在RDBMS中SQL的期望最大化
Towards Expectation-Maximization by SQL in RDBMS
摘要：
将机器学习技术集成到RDBMS中是一项重要的任务，因为存在许多需要建模的实际应用（例如，商业智能、战略分析）以及查询RDBMS中的数据。在本文中，我们提供了一个SQL解决方案，有可能支持不同的机器学习建模。作为一个例子，我们研究了如何支持无监督的概率建模，在聚类，密度估计和数据汇总有广泛的应用，并专注于期望最大化（EM）算法，这是一种通用的技术，寻找最大似然估计。用EM训练模型时，需要在while循环中通过一个E步和一个M步迭代地更新模型参数，直到收敛到某个阈值控制的水平或重复一定次数的迭代。为了在RDBMS中支持EM，我们展示了RDBMS中的矩阵/向量表示，支持EM所需的线性代数操作的关系代数操作，关系代数的参数更新，以及while循环的支持。需要注意的是，SQL'99递归不能用于处理这样的while循环，因为M步是非单调的。此外，假设一个模型已经训练的EM算法，我们进一步设计了一个自动的数据库中的模型维护机制，维护模型时，底层的训练数据的变化。我们已经进行了实验研究，并将报告我们的研究结果在本文中。
英文摘要：
Integrating machine learning techniques into RDBMSs is an important task since there are many real applications that require modeling (e.g., business intelligence, strategic analysis) as well as querying data in RDBMSs. In this paper, we provide an SQL solution that has the potential to support different machine learning modelings. As an example, we study how to support unsupervised probabilistic modeling, that has a wide range of applications in clustering, density estimation and data summarization, and focus on Expectation-Maximization (EM) algorithms, which is a general technique for finding maximum likelihood estimators. To train a model by EM, it needs to update the model parameters by an E-step and an M-step in a while-loop iteratively until it converges to a level controled by some threshold or repeats a certain number of iterations. To support EM in RDBMSs, we show our answers to the matrix/vectors representations in RDBMSs, the relational algebra operations to support the linear algebra operations required by EM, parameters update by relational algebra, and the support of a while-loop. It is important to note that the SQL'99 recursion cannot be used to handle such a while-loop since the M-step is non-monotonic. In addition, assume that a model has been trained by an EM algorithm, we further design an automatic in-database model maintenance mechanism to maintain the model when the underlying training data changes.We have conducted experimental studies and will report our findings in this paper.
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