I recently posted a link to an article on mental health in graduate school on Facebook (via a grad school friend of mine), and it sparked a fair bit of discussion there. The article is worth reading, and I am sure will echo with many of the readers. The discussion veered towards particularities of graduate school pressures in STEM, and the contributing factors to mental stress that are driven by funding structures and the advisor/student relationship. The starting point comes from this part of the article:
In this advisor-advisee arrangement, the student trades her labor as a researcher for the advisor’s mentorship and, ultimately, the advisor’s approval of her degree before she can graduate. For students seeking an academic position after graduate school, an advisor’s letter of recommendation can be the difference between landing a job and being left out in the cold, a harsh reality given today’s sparse academic job market. All of these factors mean that the faculty advisors hold tremendous power in the advisor-advisee relationships. They are the gatekeepers of success in the graduate endeavor.
This notion of “trading labor for mentorship” is most directly monetized in grant-funded fields like engineering, where graduate students are “working in the lab” on a project that is (hopefully) related to their thesis topic. In some cases, this works out fine, but in others, the research for the grant-relevant project does not contribute directly to their thesis. For funding agencies which want “deliverables,” this pressure to produce results on schedule creates a tension. The advisor becomes a boss.
Some of the points raised in the discussion on Facebook seemed important to bring out to a wider audience. One suggestion is to disentangle NSF support for projects and research from grad student salaries. So students could apply for NSF support and then they take their funding with them to find an advisor. In STEM this would be difficult, given the large number of international students who would not be qualified for such support, but it does give some power to students to walk away from a bad situation and more incentives for PIs to be more mentors than bosses. I am not entirely convinced it would help in terms of mental health though — students need more and better mentoring, not just the means to walk away. Also, Roy pointed out, having the student and advisor both convinced that a problem is important and solvable creates a shared commitment that helps students feel less isolated. For postdocs, though, this model would be a significant improvement over the status quo. Right now, there is almost no consensus on what a postdoc should be, and I’ve seen postdoc jobs that range from factotum to co-PI.
When one is on the other side (post-PhD), it’s tempting to say that grad school would have been easier if I had been a bit more organized or had better time-management skills. Perhaps the difficulties one has can be solved with “one weird trick.” I think that’s terribly naïve. As advisors, we definitely can do things to help students learn to work better — that’s the transition from being a student to being a researcher. But the notion that depression comes about as a result of simply not being productive enough, or feeling behind, or any other “outcomes”-based reason, misses the environmental and social factors that are equally important.
Graduate research is often very isolating. Perhaps some STEM students actually enjoy this kind of solitary work, but generalizing is dangerous. Having a grad student social organization, weekly happy hour, softball league, or other “outlet” isn’t enough. I used my startup funds to help buy a table-tennis table for my department at Rutgers, and while the students seem pretty happy about it, it’s not actually creating a community. One important question to ask is how the faculty and the department can help create and support that kind of community so that it can go on its own, organically.
In a department like mine, the majority of graduate students are international, and have a host of other stressors about being in a new (and often much more expensive) country. Using mental health resources may not be normalized in their home country or culture. Regardless of where they are from however, the big challenge is this:
…awareness of the existing resources among the graduate student population remains frustratingly low, due in part to the insular nature of traditional academic departments. A broader culture of wellness may prove even more elusive in the face of a rigidly hierarchical academic culture that often rewards drive and sacrifice without encouraging balance. In this climate, graduate student mental health advocates—students, staff, and administrators—face an uphill struggle in the years to come. The consequences of this struggle tear at the very fabric of the academic experience and suggest fundamental misalignment of priorities.
