On Finishing a PhD in a “Short” Period of Time

I began my PhD program in late August of 2014 and I submitted and defended my PhD dissertation in early May 2018, just shy of four years after I started grad school. Several people have asked me about “fast tracking” a PhD, I decided to write a blog post about it.

First of all, I would be careful not to extrapolate one person’s experience. Different fields vary quite a bit. In some fields, data collection can take two or three years before any analysis is even begun. Meanwhile, in other fields, there is much more required coursework (I believe this is the case for some humanities fields where fluency in a foreign language is required), so four years may not be a feasible period of time to finish in some fields. It may not even be always advisable to graduate in four years. If staying a fifth year can yield several more first-author papers and better position a student to be competitive in the job market, then it may be an excellent idea to take the extra year of funding and to produce more work.  In my case, I spoke with my advisor, and he agreed that I would be better off doing a postdoc than staying for another year.

Moreover, I was lucky that I did not have any life circumstances, existential life crises, etc. that would have derailed me in my quest to earn a PhD. Finally, there aren’t really extra “brownie points” given for graduating sooner. If you manage to finish your degree in five to six years, you’re actually doing amazing and you should be very proud of yourself for graduating on time (5-6 years is normal for a lot of STEM fields).

So I do not want to suggest that my personal experience can be replicated exactly. But I hope that this post will be enlightening and provide some insight as to how I personally stayed focused throughout my PhD studies. Some people have suggested that in order to finish sooner, one needs to start research from day one. For my particular program, this was not possible, since I had to take two years of courses and pass two written exams in my first two years. But what ultimately helped me finish faster was what I will describe below.

First, I kept my eye on the main task, which was: to write at least two papers where I: a) introduced new statistical methods that nobody else had done before, and b) proved several new theorems that nobody else knows. It is important to work hard in your classes so you can learn the material to pass the qualifying exams. But after the qualifying exams, nobody really cares about classes or grades. In order to graduate with a PhD, it’s not the coursework that will get you across the finish line, but rather: demonstrable evidence that you can contribute new knowledge to your field and that the research you have done is of publishable quality.

From the minute I began my research, I assumed full responsibility for this main task. My advisor is quite a brilliant guy, and he helped point me in the right direction by suggesting research topics, giving me a few “seminal” papers to read, and discussing these papers. However, I went above and beyond and ended up reading much more than he suggested. A lot of these papers, I read line-by-line. I realized that I had to teach myself a lot of new things and that even a very smart guy like my advisor didn’t know a lot of the answers (hence, why it was a research project). It was up to me to really tackle the problems at hand.

Since I adopted this attitude, I can confidently say that my PhD research was mostly my own ideas and my own work. I initially began by trying to extend some work that my advisor’s previous students had done. Some of this work fell within the area of linear regression models. However, it turned out that none of his former students had worked on regression problems where the number of covariates grows much faster than sample size. So how could I extend it to this new framework? From this moment, I realized that if I wanted to break new ground for very high-dimensional problems, I had to try to figure out the solutions myself. I could then discuss my ideas with my advisor and work under my advisor’s supervision to continually refine my ideas until they were correct and technically sound.

Second, not being afraid to ask questions, even when they may be “embarrassing,” was also instrumental to my ability to complete my PhD in a timely manner. In the beginning, I often asked my advisor to clarify technical details in papers that I didn’t understand (even if the questions were “dumb” and I immediately had the “a-ha!” moment the second that he pointed out the “trick”). I asked my fellow PhD students for help with things like high-performance computing, coding, and how they might approach problems (e.g. if they were aware of any useful inequalities or bounds). If you don’t know something, you can try to slog your way through it, and I definitely think that you should do that first. But if you still can’t figure it out, then it behooves you to just ask your advisor or your peers for help.

For me, it was also a matter of finding the “right” open problems, which meant: finding problems that were not adequately addressed in the literature, but that were still manageable. To do this, I started by first trying to obtain a high-level understanding of similar work that had been done in the literature. I read review articles of historical and recent developments, I skimmed though Beamer presentations and lecture slides that I had googled, and I read the “seminal” papers on my research projects to identify open problems. Once I found open problems that seemed “doable,” I narrowed my focus on a couple of papers and tried to extend the results in these papers. Although my final thesis cites about 60 papers, I would say that only ten of them were absolutely critical, since my projects mainly built upon the work that was done in these few papers. I read these papers front and back maybe 4-5 times and worked to extend their results.

Another thing which helped me a lot was to keep a consistent schedule and to put forth 5-7 hours of honest effort five to six days a week (and by this, I mean hours of work as free of distractions like social media or television as possible) and to be persistent even in the face of “failure.” Some of my initial ideas and projects I started working on were immediate dead-ends, so I had to cut my losses and abandon them. Most weeks, I didn’t really have anything totally new. Some days, I just spent time rereading a paper, while other days, I just wrote computer code.

In the end, my PhD projects produced three major new methods for high-dimensional statistics and 13 brand new theorems in total. But the inspiration for these novel discoveries only came to me in spurts here and there. The vast majority of my time was spent reading and rereading and trying to understand papers, scribbling down notes, playing around with different formulas, struggling through computer code, writing and rewriting multiple revisions of my manuscripts (each of my three papers went through about 8-10 revisions before we deemed it acceptable for submission), and trying different techniques to see if something would “click.” Most of the time, the techniques that I tried didn’t work. In fact, for one of my papers, the main theorem had a technical error that took me and my advisor over two months to resolve! For some of my computer simulations, I encountered bugs or errors that took me several weeks to fix.

So in short, the 5-7 hours of “honest” effort does not necessarily need to include making very significant progress. I often still felt very stuck on what I was doing even after expending all this effort. But that is totally okay! Even if you do not take very “significant” steps forward, believe that these 5-7 hours should be otherwise productive in some way, and they should reflect incremental progress. i.e. did you fix a small bug in your code? Did you understand the proof of a theorem?  Did you move closer towards proving a lemma or a new proposition? Did you revise part of a paper you had written so that it was clearer and/or better organized? Even when I was very frustrated, I never gave up. I just pushed through it.

The reality is that in academic research, you just have to muddle your way through a lot of things, shoot in the dark, and resort to trial-and-error. This is true even in very formal subjects like pure mathematics, theoretical computer science, or theoretical physics. Though the end results are some very beautiful theorems and theories that are mathematically sound, the actual process of arriving at these new results is not so straightforward. The path towards scientific discovery is often jagged and most likely riddled with failures and frustrations along the way. But that’s just what you have to do to break new ground.

So to those who are working on your PhD: be persistent and don’t give up!

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