# Factored language model

The factored language model (FLM) is an extension of a conventional language model introduced by Jeff Bilmes and Katrin Kirchoff in 2003. In an FLM, each word is viewed as a vector of k factors: ${\displaystyle w_{i}=\{f_{i}^{1},...,f_{i}^{k}\}.}$ An FLM provides the probabilistic model ${\displaystyle P(f|f_{1},...,f_{N})}$ where the prediction of a factor ${\displaystyle f}$ is based on ${\displaystyle N}$ parents ${\displaystyle \{f_{1},...,f_{N}\}}$. For example, if ${\displaystyle w}$ represents a word token and ${\displaystyle t}$ represents a Part of speech tag for English, the expression ${\displaystyle P(w_{i}|w_{i-2},w_{i-1},t_{i-1})}$ gives a model for predicting current word token based on a traditional Ngram model as well as the Part of speech tag of the previous word.