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[Sequential Models] week2. Natural Language Processing & Word Embeddings
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<time datetime="2018-02-26T00:00:00+01:00"><i class="fa fa-calendar"></i> Mon, 26 Feb 2018</time>
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<span class="label label-default">Series</span>
Part 15 of «Andrew Ng Deep Learning MOOC»
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目录
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<div id="toc"><ul><li><a class="toc-href" href="#i-introduction-to-word-embeddings" title="I - Introduction to Word Embeddings">I - Introduction to Word Embeddings</a><ul><li><a class="toc-href" href="#using-word-embeddings" title="Using word embeddings">Using word embeddings</a></li><li><a class="toc-href" href="#properties-of-word-embeddings" title="Properties of word embeddings">Properties of word embeddings</a></li><li><a class="toc-href" href="#embedding-matrix" title="Embedding matrix">Embedding matrix</a></li></ul></li><li><a class="toc-href" href="#ii-learning-word-embeddings-word2vec-glove_1" title="II - Learning Word Embeddings: Word2vec & GloVe">II - Learning Word Embeddings: Word2vec & GloVe</a><ul><li><a class="toc-href" href="#learning-word-embeddings" title="Learning word embeddings">Learning word embeddings</a></li><li><a class="toc-href" href="#word2vec" title="Word2Vec">Word2Vec</a></li><li><a class="toc-href" href="#negative-sampling" title="Negative Sampling">Negative Sampling</a></li><li><a class="toc-href" href="#glove-word-vectors" title="GloVe word vectors">GloVe word vectors</a></li></ul></li><li><a class="toc-href" href="#iii-applications-using-word-embeddings_1" title="III-Applications using Word Embeddings">III-Applications using Word Embeddings</a><ul><li><a class="toc-href" href="#sentiment-classification" title="Sentiment Classification">Sentiment Classification</a></li><li><a class="toc-href" href="#debiasing-word-embeddings" title="Debiasing word embeddings">Debiasing word embeddings</a></li></ul></li></ul></div>
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<h2 id="i-introduction-to-word-embeddings">I - Introduction to Word Embeddings</h2>
<p><strong>Word representation</strong><br/>
So far: representing words with one-hot encoding → word relationships are not generalized.<br/>
⇒ want to learn a <em>featurized representatin</em> for each word as a high-dim vector<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image.png"/><br/>
→ visualize word embeddings in 2-dim space, e.g. via <em>t-SNE</em><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image001.png"/> </p>
<h3 id="using-word-embeddings">Using word embeddings</h3>
<p>example: NER<br/>
transfer learning: using pretrained embeddings </p>
<ul>
<li>learn word embeddings from large text corpus (or download pre-trained embeddings) </li>
<li>transfter embedding to new task with smaller training set </li>
<li>(optional) fine-tune word embeddings with new data </li>
</ul>
<p>Word embedding ~ face encoding(embedding) in previous words. </p>
<h3 id="properties-of-word-embeddings">Properties of word embeddings</h3>
<p><em>Analogy reasoning</em> of word embeddings.<br/>
e.g. man->woman as king->?<br/>
Embedding vectors have the relationship: <code>e_man - e_woman ~= e_king - e_queen</code><br/>
Finding nearest neighbor (according to cosine-similarity).<br/>
examples:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image002.png"/> </p>
<h3 id="embedding-matrix">Embedding matrix</h3>
<p>learning an embedding matrix <code>E</code> of shape <code>(embed_dim, vocab_size)</code><br/>
e.g. embed_dim=300, vocab_size=10000<br/>
notataion: <br/>
<code>o_w</code> = one-hot encoding of a word <code>w</code>, dim=(10000,1)<br/>
→ <code>e_w = E * o_w</code>, dim=(300,1)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image003.png"/><br/>
→ Learn <code>E</code> by random-init & gradient descent.<br/>
(In practice: use lookup function instead of matrix multiplication.) </p>
