Margin Infused Relaxed Algorithm

This method is used by Watanabe et al., EMNLP 2007 to train an MT system a with a very large number of features of the order of millions. The training step was performed using a specific algorithm called the Margin Infused Relaxed Algorithm (MIRA) proposed by Crammer et al., 2006

Summary

MIRA is an online large-margin training algorithm which updates the weight vector according to certain margin constraints and loss function.

It is used to learn the weights of features after processing each training instance similar to structured perceptron algorithm with an additional loss function and margin constraint in its update rule.

Definition

A general definition of online training algorithms can be written down as follows:

• $\forall t,\quad (f^{t},\mathbf {e} ^{t})\in {\mathcal {T}}$ and a list of $m$ -best oracles ${\mathcal {O}}^{t}$:

A $k$ -best list of candidates is generated by $best_{k}(\cdot )$ using the current weight vector $\mathbf {w} _{i}$. Each training instance $f_{t}$ can have a multiple number of correct outputs or references, $\mathbf {e} ^{t}$, in this case target translations.

• Using the $k$-best list, $m$-best oracle translations ${\mathcal {O}}^{t}$ is updated by $oracle_{m}(\cdot )$ in each iteration.

• New weight vector $\mathbf {w} ^{i+1}$ is computed using the $k$-list ${\mathcal {C}}^{t}$ with respect to the oracle ${\mathcal {O}}^{t}$.

• After $N$ iterations, the algorithm returns an averaged weight vector over $T$ training instances to avoid overfitting.

MIRA

The difference in MIRA lies in the weight update rule which differs from one algorithm to the other.