标题： 估计多层感知器混合模型的成分数量 显示英文标题

标题： Estimating the Number of Components in a Mixture of Multilayer Perceptrons

摘要： 贝叶斯信息准则（BIC）在神经网络社区中被广泛用于模型选择任务，尽管其收敛性质并不总是理论上得到确立。 本文我们将专注于估计多层感知器混合模型中的分量数量，并证明在此框架下BIC准则的收敛性。 Keribin（2000）和Gassiat（2002）分别引入的用于混合模型和隐马尔可夫模型的惩罚边际似然被推广到多层感知器混合模型，为此提出了一种惩罚似然准则。 我们在一些假设下证明了其收敛性，这些假设主要涉及广义得分函数类的括号熵，并通过一些数值例子加以说明。 显示英文摘要

摘要： BIC criterion is widely used by the neural-network community for model selection tasks, although its convergence properties are not always theoretically established. In this paper we will focus on estimating the number of components in a mixture of multilayer perceptrons and proving the convergence of the BIC criterion in this frame. The penalized marginal-likelihood for mixture models and hidden Markov models introduced by Keribin (2000) and, respectively, Gassiat (2002) is extended to mixtures of multilayer perceptrons for which a penalized-likelihood criterion is proposed. We prove its convergence under some hypothesis which involve essentially the bracketing entropy of the generalized score-functions class and illustrate it by some numerical examples.