Word Embeddings through Hellinger PCA
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1 Word Embeddings through Hellinger PCA Rémi Lebret and Ronan Collobert Idiap Research Institute / EPFL EACL, 29 April 2014
2 2 Word Embeddings Continuous vector-space models. Represent word meanings with vectors capturing semantic + syntactic information. Similarity measures by computing distances between vectors. Useful applications: Information retrieval Document classification Question answering Successful methods: Neural Language Models [Bengio et al., 2003, Collobert and Weston, 2008, Mikolov et al., 2013].
3 Neural Language Model Understanding 3
4 4 Neural Language Model Trained by backpropagation
5 Neural Language Model 4
6 Neural Language Model 4
7 Neural Language Model 4
8 Neural Language Model 4
9 Neural Language Model 4
10 Neural Language Model 4
11 5 Use of Context You shall know a word by the company it keeps [Firth, 1957]
12 5 Use of Context Next word probability distribution: P(W t W t 1 )
13 5 Use of Context Next word probability distribution: P(W t W t 1 )
14 5 Use of Context Next word probability distribution: P(W t W t 1 )
15 6 Neural Language Model Critical Limitations: Large corpus needed for rare words Difficult to train finding the right parameters Time-consuming weeks of training
16 6 Neural Language Model Critical Limitations: Large corpus needed for rare words Difficult to train finding the right parameters Time-consuming weeks of training Alternative Estimate P(W t W t 1 ) by simply counting words. Dimensionality reduction PCA with an appropriate metric.
17 Hellinger PCA of the Word Co-occurence Matrix A simpler and faster method for word embeddings
18 8 A Spectral Method Word co-occurence statistics: Counting number of times W t D occurs after a sequence W t 1:t T : P(W t W t 1:t T ) = P(W t, W t 1:t T ) P(W t 1:t T ) Sequence size from 1 to T words. = n(w t, W t 1:t T ) W n(w, W t 1:t T ), Next word probability distribution P for each sequence. Multinomial distribution of D classes (words). Co-occurence matrix of size N D. For word embeddings, T = 1.
19 8 A Spectral Method Word co-occurence statistics: Counting number of times W t D occurs after a sequence W t 1:t T : P(W t W t 1:t T ) = P(W t, W t 1:t T ) P(W t 1:t T ) = n(w t, W t 1:t T ) W n(w, W t 1:t T ), Example of word co-occurence probability matrix: W t 1 W t breeds computing cover food is meat named of cat dog cloud
20 9 A Spectral Method Hellinger distance: H(P, Q) = 1 k ( p i q i ) 2, (1) 2 with P = (p 1,..., p k ), Q = (q 1,..., q k ) discrete probability distributions. i=1 Related to Euclidean norm: H(P, Q) = 1 2 P Q 2. (2) Normalized distributions: P = 1.
21 10 A Spectral Method Dimensionality reduction in practice: PCA with square roots of probability distributions: W t 1 W t breeds computing cover food is meat named of cat dog cloud
22 Word Embeddings Evaluation 11
23 12 Word Embeddings Evaluation Supervised NLP tasks: Syntactic: Named Entity Recognition Semantic: Movie Review
24 Sentence-level Architecture 13
25 Example of Movie Review 14
26 Document-level Architecture 15
27 16 Word Embeddings Fine-Tuning Embeddings are generic.
28 16 Word Embeddings Fine-Tuning Embeddings are generic.
29 16 Word Embeddings Fine-Tuning Embeddings are generic. Task-specific tuned embeddings.
