fasttext原理

 模型的优化目标如下：

其中，$<x_n,y_n>$是一条训练样本，$y_n$是训练目标，$x_n$是normalized bag of features。矩阵参数A是基于word的look-up table，也就是A是词的embedding向量。$Ax_n$矩阵运算的数学意义是将word的embedding向量找到后相加或者取平均，得到hidden向量。矩阵参数B是函数f的参数，函数f是一个多分类问题，所以$f(BAx_n)$是一个多分类的线性函数。优化目标是使的这个多分类问题的似然越大越好。

将优化目标表示为图模型如下：

与Word2Vec的区别：

相似的地方：

1. 图模型结构很像，都是采用embedding向量的形式，得到word的隐向量表达。
2. 都采用很多相似的优化方法，比如使用Hierarchical softmax优化训练和预测中的打分速度。

不同的地方：

1. word2vec是一个无监督算法，而fasttext是一个有监督算法。word2vec的学习目标是skip的word，而fasttext的学习目标是人工标注的分类结果。

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word2vec treats each word in corpus like an atomic entity and generates a vector for each word（word2vec中每个Word对应一个词向量，fasttext中每个Word可以产生多个character字符ngrams，每个ngram对应一个词向量，word的词向量是所有ngrams的词向量的和，需要指定ngrams的长度范围）. Fasttext (which is essentially an extension of word2vec model), treats each word as composed of character ngrams. So the vector for a word is made of the sum of this character n grams. For example the word vector “apple” is a sum of the vectors of the n-grams “<ap”, “app”, ”appl”, ”apple”, ”apple>”, “ppl”, “pple”, ”pple>”, “ple”, ”ple>”, ”le>” (assuming hyperparameters for smallest ngram[minn] is 3 and largest ngram[maxn] is 6). This difference manifests as follows.

1. Generate better word embeddings for rare words ( even if words are rare their character n grams are still shared with other words - hence the embeddings can still be good).
2. Out of vocabulary words（即使不在训练集语料中的Word也能得到词向量） - they can construct the vector for a word from its character n grams even if word doesn't appear in training corpus.
3. From a practical usage standpoint, the choice of hyperparamters for generating fasttext embeddings becomes key：since the training is at character n-gram level, it takes longer to generate fasttext embeddings compared to word2vec - the choice of hyper parameters controlling the minimum and maximum n-gram sizes has a direct bearing on this time.
4. The usage of character embeddings (individual characters as opposed to n-grams) for downstream tasks have recently shown to boost the performance of those tasks compared to using word embeddings like word2vec or Glove.

https://heleifz.github.io/14732610572844.html

https://arxiv.org/pdf/1607.04606v1.pdf

http://www.jianshu.com/p/b7ede4e842f1

https://www.quora.com/What-is-the-main-difference-between-word2vec-and-fastText