(I posted this in a few different places, so apologies if you've seen it somewhere else)
I'm a software engineer looking to go back to school and get a phd in computer science with a focus on machine learning. I have a BS in a non-CS engineering field and an MS in applied math (where I took a lot of CS classes), both from top 5 institutions in their respective fields. After graduating from my MS ten years ago, I've worked at two startups as a software engineer / manager. The first startup got sold to a large company and the second (current) startup has been gaining traction and I'm now at the VP level managing a pretty sizable team.
I do enjoy my job, but I don't love management and I've been intellectually curious about machine learning for a while now, doing a lot of self-teaching on nights / weekends. Originally, it was just to keep up with the current research and see if anything was applicable for work, but as I dug deeper I've found a few areas that I'm very interested in doing further research. I've also saved up enough money that I can afford a grad school salary for a few years and still support my family.
Unfortunately, outside of my self-study, I've only worked tangentially with machine learning (mostly using existing libraries and services). I had taken some related classes during my MS, but that was ten years ago. I also don't have any research experience in the field, although I did do some undergrad research during my BS -- unfortunately, no publications and in an unrelated field. Plus it was over 10 years ago.
I had a few questions I was hoping to get some guidance on:
I'm looking to apply for Fall 2019 admission, so I have some time between now and the end of the year to strengthen my profile. Assuming I keep my current job (so I only have nights and weekends free), what are the best things I can do at this point? I had a few projects in mind, but would these help my admission chances?
I think I can get strong recommendations from my managers at the companies I worked for. They're at the CTO level and well respected in industry, but probably not in academia. I think it'll be a bit of a stretch asking my MS professors since it was so long ago, and they probably won't be able to write anything meaningful at this point. A third option I was thinking about is asking the same professors I got recommendations from when I first applied to my MS -- they knew me well at the time and wrote strong recommendations, so hopefully they still have those LoRs around. Which one of these options would look best to the admissions committee?
Assuming I can do well on my GRE and my grades are decent (3.9+ both BS and MS), where should I be aiming? I understand the lack of research experience is a huge negative. Should I consider applying to any MS programs with the intention of doing some research and getting stronger LoRs, and then reapplying to phds afterwards?