Which of the following methods can scale Hyperopt with Apache Spark?

Utilizing distributed Hyperopt with single-machine training algorithms using the SparkTrials class is the correct approach to scale Hyperopt with Apache Spark. The SparkTrials class allows users to leverage the distributed computing capabilities of Apache Spark while performing hyperparameter tuning tasks, making it feasible to efficiently search through hyperparameter space across multiple trials concurrently.

This method takes advantage of Spark's ability to manage parallel processing, which is crucial when dealing with large datasets or complex models that require significant computation. By distributing the workload, the trials can be executed across various nodes in the Spark cluster, effectively speeding up the optimization process.

In contrast, using a single-machine Hyperopt with singular algorithms limits the scaling capabilities, as it does not harness the parallel processing power offered by Spark. Running all processes on single machines only would similarly restrict performance and scalability. Additionally, while Hyperopt can be used with various machine learning frameworks, limiting its integration to TensorFlow does not inherently facilitate scaling with Apache Spark effectively. Therefore, utilizing the SparkTrials class is the optimal choice for scaling Hyperopt in a Spark environment.