Kernel-based non-parametric Bayesian clustering models

基于核的非参数贝叶斯聚类模型

• 批准号: 327689-2013
• 负责人: Murua, Alejandro
• 金额: $ 1.38万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572102
• 关键词: Kernel; based; non; parametric; Bayesian

This proposal is based on the belief that the key to the success of modeling complex data structures lies in the embedding of kernel-based or kernel-induced methods within Bayesian non-parametric models. The Bayesian paradigm gives a rich framework for modeling structural data constraints, whereas kernel-based methods incorporates flexibility (e.g. local, spatial and/or temporal adaptation). Two main ingredients proposed are the introduction of locally adaptive kernels, and the use of discrete Gibbs random fields (such as the auto-logistic and Potts models) and determinantal point processes as priors or penalization for the unknown clustering data structure in classification and regression models. We can show that the adaptive kernels are linked to kernel density and regression estimators. Consequently, the theory developed for these estimators can be adapted to more complex learning algorithms. Discrete Gibbs random fields offer an interesting alternative to the commonly used Dirichlet process priors. Their clusters are linked to data graphs. Therefore, the rich theory developed for discrete graphs may be used to guide the choice of parameters and their estimation. Determinantal point processes offer another alternative to guide the discovery of clusters. Computational techniques such as the Wang-Landau algorithm will be extended to our models in an efficient way. For example, in some cases, multi-dimensional parameter dependent quantities may be factorized in lower-dimensional parameter quantities so as to reduced the complexity of the stochastic sampling algorithms. Bayesian variational techniques, such as the mean-field approximation, will be developed explicitly to address the computational needs of our models. Indeed, for the particular case of the Potts model, several other better approximating variational techniques have been suggested in the Physics literature. We will study, adapt and extend these techniques to more complex models for clustering for classification and regression.

这个建议是基于这样一种信念，即复杂数据结构建模成功的关键在于在贝叶斯非参数模型中嵌入基于核或核诱导的方法。贝叶斯范式为结构数据约束建模提供了丰富的框架，而基于核的方法具有灵活性（例如局部，空间和/或时间适应）。提出的两个主要成分是引入局部自适应内核，并使用离散吉布斯随机场（如自逻辑和波茨模型）和行列式点过程作为先验或惩罚的未知聚类数据结构的分类和回归模型。我们可以证明自适应核与核密度和回归估计有关。因此，为这些估计器开发的理论可以适用于更复杂的学习算法。离散吉布斯随机场提供了一个有趣的替代常用的狄利克雷过程先验。它们的聚类与数据图相关联。因此，离散图的丰富理论可以用来指导参数的选择和估计。行列式点过程提供了另一种选择来指导集群的发现。 计算技术，如Wang-Landau算法将以有效的方式扩展到我们的模型。例如，在某些情况下，多维参数相关量可以被分解为低维参数量，以便降低随机采样算法的复杂度。贝叶斯变分技术，如平均场近似，将明确开发，以解决我们的模型的计算需求。事实上，对于波茨模型的特殊情况，物理学文献中已经提出了其他几种更好的近似变分技术。我们将研究，调整和扩展这些技术，以更复杂的模型进行聚类分类和回归。