## A bayesian interpretation of interpolated kneserney (2006)

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@TECHREPORT{Teh06abayesian,

author = {Yee Whye Teh},

title = {A bayesian interpretation of interpolated kneserney},

institution = {},

year = {2006}

}

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### Abstract

Interpolated Kneser-Ney is one of the best smoothing methods for n-gram language models. Previous explanations for its superiority have been based on intuitive and empirical justifications of specific properties of the method. We propose a novel interpretation of interpolated Kneser-Ney as approximate inference in a hierarchical Bayesian model consisting of Pitman-Yor processes. As opposed to past explanations, our interpretation can recover exactly the formulation of interpolated Kneser-Ney, and performs better than interpolated Kneser-Ney when a better inference procedure is used. 1

### Citations

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Citation Context ...ial priors. We will give a new interpretation of interpolated Kneser-Ney as an approximate inference method in a Bayesian model. The model we propose is a straightforward hierarchical Bayesian model (=-=Gelman et al. 1995-=-), where each hidden variable represents the distribution over next words given a particular context. These variables are related hierarchically such that the prior mean of a hidden variable correspon... |

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Citation Context ...essing and language modelling given the probabilistic nature of most approaches. Maximum-entropy models have found many uses relating features of inputs to distributions over outputs (Rosenfeld 1994; =-=Berger et al. 1996-=-; McCallum et al. 2000; Lafferty et al. 2001). Use of priors is widespread and a number of studies have been conducted comparing different types of priors (Brand 1999; Chen and Rosenfeld 2000; Goodman... |

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Citation Context ...ng arrangement and over all trigrams that occurred c times in the full training set. The last entry is averaged over all trigrams that occurred at least 50 times. cross-entropy on the validation set (=-=Chen and Goodman 1998-=-). At the optimal values, we folded the validation set into the training set to obtain the final trigram probability estimates. For the hierarchical Pitman-Yor language model we inferred the posterior... |

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Citation Context ... namely interpolated Kneser-Ney, is a great approximation to a Bayesian model. The hierarchical Pitman-Yor process is a natural generalization of the recently proposed hierarchical Dirichlet process (=-=Teh et al. 2006-=-). The hierarchical Dirichlet process was proposed to solve a clustering problem instead and it is interesting to note that such a direct generalization leads us to a well-established solution for a d... |

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Citation Context ...modelling given the probabilistic nature of most approaches. Maximum-entropy models have found many uses relating features of inputs to distributions over outputs (Rosenfeld 1994; Berger et al. 1996; =-=McCallum et al. 2000-=-; Lafferty et al. 2001). Use of priors is widespread and a number of studies have been conducted comparing different types of priors (Brand 1999; Chen and Rosenfeld 2000; Goodman 2004). Even hierarchi... |

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Citation Context ...and d control the amount of variability around the base distribution G0. An explicit construction of draws G1 ∼ PY(d,θ,G0) from a Pitman-Yor process is given by the stick-breaking construction 4 (7)s(=-=Sethuraman 1994-=-; Ishwaran and James 2001). This construction shows that G1 is a weighted sum of an infinite sequence of point masses (with probability one). Let V1,V2,... and φ1,φ2,... be two sequence of independent... |

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Citation Context ...ed according to a well-studied nonparametric generalization of the Dirichlet distribution variously known as the twoparameter Poisson-Dirichlet process or the Pitman-Yor process (Pitman and Yor 1997; =-=Ishwaran and James 2001-=-; Pitman 2002) (in this paper we shall refer to this as the Pitman-Yor process for succinctness). As we shall show in this paper, this hierarchical structure corresponds exactly to the technique of in... |

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Citation Context ... outputs (Rosenfeld 1994; Berger et al. 1996; McCallum et al. 2000; Lafferty et al. 2001). Use of priors is widespread and a number of studies have been conducted comparing different types of priors (=-=Brand 1999-=-; Chen and Rosenfeld 2000; Goodman 2004). Even hierarchical Bayesian models have been applied to language modelling—MacKay and Peto (1994) have proposed one based on Dirichlet distributions. Our model... |

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Citation Context ...l. 1996; McCallum et al. 2000; Lafferty et al. 2001). Use of priors is widespread and a number of studies have been conducted comparing different types of priors (Brand 1999; Chen and Rosenfeld 2000; =-=Goodman 2004-=-). Even hierarchical Bayesian models have been applied to language modelling—MacKay and Peto (1994) have proposed one based on Dirichlet distributions. Our model is a natural generalization of this mo... |

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Citation Context ...obabilistic nature of most approaches. Maximum-entropy models have found many uses relating features of inputs to distributions over outputs (Rosenfeld 1994; Berger et al. 1996; McCallum et al. 2000; =-=Lafferty et al. 2001-=-). Use of priors is widespread and a number of studies have been conducted comparing different types of priors (Brand 1999; Chen and Rosenfeld 2000; Goodman 2004). Even hierarchical Bayesian models ha... |

1 | a model for words have been used in, e.g. Vinciarelli et al - Such - 2004 |

1 | Two decades of statistical language modeling: Where do we go from here - unknown authors - 2000 |