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I currently work as an Aerospace Engineer for the Department of Defense for nearly 6 years now, and I have a PhD in Aerospace Engineering from a top-10 university in the United States. I am seriously thinking of doing a 2nd PhD in Computer Science, because I want to eventually own an Algorithmic Energy Trading Firm and need to become an expert in Machine Learning algorithms.

As of now, I am working on a few journal papers to publish and I am not going to have any problems getting strong letters of recommendation from my employer and professors on campus. I ought to be able to get a letter from the Dean of my college as well. So, I am thinking of a second PhD in Computer Science because I really want to immerse myself in Machine Learning and figured a PhD was the way to go.

Question for everyone: Would it be a challenge for me to acquire entrance into a top 5 school in Computer Science for a PhD?

I ought to mention that my PhD research was in Computational Fluid Dynamics, Turbulent Flow and I had to develop my numerical solver and turbulence models in Object-Oriented C++.

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    Question is: do you need a second PhD? There are other ways of becoming an expert in a given field than getting a second PhD… Ways that can be less costly (in financial terms, but not only) – F'x Nov 21 '13 at 8:49
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    I suggest learning some statistics. Bayesian statistics in particular. Take some classes, perhaps? Machine Learning is basically statistics, except CS people are doing it. Doing a second PhD really sounds like overkill in your case. – Faheem Mitha Nov 21 '13 at 10:15
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    Related: academia.stackexchange.com/questions/1836/… – Bravo Nov 21 '13 at 13:06
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    In addition to the objections in the other answers, you should know that some institutions, as a matter of policy, do not award second PhDs (even if the first one was at a different university and in a different field). The University of California is one such. – Nate Eldredge Nov 21 '13 at 14:30
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    Seconding @NateEldredge's point: many places in the U.S. will not consider an applicant who already has a Ph.D. Univ of Minnesota is another, in addition to Univ of California. And, as in other comments and answers, probably the kind of certification that'd provide is mostly irrelevant to you by this point, and the style of education might be inefficient, too, for an experienced, practiced person. – paul garrett Nov 21 '13 at 23:42
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A major part of doing a PhD is learning how to do research and handle working on problems which sit on the edge of what is known. You've done that already. Doing it a second time is unnecessary, expensive and time consuming.

If you've been doing aerospace engineering then you almost certainly have the necessary calculus under your belt already. And if you have a PhD you can teach yourself stuff. Buy a few good textbooks - I recommend "Pattern recognition and Machine Learning" by C.M. Bishop; "Information Theory, Inference and learning Algorithms" by D.J.C. Mackay (this one is free to download on the author's website because he's nice like that). Look up material universities and other insitutions put online - e.g. https://www.coursera.org/course/ml is a free course, whose description sounds like it covers a lot of the necessary basics. A lot of machine learning conferences make their proceedings available for free - ICML and NIPS I think both do this, and the work is good quality.

Start getting up to speed on all this stuff. If it still interests you and you want to go the academic route, go looking for postdoc positions and then try to find a couple of talented people you can form a startup company with.

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    +1. I agree that a second PhD sounds unnecessary in this case. – Faheem Mitha Nov 21 '13 at 10:13
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    I agree that a second PhD is unnecessary in every case. You know how to do research, read papers, write papers, etc. Need some background on a new area? Sure, that's what online courses, books and papers are there for (and stack exchange sites, and so many things). Bureaucrazy, a supervisor and mandatory useless courses would be of no help, that would only be a handicap. – Trylks Nov 21 '13 at 10:35
  • @Trylks, if a "supervisor" is generally of no help, even to a slightly experienced person, the purported "supervisor" is simply incompetent. Not that I necessarily make any claims of competence or not for "supervisors as a class". :) But, srsly, an expert mentor is helpful. – paul garrett Nov 22 '13 at 0:05
  • @paulgarrett maybe my supervisor is incompetent, actually other people have agreed on that, I have also seen worse cases. By being incompetent and not spending much time on a PhD student he is able to have many PhD students at the same time, check the grammar in many papers, publish some of them (because his students don't want to perish), get a nice h-index, projects, etc. Maybe he is perfectly competent at getting good positions in the rankings that should measure how competent researchers are, and only at that. (I continue in the next comment) – Trylks Nov 22 '13 at 10:19
  • To complement your postdoc position, you may be able to find a fellowship that encourages people with previous experience to enter CS. These are fairly common in biology. – adam.r Dec 2 '13 at 16:38
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I received my PhD in Mathematics 40+ years ago and considered getting a second PhD in Computer Science. Spoke to a professor at a University about my plans and the advice he gave me "You have a PhD from an excellent University. Take a sabbatical come here for a year, publish a few papers and join the club". Ultimately I went into the medical instrumentation industry where I have been for the last 31 years and I am now planning to semi retire and start my own business.

My advice to you, why bother with the second PhD. Get more focused on your goal.

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You gain nothing from doing a second PhD in a professional capacity. If you want to do some type of algo trading work the best thing to do is get a job in the algo trading world. Given your background they are likely to hire you.

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I think you should study Machine learning by yourself instead of going for a second PhD, which is a huge task! You can learn a lot about any subject by yourself specially when you already have a PhD that proves you can do research by yourself. There are free online lectures from MIT almost about anything related to AI, including Bayesian inference and machine learning. I don't know what your needs are specifically but I suggest you try to research by yourself first and then decide if you need more.

I will give you a personal experience that may or may not be relevant to you, so don't laugh. It seems your interests are similar to mine if not exactly the same (according to your last paragraph c++,turbulence,CFD..). I presume you frequent CFD-online too? Anyway I recently got a PhD in CFD related engineering field, but before that I was very interested in artificial intelligence. So I have acquired a lot of knowledge about it by myself as to even write a top-10 computer chess program that can beat almost any human. Computer chess is not really AI but there are other games like GO where many machine learning / data mining techniques are used to write the best programs. I have been doing this as a hobby, but anyone can learn anything programming/AI related, and you don't necessarily need a degree in Computer Science even for AI.

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You do not need to be an expert in machine learning to own an Algorithmic Energy Trading Firm. If you had a choice between (i) going as a junior researcher to an existing firm right now, or (ii) spending 3-5 years in a machine learning PhD; well, (i) will take you much faster to your end goal.

It is also not just about machine learning. You also need to be good at signal processing, econometrics, object oriented programming, have great domain knowledge, big data experience, linux programming skills, scientific programming ability (R,Matlab), scripting experience, etc. The best way to get good at all areas at the same time is just to go into a firm right now.

What is most important is research experience. It matters far less what type of research you did (as long as it was heavily quantitative) than the fact that you actually have good research experience.

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