On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis
- 作者：Keisuke Yamazaki ; k-yam@math.dis.titech.ac.jp
- 关键词：Sequential data model ; Feature selection ; Bayes learning ; Algebraic geometry
- 刊名：Neural Networks
- 出版年：2012
- 期刊代码：94_08936080
- 类别：cp
- 出版时间：July, 2012
- 卷：31
- 期：Complete
- 页码：73-80
- 文件大小：376 K
摘要
Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models.