In this article, we define a new boosting-type algorithm for multiplicative model combination using as loss function the Hyvärinen scoring rule. In particular, we focus on density estimation problems and the aim is to define a suitable estimator, using a multiplicative combination of elementary density functions, which correspond to simplified or partially specified probability models for the interest random phenomenon. The boosting algorithm provides a simple sequential procedure for updating the weights of the component density functions, until an optimality criterion is satisfied. An extension of this procedure can be useful for composite likelihood inference, in order to specify the weights of the component likelihood objects and, simultaneously, implement parameter estimation. Finally, three applications are presented. The first one regards prediction and inference for autoregressive models, the second one is the use of model pools for prediction in a time series framework, and the third one is the estimation of the covariance and the precision matrices of a multivariate Gaussian distribution. Empirical results on real-world financial data are presented in challenging contexts, where we have to deal with a large dataset or with sparse matrices and a large number of unknown parameters.

中文翻译：

---

提升乘法模型组合

在本文中，我们使用 Hyvärinen 评分规则作为损失函数为乘法模型组合定义了一种新的 boosting 类型算法。特别是，我们关注密度估计问题，目的是定义一个合适的估计器，使用基本密度函数的乘法组合，对应于兴趣随机现象的简化或部分指定的概率模型。提升算法提供了一个简单的顺序程序来更新分量密度函数的权重，直到满足最优性标准。此过程的扩展可用于复合似然推理，以便指定分量似然对象的权重，同时实现参数估计。最后，介绍了三个应用程序。第一个是关于自回归模型的预测和推理，第二个是在时间序列框架中使用模型池进行预测，第三个是多元高斯分布的协方差和精度矩阵的估计。现实世界金融数据的实证结果在具有挑战性的环境中呈现，我们必须处理大型数据集或稀疏矩阵和大量未知参数。