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XGBoost: A Scalable Tree Boosting System

Presented by

Jiang, Cong

Song, Ziwei

Ye, Zhaoshan

Zhang, Wenling

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Recurrent neural networks are a variation of deep neural networks that are capable of storing information about previous hidden states in special memory layers.<ref name=lstm> Hochreiter, Sepp, and Jürgen Schmidhuber. "Long short-term memory." Neural computation 9.8 (1997): 1735-1780. </ref> Unlike feed forward neural networks that take in a single fixed length vector input and output a fixed length vector output, recurrent neural networks can take in a sequence of fixed length vectors as input, because of their ability to store information and maintain a connection between inputs through this memory layer. By comparison, previous inputs would have no impact on current output for feed forward neural networks, whereas they can impact current input in a recurrent neural network. (This paper used the LSTM formulation from Graves<ref name=grave> Graves, Alex. "Generating sequences with recurrent neural networks." arXiv preprint arXiv:1308.0850 (2013). </ref>)

Where [math]\displaystyle{ \,S }[/math] is the base/source sentence, [math]\displaystyle{ \,T }[/math] is the paired translated sentence and [math]\displaystyle{ \,T_r }[/math] is the total training set. This objective function is to maximize the log probability of a correct translation [math]\displaystyle{ \,T }[/math] given the base/source sentence [math]\displaystyle{ \,S }[/math] over the entire training set. Once the training is complete, translations are produced by finding the most likely translation according to LSTM:

[math]\displaystyle{ \hat{T} = \underset{T}{\operatorname{arg\ max}}\ p(T|S) }[/math]

It has been showed that Long Short-Term Memory recurrent neural networks have the ability to generate both discrete and real-valued sequences with complex, long-range structure using next-step prediction <ref name=grave> Reference </ref>.