30 Experimental Setup 17
31 18 Experimental Setup Building Word Embeddings over Large Corpora: English corpus = Wikipedia + Reuters + Wall Street Journal billion words. Vocabulary = words that appear at least 100 times 178,080 words Context vocabulary = 10,000 most frequent words Co-occurence matrix of size 178, , dimensional vector after PCA
32 19 Experimental Setup Comparison with Existing Available Word Embeddings: LR-MVL: 300,000 words with 50 dimensions trained on RCV1 corpus. Another spectral method CW: 130,000 words with 50 dimensions trained over Wikipedia. Neural network language model Turian: 268,810 words with 50 dimensions trained over RCV1 corpus. Same model as CW HLBL: 246,122 words with 50 dimensions trained over RCV1 corpus. Probabilistic and linear neural model
33 20 Experimental Setup Supervised Evaluation Tasks: Named Entity Recognition (NER) Reuters corpus: Training set 203,621 words Test set 46,435 words Number of tags = 9 Features: Word embeddings Capital letter feature
34 Experimental Setup Supervised Evaluation Tasks: Movie Review IMDB Review Dataset: Training set 25,000 reviews Test set 25,000 reviews Even number of positive and negative reviews Features: Word embeddings
35 Results 22
36 23 Named Entity Recognition Other models Brown 1000 clusters 88.5 Ando & Zhang (2005) 89.3 Suzuki & Isozaki (2008) 89.9 Lin & Wu (2009) 90.9 Our model* No Tuned Tuned LR-MVL CW Turian HLBL H-PCA E-PCA Results in F1 score Mainly syntactic Slight increase with fine-tuning *Only word embeddings + capital letter as features. No gazetteers. No previous predictions.
37 IMDB Movie Review Other models LDA 67.4 LSA 84.0 Maas et al. (2011) 88.9 Wang & Manning (2012) with unigram 88.3 Wang & Manning (2012) with bigram 91.2 Brychcin & Habernal (2013) 92.2 Our model* No Tuned Tuned LR-MVL CW Turian HLBL H-PCA E-PCA Results in classification accuracy Clearly semantic Fine-tuning do help *Only word embeddings as features. No global context.
38 25 Computational Cost Core Completion Time LR-MVL 70 CPU 3 days CW 1 CPU 2 months Turian 1 CPU few weeks HLBL GPGPU 7 days H-PCA 1 CPU 3 hours H-PCA 100 CPU 3 minutes
39 26 Fine-Tuning 10 nearest neighbors with and without fine-tuning BORING BAD AWESOME BEFORE AFTER BEFORE AFTER BEFORE AFTER SAD CRAP HORRIBLE TERRIBLE SPOOKY TERRIFIC SILLY LAME TERRIBLE STUPID AWFUL TIMELESS SUBLIME MESS DREADFUL BORING SILLY FANTASTIC FANCY STUPID UNFORTUNATE DULL SUMMERTIME LOVELY SOBER DULL AMAZING CRAP NASTY FLAWLESS TRASH HORRIBLE AWFUL WRONG MACABRE MARVELOUS LOUD RUBBISH MARVELOUS TRASH CRAZY EERIE RIDICULOUS SHAME WONDERFUL SHAME ROTTEN LIVELY RUDE AWFUL GOOD KINDA OUTRAGEOUS FANTASY MAGIC ANNOYING FANTASTIC JOKE SCARY SURREAL
40 27 Valuable feature
41 28 Conclusion Appealing word embeddings from Hellinger PCA of the word co-occurence matrix. Simply counting words over a large corpus. PCA of a N 10, 000 matrix fast and not memory consuming. Practical alternative to neural language models. H-PCA s embeddings available online: 50, 100 and 200 dimensions Demo
42 28 Conclusion Appealing word embeddings from Hellinger PCA of the word co-occurence matrix. Simply counting words over a large corpus. PCA of a N 10, 000 matrix fast and not memory consuming. Practical alternative to neural language models. H-PCA s embeddings available online: 50, 100 and 200 dimensions Demo Thank you!
43 29 References I Bengio, Y., Ducharme, R., Vincent, P., and Janvin, C. (2003). A neural probabilistic language model. J. Mach. Learn. Res., 3: Collobert, R. and Weston, J. (2008). A unified architecture for natural language processing: Deep neural networks with multitask learning. In International Conference on Machine Learning, ICML. Collobert, R., Weston, J., Bottou, L., Karlen, M., Kavukcuoglu, K., and Kuksa, P. (2011). Natural language processing (almost) from scratch. Journal of Machine Learning Research, 12: Firth, J. R. (1957). A synopsis of linguistic theory :1 32.
44 30 References II Mikolov, T., Sutskever, I., Chen, K., Corrado, G., and Dean, J. (2013). Distributed representations of words and phrases and their compositionality. In Burges, C., Bottou, L., Welling, M., Ghahramani, Z., and Weinberger, K., editors, Advances in Neural Information Processing Systems 26, pages Curran Associates, Inc.
45 31 NNLM Architecture Figure: Neural Language model ([Bengio et al., 2003])
46 Word-tagging Architecture Figure: Sentence Approach ([Collobert et al., 2011]) 32
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