Machine learning as a service (MLaaS) is an umbrella definition of various cloud-based platforms that cover most infrastructure issues such as data pre-processing, model training, and model evaluation, with further prediction. Prediction results can be bridged with your internal IT infrastructure through REST APIs.
Amazon Machine Learning services, Azure Machine Learning, Google Cloud AI, and IBM Watson are four leading cloud MLaaS services that allow for fast model training and deployment. These should be considered first if you assemble a homegrown data science team out of available software engineers. Have a look at our data science team structures story to have a better idea of roles distribution.
Within this article, research firm Topbots first gives an overview of the main machine-learning-as-a-service platforms by Amazon, Google, Microsoft, and IBM, and follow it by comparing machine learning APIs that these vendors support.