Algorithms for Matrix Estimation

矩阵估计算法

• 批准号: 2436329
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2436329
• 关键词: Algorithms; Matrix; Estimation

There are many real-world applications in which predictions have to be made based on observed or measured data. In most cases, the measured data can be represented as a large m x n matrix Z with several missing entries and the problem becomes "completing" this matrix based on the observed entries. One such case of this matrix estimation problem is recommender systems, where items are recommended to users based on partial knowledge of their past preferences.Generally, this can be done by applying a low-rank factor model. A low-rank prediction of the original matrix can be obtained as the product of two factor matrices.Within the research area of digital signal processing, the goal of matrix estimation is to investigate the most effective ways of achieving this low-rank representation of the matrix factors and recover the missing entries with the lowest possible error.Having studied matrix estimation during my Part IIB Project in Cambridge, I have understood the principles behind matrix estimation but become aware of the mathematical depth of the technique and the broad range of possibilities associated with it. Matrix estimation has the potential to be useful in many real-world applications, as all it needs is associations between two entities, from biomedical research (gene-disease) to movie recommender systems (user-film associations).In these real-world applications, there is often previous knowledge of the data (side information) available which can be used to significantly improve accuracy as well as reducing complexity. During my PhD, I would like to develop matrix completion algorithms tailored to use different kinds of side information about the factors.

在许多实际应用中，预测必须基于观察到的或测量到的数据。在大多数情况下，测量的数据可以表示为一个大的mXn矩阵Z，其中有几个缺失的条目，问题变成了基于观察到的条目来“完成”这个矩阵。这种矩阵估计问题的一个例子是推荐系统，在推荐系统中，项目是基于用户过去偏好的部分知识推荐给用户的。通常，这可以通过应用低秩因子模型来完成。原始矩阵的低秩预测可以作为两个因子矩阵的乘积获得。在数字信号处理的研究领域中，矩阵估计的目标是研究实现矩阵因子的低秩表示的最有效方法，并以尽可能低的误差恢复丢失的项。在剑桥的Part IIB项目期间研究了矩阵估计，我已经理解了矩阵估计背后的原理，但也意识到了该技术的数学深度和与之相关的广泛可能性。矩阵估计在许多现实世界的应用中都有潜力，因为它所需要的只是两个实体之间的关联，从生物医学研究（基因疾病）到电影推荐系统（用户-电影关联）。在这些现实世界的应用中，通常存在可用的数据的先前知识（辅助信息），其可用于显著地提高准确性以及降低复杂性。在我的博士学位期间，我想开发矩阵补全算法，以使用关于因子的不同类型的辅助信息。