<h2 id="ii-learning-word-embeddings-word2vec-glove_1">II - Learning Word Embeddings: Word2vec & GloVe</h2>
<h3 id="learning-word-embeddings">Learning word embeddings</h3>
<p>Some concrete algos to learn embedding matrix E. Start with complex algos and show simpler algos with good result.<br/>
e.g. Neural language model, i.e. <em>predict next word in the sequence</em>.<br/>
with fixed window size(e.g. =4), predict next word. Context=last 4 words, target=next word.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image004.png"/><br/>
→ Using gradient-descent to update params (<code>E, W, b</code>). </p>
<p>Other kinds of (simpler) context/targets: </p>
<ul>
<li>context=4 words to the left & right, target=the word in the middle </li>
<li>context=previous word, target=next word </li>
<li>context=nearby 1 word (skip-gram model) </li>
</ul>
<h3 id="word2vec">Word2Vec</h3>
<p><strong>Skip-grams</strong><br/>
supervised problem: context/target pairs, given context word, predict target word <br/>
(|v| classes in total) → softmax </p>
<ul>
<li>context <code>c</code>: <em>randomly</em> pick a context word </li>
<li>target <code>t</code>: <em>randomly</em> pick a target word in +/- 4 word window. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image005.png"/><br/>
<strong>Skip-gram Model</strong><br/>
model: context <code>c</code> -> onehot <code>o_c</code> -(<code>E</code>)-> embedding <code>e_c</code> → softmax → prediction <code>yhat</code><br/>
→ target word <code>y</code><br/>
loss = cross-entropy(y, yhat) / log-loss(y, yhat)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image006.png"/><br/>
<strong>how to sample context c</strong><br/>
uniform sampling for <code>c</code>: frequent words might dominant the training set.<br/>
→ heuristics to sample less common words via <code>P(c)</code>.p </p>
<p><strong>problem with skip-gram model</strong><br/>
<em>slow speed</em>: to compute <code>p(t|c)</code> with softmax → involves <em>summing up all 10000(vocab_size) logits</em> in denominator of sotmax:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image007.png"/> </p>
<ul>
<li>method 1: using hierachical softmax: split all vocabs into buckets/binary trees — <code>log(|v|)</code> instea of <code>O(|v|)</code><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image008.png"/> </li>
<li>method 2: <em>negative sampling</em>, modify training objective </li>
</ul>
<h3 id="negative-sampling">Negative Sampling</h3>
<p>To simplify the computation of softmax denominator: a different learning problem.<br/>
<strong>new learning problem</strong><br/>
given a pair of word → predict <em>if this pair is a context/target pair</em>. <br/>
— binary classification instead of |v| classes. </p>
<ul>
<li>positive examples: sampled as before (sample context word <code>c</code>, then sample target word <code>t</code> in word window) </li>
<li>negative examples: sample context word <code>c</code>, then <em>pick rand word </em><code>t</code><em> from dictionary</em>. Sample <em>k=5~20</em> negative examples for each context word <code>c</code>. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image010.png"/><br/>
Model: <em>logistic regression</em><br/>
For context word c, there are <em>|v|=10000 potential binary classification problems</em> to train<br/>
→ <em>and we train only (k+1) of them</em>.<br/>
<strong>negative sampling</strong>: trun 10000-way softmax problem into 10000 binary classification problems, and each iteration only train k+1 of them.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image011.png"/><br/>
<strong>How to sampling negative examples</strong> </p>
<ul>
<li>sample according to empirical word frequence P(w) ~= tf(w) → might have a lot stop words sampled </li>
<li>sample uniformly: P(w) = 1/|v| </li>
<li>empirical best-choice: P(w) = tf(w)^0.75 / sum(tf(w')^0.75) </li>
</ul>
<h3 id="glove-word-vectors">GloVe word vectors</h3>
<p>GloVe(Global Vectors for word representation): even simpler than negative sampling.<br/>
