Sounds like data science for you. But I'm curious: What is your academic background exactly? Where are you learning machine learning without programming?
Sorry for the confusion - it's not that I'm learning machine learning without programming, but rather that most of the programming I know I learned in the context of machine learning. In particular, I'm only familiar with the small portion of the standard undergrad cs curriculum that's relevant to those things.
Okay then, data science is probably a better fit over generic software engineering.
As you surmised, the latter is more focused on algorithms and data structures as the basis for solving problems. Your gut response is good. Go with your gut.
Well, given that I made a statement about machine learning and not data science, the point still stands.
Machine learning is a CS field. It emerged out of CS. Any claims to the contrary are hokey revisionism. As to what "data science" entails, that's become a super loaded buzzword, so I'm not even sure where to begin. And "data engineering," please don't even. Just fancy terms for statistics and discrete math.
I define data engineering as something like "implementing ML algorithms on servers for real-world use cases", in which case they're mostly just gluing together function calls that other people figured out. "Data science" on the other hand is the stuff that actually requires using statistics and math to figure out what operations are necessary on a data set.
Plus, I could say the same thing about ML. It's just graph theory, linear algebra and calculus with some statistics mixed in. Where's the absolutely necessary programming? There are plenty of opportunities to do ML theory with little programming, if any. There absolutely needs to be a distinction between theorists and engineers, because they aren't the same thing. Most of the programming is the grunt work you pass off to the engineers.