do all calculations using logarithmic values. log t p(w t w t 1,,,,. w t+n 1 ) = t log p(w t w t 1,,,,. w t+n 1 ) 9

10 n-gram Model: Long-Term Dependencies The computer that I just installed the new operating system on crashed. Small values of n: Better estimates of n-gram probabilities but lack of context. Increasing n to 4, 5, 6, There will be increasingly many combinations of word n-grams that have never been observed. 1

11 Linear Interpolation Simple interpolation: P w n w n 1,, w 1 = λ n P n w n w n 1,, w λ 2 P 2 w n w n 1 + λ 1 P 1 w n Context-dependent interpolation weights: P w n w n 1,, w 1 = λ n (w n 1, w n 2 )P n w n w n 1,, w λ 2 (w n 1, w n 2 )P 2 w n w n 1 + λ 1 (w n 1, w n 2 )P 1 w n 11

12 Linear Interpolation Setting the interpolation coefficients. Split training data into 8% training and 2% tuning data. Estimate parameters θ x1,,x m on training part. Then, tune parameters λ i to maximize likelihood of the tuning data. 12

13 Resources Google has published a large n-gram corpus. 13

14 Resources Google has published data on the evolution of ngram counts over time from Google Books. 14

15 Limitations of the n-gram Model Capability of reflecting contect limited to n words. Independent parameter for each n-word combination. Semantically similar terms have independent parameters. Idea: Improve genralization by treating semantically similar words in a similar way. Linear interpolation is an attempt at improving generalization. Also, n-gram class models are an attempt at improving generalization. Continuous-space language models. 15

16 Continuous-Space Language Models Predict w t based on features extracted from w t 1,, w t n+1. Maximize P(w t w t 1,, w t n+1 ) t Output x t 1 x t x t+1 x T Language model Input x 1 x t n+1 x t 1 x T. 16

17 Continuous-Space Language Models Predict w t based on features extracted from w t n,, w t+n. Maximize P(w t w t+j ) t j= n +n j Model looks into the future. Output x t 1 x t x t+1 x T Language model Input x 1 x t n x t n x T. 17

18 Continuous-Space Language Models Skip-gram model: Predict w t n,, w t 1, w t+1, w t+n based on features extracted from w t. Maximize P(w t+j w t ) t j= n +n j Output x t 1 x t x t+1 x T Language model Input x 1 x t n x t n x T. 18

19 Continuous-Space Language Models For a word-level language model, words are usually represented by one-hot coded feature vector. x t = 1 Hippopotamus Dictionary: Aardvark Hippie Hippopotamus Hipster Zyzzogeton 19

20 Continuous-Space Language Models For a letter-level language model, latters are usually represented by one-hot coded feature vector. x t = 1 Dictionary: A Z " "! 9 2

21 Continuous-Space Language Models Continuous-space language models are usually implemented by neural networks. Forward propagation leads to activation of the hidden units. The activation of the hidden units creates the embedding (feature representation) φ(x t ) of each word. This feature representation φ(x t ) is useful for many tasks. Words that occur in similar contexts have similar feature representations. 21

22 Neural Language Model Output x t 1 x t x t+1 x T Input x 1 x t n+1 x t 1 x T. = = φ(x t ) = 1 Also uses Markov assumption of order n 1! Softmax output layer Rectified linear units 22

23 Neural Skip-Gram Language Model Output x t 1 x t x t+1 x T Input x 1 x t n+1 x t n+1 x T. = 1 = φ(x t ) =

24 Language Model with Context Memory Additionally provide paragraph ID as input. Allows model to lean an embedding for paragraphs in addition to the embedding for words. Paragraph vector: one-hot endocing of paragraph ID. p t = 1 Paragraph 17 24

25 Neural Language Model with Context Output x t 1 x t x t+1 x T = φ(x t ) Softmax output layer Rectified linear units Input (x 1, p 1 ) (x t n+1, p t n+1 ) (x t 1, p t 1 ) x T. = 1, 1 = 1, 1 25

26 Using Word Embeddings Feature vectors φ(x t ) can replace one-hot coding of words in many applications. Text classification (aggregate over text), Sentiment analysis, Information extraction, 26

27 Using Language Models Auto-correct: find most likely intended sentence w 1,, w T given word entries x 1,, x T. w 1,, w T = arg max w1,,w T P w 1,, w T x 1,, x T = arg max P x 1,, x T w 1,, w T P w 1,, w T w 1,,w T = arg max w 1,,w T Maximization is Exponential in T t P x t w t Learn from corpus of spelling mistakes P w 1,, w T Language model 27

28 Using Language Models Auto-correct: find most likely intended sentence w 1,, w T given word entries x 1,, x T. w 1,, w T = arg max w1,,w T P w 1,, w T x 1,, x T = arg max P x 1,, x T w 1,, w T P w 1,, w T w 1,,w T = arg max w 1,,w T t P x t w t P w 1,, w T When the language model is based on n-th order Markov assumption, maximization by Viterbi is exponential in n (not T). 28

29 Using Language Models Auto-correct: find most likely intended sentence w 1,, w T given word entries x 1,, x T. w 1,, w T = arg max w1,,w T P w 1,, w T x 1,, x T = arg max P x 1,, x T w 1,, w T P w 1,, w T w 1,,w T = arg max w 1,,w T P x t w t If O(k n ) is still too slow, use beam search instead of maximizing over all sequences. t P w 1,, w T 29

30 Evaluating Language Models Extrinsic evaluation: how well deoes the model perform at the task that it is intended for? Machine translation: Apply translation system with different language models. The have human judge score the output sencences. Auto completion: Install two models on smartphones. Measure how frequently users accept the proposed completions. 3

31 Evaluating Language Models Intrinsic evaluation: Does the language model assign a high likelihood to actual sentences? Cannot evaluate on training corpus: Has been used to train the model. Does not imply that model will assign high likelyhood to any out-of-corpus sentence. Training-Test-Split: Estimate parameters on 8% of the corpus. Evaluate model on remaining 2%. 31

32 Evaluating Language Models What is a good evaluation measure? Log-Likelihood of the test corpus? Possible to compare multiple language models. Not possible to compare sencences because short sentences tend to have a higher likelihood than long one (fewer factors). Perplexity of the test corpus: Inverse likelihood, normalized by number of words. PP w 1,, w T = P w 1,, w T 1 T = T t 1 P(w t w t 1, ) 32

33 Evaluating Language Models Perplexity of the test corpus: Inverse likelihood, normalized by number of words. PP w 1,, w T = P w 1,, w T 1 T = Example: p w t = 1 1 PP w 1,, w T = 1 T 1 T 1 = 1 1 T 1 = 1 1 t P(w t w t 1, ) Perplexity: average branching factor. 33

34 Evaluating Language Models Different corpora reflect different distributions. A model that has been trained on the Wall Street Journal corpus may assign a log likelihood to sentences from a belletristic corpus. If a language model infers P w 1,, w T =, then the perplexity is undefined. Sign of overfitting to the training data, lack of regularization. 34

35 Summary Stochastic language models quantify the likelihood of a sencence. Markov assumption of order n 1: word w t only dependent on w t 1,, w t n+1. The n-gram model has a discrete parameter for each n-word combination. Continuous-space (neural) language models learn embedding of words into a feature space; this gives better generalization. Language models are a useful tools for many applications. 35