1. A system, comprising: one or more computing devices configured to: receive, via a particular programmatic interface of a set of programmatic interfaces implemented at a network-accessible machine learning service of a provider network, a first request from a client to perform a particular operation associated with an instance of an entity type, wherein the entity type comprises one or more of: (a) a data source to be used for a machine learning model, (b) a set of statistics to be computed from a particular data source, (c) a set of feature processing transformation operations to be performed on a specified data set, (d) a machine learning model employing a selected algorithm, (e) an alias associated with a machine learning model, or (f) a result of a particular machine learning model; insert a job object corresponding to the first request in a job queue of the machine learning service; provide an indication to the client that the first request has been accepted for execution; determine, in accordance with a first workload distribution strategy identified for the first request, a first set of provider network resources to be used to perform the particular operation; receive, prior to a completion of the particular operation indicated in the first request, a second request from the client to perform a second operation dependent on a result of the particular operation; insert a second job object corresponding to the second request in the job queue, wherein the second job object includes an indication of a dependency of the second operation on a result of the particular operation; prior to initiating execution of the second operation, provide a second indication to the client that the second request has been accepted for execution; and in response to a determination that the particular operation has been completed successfully, schedule the second operation on a second set of provider network resources.