previously: sampling skip-grams, i.e. pairs of words (<code>c</code>,<code>t</code>)<br/>
glove: Count appearance of co-occurrence, <code>X_ij = #(i in the context of j)</code>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image012.png"/><br/>
<strong>GloVe Model</strong><br/>
Trying to approximate <code>theta_i*e_j</code> to <code>-logX_ij</code>, by solving <code>theta_i</code> and <code>e_j</code>. </p>
<ul>
<li>add weighting term <code>f(X_ij) = 0</code> if <code>X_ij=0</code>, (0*log0 = 0), and f gives more weight to less frequent words </li>
<li><code>theta_i</code> and <code>e_i</code> are <em>symmetric</em> in optimization ⇒ final embedding <code>e_i = (e_i+theta_i)/2</code> </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image013.png"/> </p>
<p><strong>Featurization view of word embeddings</strong><br/>
Learning embeddings are not guaranteed to align with featurized components in each axis.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image014.png"/> </p>
<h2 id="iii-applications-using-word-embeddings_1">III-Applications using Word Embeddings</h2>
<h3 id="sentiment-classification">Sentiment Classification</h3>
<p>mapping a piece of text into a rating<br/>
<strong>simple model</strong><br/>
sum/average all word embedding vectors as feature vector → pass to softmax clf.<br/>
pb: ignoring all word order </p>
<p><strong>RNN model</strong><br/>
take embedding vectors → sequence embedding matrix → feed to RNN<br/>
→ using last step output and feed to softmax.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image015.png"/> </p>
<h3 id="debiasing-word-embeddings">Debiasing word embeddings</h3>
<p>Eliminate biases in word embeddings, e.g. gender bias, due to biases in training text.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk2/pasted_image016.png"/> </p>
<ul>
<li>Dentify bias direction: e.g. gender bias </li>
</ul>
<p>take differences of vectors: e.g. <code>e_he - e_she</code>, <code>e_male - e_female</code><br/>
→ find bias and non-bias directions </p>
<ul>
<li>Neutralization: project embeddings (of <em>non-definitional words</em>) to non-bias directions </li>
<li>Equalize pairs: for definitional words(e.g. grandmother/grandfather, boy/girl), let them be equally-distant to axis </li>
</ul>
<p>→ How to find defnitional words: train a classifier. </p>
</div>
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目录</h4>
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<div id="toc"><ul><li><a class="toc-href" href="#i-introduction-to-word-embeddings" title="I - Introduction to Word Embeddings">I - Introduction to Word Embeddings</a><ul><li><a class="toc-href" href="#using-word-embeddings" title="Using word embeddings">Using word embeddings</a></li><li><a class="toc-href" href="#properties-of-word-embeddings" title="Properties of word embeddings">Properties of word embeddings</a></li><li><a class="toc-href" href="#embedding-matrix" title="Embedding matrix">Embedding matrix</a></li></ul></li><li><a class="toc-href" href="#ii-learning-word-embeddings-word2vec-glove_1" title="II - Learning Word Embeddings: Word2vec & GloVe">II - Learning Word Embeddings: Word2vec & GloVe</a><ul><li><a class="toc-href" href="#learning-word-embeddings" title="Learning word embeddings">Learning word embeddings</a></li><li><a class="toc-href" href="#word2vec" title="Word2Vec">Word2Vec</a></li><li><a class="toc-href" href="#negative-sampling" title="Negative Sampling">Negative Sampling</a></li><li><a class="toc-href" href="#glove-word-vectors" title="GloVe word vectors">GloVe word vectors</a></li></ul></li><li><a class="toc-href" href="#iii-applications-using-word-embeddings_1" title="III-Applications using Word Embeddings">III-Applications using Word Embeddings</a><ul><li><a class="toc-href" href="#sentiment-classification" title="Sentiment Classification">Sentiment Classification</a></li><li><a class="toc-href" href="#debiasing-word-embeddings" title="Debiasing word embeddings">Debiasing word embeddings</a></li></ul></li></ul></div>
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