First, an annoyance. To be able to deploy Data Science virtual machines in Azure programmatically you first have to login to the portal and click some buttons.
In the Portal click new and then marketplace and then search for data science. Choose the Windows Data Science Machine and under the blue Create button you will see a link which says “Want to deploy programmatically? Get started” Clicking this will lead to the following blade.
Click through for a screenshot-laden explanation which leaves you with a working VM in Azure.