Enabling Profiling for deployments via the REST API

We have an application which is being deployed via the REST API. Our logging has captured some errors related to memory consumption that we'd like to examine using profiling. All the examples of profiling in Azure that I can find discuss deployment via Visual Studio which is not feasible in this instance.

Is there a way to enable profiling via the REST API and if so are there any examples or documentation for this? We're using Linq2Azure to access the APIs but we can extend it if necessary.

Thanks

Colin