It’s only a misalignment of priorities if we don’t interrogate our priorities. This isn’t two trains crashing into each other, but it does require a “structural” recognition that graduate students are a part of the family, as it were, and treating them as such.
and deterministic, rather than randomized, quantization. They consider two types — rounding and truncation (essentially the floor operation). The update rule is 
where 
is the quantization operation. They shoe that in finite time the agents either reach a consensus on the floor of the average of their initial values, or that the cycle indefinitely in a neighborhood around the average. They they show how to control the size of the neighborhood in a decentralized way. There are a lot of works on quantized consensus that have appeared in the last 5 years, and to be honest I haven’t really kept up on the recent literature, so I’m not sure how to compare this to the other works that have appeared, but perhaps some of the readers of the blog have…
is strongly convex, the regularizer 
is lower semicontinuous and convex, and the term 
separates into a sum of function 
which are Lipschitz continuous. The proximal gradient method is an iterative procedure for solving this program that does the following:
function as
is sampled uniformly from 
at each time. The advantage of the SG variant is that it takes less time to do one iteration, but each iteration is much noisier. The goal of this paper is to adapt a previous method/approach to variance reduction to improve the performance of the Prox-SG algorithm. The approach is one or resampling points according to the Lipschitz constants. This sort of “sampling based adaptivity” was also used by my ex-colleague 
and at each time the learner picks an action 
and observes an outcome 
which is assigned a reward by a function 
. The rewards are assumed to be i.i.d. across time for each action with distributions 
that are unknown to the learner. The goal is to maximize the reward, which is the same as finding the arm with the largest expected reward. This leads to a classical explore/exploit tradeoff where the learner has to decide whether to explore new arms which may have higher expected reward, or continue exploiting the reward offered by the current arm. Thompson sampling is a Bayesian approach where the learner starts with a prior on the best action and then samples actions at each time according to its posterior belief on the best arm. The authors here analyze the regret of such a policy in terms of what they call the information gain of the system. This gain depends on the ratio between two quantities that are functions of the outcome distributions 
?” There a lot of ways of answering this but one way that seems to make more sense to people who actually think about risk, hypothesis testing, and prediction error is through the “area under the curve” metric, or AUC. This post came out of a discussion from a talk I gave recently at Boston University, and I’d like to thank 
) and 
experts (agents 
). The agent is trying to do an 
-ary hypothesis test. The experts (and the agent) have access to local (private) observations ![Y_k[1], Y_k[2], \ldots, Y_k[n_k]](https://s0.wp.com/latex.php?latex=Y_k%5B1%5D%2C+Y_k%5B2%5D%2C+%5Cldots%2C+Y_k%5Bn_k%5D&bg=ffffff&fg=333333&s=0&c=20201002)
for 
. The observations come from a family of distributions determined by the true hypothesis 
. The agent 
which is a function of the amount of data it has as well as the true hypothesis and the decision it makes. This is supposed to model a “bias” for the expert — for example, they may not care to distinguish between two hypotheses. The rest of the paper looks at finding policies/decision rules for the agents that optimize the exponents with respect to their local loss functions, and then looking at how agent 
is a version of 
that actually existed in the shared memory at some point in time.” What does this mean? It means that a local processor, when it reads the current state of the iterate, may be performing an update with respect to a point not on the sample path of the algorithm. They do assume that the delay between reading and updating the common state is bounded. To analyze this method they need to use a different analysis technique. The analysis is a bit involved and I’ll have to take a deeper look to understand it better, but from a birds-eye view this would make sense as long as the step size is chosen properly and the “hybrid” updates can be shown to be not too far from the original sample path. That’s the stochastic approximator in me talking though.
such that the following holds. Let ![A = [a_1\ a_2\ \cdots \ a_n]](https://s0.wp.com/latex.php?latex=A+%3D+%5Ba_1%5C+a_2%5C+%5Ccdots+%5C+a_n%5D&bg=ffffff&fg=333333&s=0&c=20201002)
be an 
real matrix such that the 
-th column 
satisfies 
for 
, and let 
be a convex body in 
such that 
, where 
. Then there exists a vector 
such that 
.
, then for any arbitrary collection of sub-unit-norm vectors 
, I can find a way to add and subtract them from each other so that the result ends up in 
An Ergodic Walk 