Which AWS service automates the training of machine learning models using built-in algorithms?

Amazon SageMaker is the correct choice because it is specifically designed to facilitate the entire machine learning workflow, from data preparation to model deployment. One of its key features is the ability to automate the training of machine learning models using a variety of built-in algorithms. SageMaker provides a fully managed environment that allows developers and data scientists to quickly build, train, and deploy machine learning models at scale.

The service includes features like SageMaker Autopilot, which automatically selects the best algorithms and tuning settings for your data, thereby streamlining the training process. Additionally, SageMaker's built-in algorithms are optimized for performance, making it easier for users to get started without needing in-depth knowledge of machine learning.

Other services mentioned do not focus on automating machine learning model training specifically. For example, Amazon Glue is primarily a data integration service used for ETL (Extract, Transform, Load) tasks, Amazon Redshift is a data warehousing service for analytics, and Amazon CodeGuru is a developer tool that helps in code reviews and optimizations but does not pertain to machine learning model training.