Fast Maximum Likelihood Estimation and Supervised Classification for the Beta-Liouville Multinomial
The multinomial and related distributions have long been used to model categorical, count-based data in fields ranging from bioinformatics to natural language processing. Commonly utilized variants include the standard multinomial and the Dirichlet multinomial distributions due to their computational efficiency and straightforward parameter estimation process. However, these distributions make strict assumptions about the mean, variance, and covariance between the categorical features being modeled. If these assumptions are not met by the data, it may result in poor parameter estimates and loss in accuracy for downstream applications like classification. Here, we explore efficient parameter estimation and supervised classification methods using an alternative distribution, called the Beta-Liouville multinomial, which relaxes some of the multinomial assumptions. We show that the Beta-Liouville multinomial is comparable in efficiency to the Dirichlet multinomial for Newton-Raphson maximum likelihood estimation, and that its performance on simulated data matches or exceeds that of the multinomial and Dirichlet multinomial distributions. Finally, we demonstrate that the Beta-Liouville multinomial outperforms the multinomial and Dirichlet multinomial on two out of four gold standard datasets, supporting its use in modeling data with low to medium class overlap in a supervised classification context.
Code (0)
등록된 구현이 없습니다.
Tasks
ClassificationComputational EfficiencyGeneral Classificationparameter estimationSimilar Papers 제목 키워드 기반
Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods
In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood func…
parameter estimationUncertainty QuantificationA generalized linear joint trained framework for semi-supervised learning of sparse features
The elastic-net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its nice properti…
Comparison of Maximum Likelihood Classification Before and After Applying Weierstrass Transform
The aim of this paper is to use Maximum Likelihood (ML) Classification on multispectral data by means of qualitative and quantitative approaches. Maximum Likelihood is a supervised classification algorithm which is based…
Composite Likelihood Estimation for Restricted Boltzmann machines
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximu…
GAN-EM: GAN based EM learning framework
Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural im…
ClusteringDimensionality ReductionGeneral ClassificationImage Clustering