NCE Loss

原文链接：https://stats.stackexchange.com/questions/244616/how-sampling-works-in-word2vec-can-someone-please-make-me-understand-nce-and-ne/245452#245452

语言模型要根据之前出现的单词预测下一次出现的单词，单词数量很多，如果用softmax则每个单词需要对应一个隐含层节点，参数过多，计算开销太大；

NCE loss将所有单词分为两类，正例和负例，word2vec中只需给出上下文和相关的正例，tf.nn.nce_loss()中会自动生成负例。

There are some issues with learning the word vectors using an "standard" neural network. In this way, the word vectors are learned while the network learns to predict thenext word given awindow of words (the input of the network).

Predicting the next word is like predicting the class. That is, such a network is just a "standard" multinomial (multi-class) classifier. And this network must have as many output neurons as classes there are. When classes are actual words, the number of neurons is, well, huge.

A "standard" neural network is usually trained with a cross-entropy cost function which requires the values of the output neurons to represent probabilities - which means that the output "scores" computed by the network for each class have to be normalized, converted into actual probabilities for each class. This normalization step is achieved by means of the softmax function. Softmax is very costly when applied to a huge output layer.

The (a) solution

In order to deal with this issue, that is, the expensive computation of the softmax, Word2Vec uses a technique callednoise-contrastive estimation. This technique was introduced by [A] (reformulated by [B]) then used in [C], [D], [E] to learn word embeddings from unlabelled natural language text.

The basic idea is to convert a multinomial classification problem (as it is the problem of predicting thenext word)to a binary classification problem. That is, instead of using softmax to estimate a true probability distribution of the output word, a binary logistic regression (binary classification) is used instead.

For each training sample, the enhanced (optimized) classifier is fed a true pair (a center word and another word that appears in its context) and a number of kkrandomly corrupted pairs (consisting of the center word and a randomly chosen word from the vocabulary). By learning to distinguish the true pairs from corrupted ones, the classifier will ultimately learn the word vectors.

This is important: instead of predicting the next word (the "standard" training technique), the optimized classifier simply predicts whether a pair of words isgood orbad.

Word2Vec slightly customizes the process and calls itnegative sampling. In Word2Vec, the words for the negative samples (used for the corrupted pairs) are drawn from a specially designed distribution, which favours less frequent words to be drawn more often.

References

[A] (2005) - Contrastive estimation: Training log-linear models on unlabeled data

[B] (2010) - Noise-contrastive estimation: A new estimation principle for unnormalized statistical models

[C] (2008) - A unified architecture for natural language processing: Deep neural networks with multitask learning

[D] (2012) - A fast and simple algorithm for training neural probabilistic language models.

[E] (2013) - Learning word embeddings efficiently with noise-contrastive estimation.