If this is a course you're interested in, here's what I suggest.

1) Read up on AI breadth first and shallowly. Focus more on machine learning, search, filtering, and so forth, than heavier (and less successful) topics such as knowledge systems and computer vision.

2) Go through a list of startups that you like, use, or admire. Imagine the simplest cool/good/useful thing the startup could do with a cute little algorithm.

3) Develop the basic idea for it, contact the company, say you'd like to hack on it for cheap.

4) Kill the problem.

5) Use that startup as a reference. Find another one, but this time, ask that you can publish the method.

6) Repeat. Blog about your conquests. Explain how to replicate and extend your results. Eventually, focus on a bigger project to tackle. If your interests align with a research program at a university, consider entering the PhD program then. With this behind you, you'll probably get in anywhere.

If you're interested, I can give you some pointers on the development of quick and useful recommendation engines, which practically every startup can use. If you'd like, send me an email at daniellefong@daniellefong.com

See this line from your autobiography?

Entered pure-math grad program in fall 2005. Passed quals but did poorly in courses. Left after 1 year (no degree) to work on Wall Street...

You're right to think that grad schools might look at this and say "hmmm". Sometimes past behavior does predict future results: You will have one eye on the door throughout your graduate career.

(Although some grad school, somewhere, will admit you anyway -- there's not a lot to lose; they get a very smart and cheap TA for 1 to N years. So you should be as sure as you can before you start school that you have found an adviser worth having who will take you on, so that you don't end up wandering around campus post-quals with a "will write thesis for food" sign.)

Whatever you do, don't tell them up-front that you're uninterested in academia. To an academic, that's like saying "I have no self-confidence and I'm going to quit under pressure" -- because precious few of them accept, deep in their hearts, that quitting academia is a meaningful career choice. You don't need to go into detail about your imaginary academic plans, but do make some vague noises about the possibility. Talk about how your brief excursion into the working world served to remind you of how much you prefer really meaningful, advanced research problems that could change the whole game. They'll eat that up.

But to heck with what other people think about your resume. Let's consider what you should be thinking: You've been to grad school, you obviously didn't like it much the first time, but now it looks really good compared to life on Wall Street. My take on this is that perhaps you need to try door number three: You ought to get out of Wall Street, a land of credentialists in suits, and try another job or two before you try grad school. Because

I'm interested in AI/machine learning research, which practically require a PhD, even in industry.

sounds frighteningly like the kind of thing I would have said before I started grad school. You know, back when I was really used to jumping through hoops. I had a really awesome track record at hoop-jumping -- big GPA, big GREs, NSF Fellowship, etc, etc. -- and, whenever I got confused about my future, I would just look around the arena until I found another hoop!

Try something else for a while. At this point, the Ph.D. program will wait for you. Take your future out for some casual dates before you marry it. If nothing else, why not start with an M.S. degree? Two years will give you plenty of time to network with folks in your new field.

Your stats look fine for applying to CS PhD. Top 5 is probably a long shot (but it always is). But, they love math backgrounds. The only problem is no publications. Top tier CS schools virtually require a strong research background.

1. It's probably going to hurt more than help, to be honest. Even though EE and CS and the like -do- have industrial applications, the people who are reading your application chose to stay in academia. That means they don't necessarily look kindly on people diminishing that. My suggestion say "financial obligations" and leave it at that. The key is to seem really really really really excited about CS and that's why you are applying.

2. This is a serious longshot.

3. AI research groups will care alot more about your research than the school. And yes, top tier schools will tend to have smarter people and therefore better co-founders. Any "decent" school though will have plenty of smart people.

4. The money is there at any CS school so you'll more then likely go to school for free and work on funded research projects. The career possibilities are as good as they get with any PhD.

My experience is that top departments, and fellowships like NSF, basically want people who are already grad students. Actually, NSF seems to have more to do with the merits of the research problem than the student, per se. I don't think I have a shot without enough research experience to have a rough idea of what "my problem" will be.

More to the point: the competition is at such a high level that the outcome rests on things that are far more subjective than you might like. For example, volunteer experience and educational outreach can be decisive factors when all the candidates are equally good on paper.

"Applying to Ph.D. Programs in Computer Science", by Mor Harchol-Balter ( http://www.cs.cmu.edu/~harchol/gradschooltalk.pdf )

It's quite good. Since you have been in grad school already, many of the things won't be news to you.

I would say that the fact that you left grad school for a Wall Street job will hurt your application. The admissions committee might think that you're not determined and self-motivated enough for grad school. They might think "If this dude likes CS so much, why didn't he jump to the CS department back then?". Might be a good idea to explain in your statement of purpose that you discovered your passion for CS while in Wall Street.

Now for picking a grad school a lot of things are really important. 1) Will they fund you? 2) Are they teaching what you want to learn? 3) Is it a happy place?

Don't want to start a fight here- but schools vary by A LOT on these criteria.

As you leave school and prepare to enter industry or academia, my experience has generally been that the strength of the recommendations backing you matters far more than whatever rank your institution may have.

As you mentioned AI/machine learning, I believe these factors are even more important. There are some very distinct schools of thought when it comes to those things, so make sure you look for philosophical compatibility when picking programs. AI has a few deep schisms and widely separated sub-fields, so tread carefully.

It may be worth it to consider some of these: What's your philosophy of mind? Symbolic/statistical/neural? How important is biology/neuroscience when looking at artificial intelligence? What general approach to AI/machine learning most interests you?

Make your own path.

#2. I received an NSF fellowship in grad school with 6 months of research experience. The experience probably helped, but getting an NSF is a long shot no matter what. I know of other students with similar qualifications who didn't get it.

#3. The prestige of your grad school matters in some circles but not in others. If there are particular companies that you want to work for, try to find out what their hiring practice is. Some companies place a high value on the school you graduated from, and some don't care at all.

The upside is that you'll have lots of free time during a PhD curriculum to chase down your own ideas, and find the handful of like-minded people around campus. A PhD is a free time to pursue your own intellectual pursuit, and if you're already so energized, you'll do well.