A1419
Title: A comparison of numerical maximum likelihood and noise-contrastive estimation for unnormalized statistical models
Authors: Marco Bee - University of Trento (Italy) [presenting]
Flavio Santi - University of Trento (Italy)
Abstract: Unnormalized statistical models are commonly used in many fields of statistics. However, their maximum likelihood estimation is difficult because the intractable normalizing constant depends on the unknown parameters. One way of proceeding is based on the maximization of an approximation of the likelihood obtained by means of a numerical estimate of the normalizing constant, even though the estimation error caused by the numerical evaluation of the normalizing constant is difficult to quantify. A popular alternative is noise-contrastive estimation (NCE), where a classification algorithm tries to discriminate synthetic and observed data and the normalizing constant is estimated alongside the other parameters of the model. The two approaches outlined above are used in two examples: the estimation of the parameters of the Bingham distribution for directional data on the unit sphere and the estimation of a dynamic mixture for loss data. For NCE, the well-known issue of finding an "optimal" noise distribution is also studied. Numerical maximum likelihood is usually more efficient in terms of root-mean-squared-error, whereas noise-contrastive estimation is faster and less affected by convergence problems.
