I've always been impressed how the SIGCOMM conference accepts a very small number of papers, but many hundreds of people attend the conference. (This is true for some other conferences as well; SIGCOMM is just he one I happen to know best.) The conference is somehow an "attend-if-possible" venue for the networking community. Most other large conferences I know work instead by accepting a lot of papers. ISIT is a week-long event with 9 parallel sessions (in 2014). Location may certainly be helpful; ISIT was in Honolulu in 2014 and
Hong Kong in 2015; SIGCOMM will be in London this year. But it also isn't decisive; the Allerton conference has been steadily growing, so it's a few hundred people, even though Urbana-Champaign, where the conference is held, really can't be the biggest draw. (No offense to those who are there -- I always enjoy visiting!) In fact, really, at this point, Allerton has been so successful it has seemingly outgrown the Allerton conference center!

If you have ideas for what makes a conference a "must-attend" venue, I'd be interested in hearing them. The question has arisen because of a Windows on Theory post about changing the format for STOC 2017; for those of you on the theory side who haven't seen it, I'd recommend looking at the post and registering an opinion by comment or by e-mail to the appropriate parties, after you've considered the issue. The underlying question is what role should the STOC/FOCS conferences play in the world these days, and how might we change things to get them to play that role. I think another way of framing this is that I don't think STOC/FOCS aren't really "attend-if-possible" venues for much of the theory community -- particularly for certain subareas -- and the question is whether this can change. Again, I'd be happy for insights from other communities as well.

There are a large number of comments already. I'd say in terms of my personal opinion on what to do I'm most aligned with Alex Lopez-Ortiz and Eric Vigoda. Alex's point is straightforward -- accept more papers. I've been in the accept more papers camp for a while (a very old post on the topic suggests one way it could be done), but for some reason there seems to be huge numbers of people in the theory community against the idea, based on some sort of quality argument. For me, the tradeoffs are pretty simple; I generally prefer not to travel, so I need a good reason to go to a conference, and one very good reason is that I have a paper in the conference that I or a colleague is presenting. (I recognize this is not true for everyone, but being selective in travel is an issue that arises for people with families, or other regular obligations.) Clearly conferences such as SIGCOMM show that there are other paths possible, but I'm not clear on how to reproduce that kind of buy-in from the theory community. Eric's suggestion was that lots of theory conferences happen during the summer, so instead of trying other ways to create a larger "STOC festival", why not co-locate a number of conferences (that would have parallel sessions) that would get more of the theoretical computer science community together. That makes sense to me, and seems like it could be particularly beneficial for some of the smaller conferences.

But my personal opinion, while undoubtedly fascinating to some (most notably myself), is really not the point. The point is for the community to examine the current situation, think if there are ways to make it better, and then act on what they come up with. The bet way for this to happen is if people actively participate in discussions. So please, go opine! There's no reason the post shouldn't have 100+ comments, so comment away.

## Monday, May 18, 2015

## Friday, May 15, 2015

### New Work on Equitability and MIC

A few years ago, working with a diverse group of scientists, I was looking at a problem related to big data analysis. The setting was data exploration, where you are working with a high-dimensional dataset, and you are seeking pairs of dimensions that are related in interesting but a priori unknown ways; that is, maybe there's a linear relationship, but maybe there's a more complicated relationship (sinusoidal, parabolic, etc.), and you don't know what you're looking for in advance.

One statistical approach is to throw a so-called measure of dependence at the problem, which will tell you whether variables are related or unrelated. But in big data sets, you may expect to have lots of dependent pairs; what you really want is not just a "dependent-independent" test, but a scoring mechanism that ranks the extent of dependence appropriately over a wide range of possible relationships. This methodology seemed underserved by the literature. We dubbed what we were aiming for "equitability", and designed a statistic we dubbed MIC (maximal information coefficient), a "bucketed" version of mutual information, that seemed to be a good ranking mechanism for equitability. The work appeared in Science some years back (the link here will allow you to access it).

The work has, I think, been quite successful -- a number of people have used MIC in their research to analyze data sets, and the idea of equitability seems to be catching on. But after it came out, there were some questions and issues raised primarily by statisticians. We had always planned to go back and revisit some of these issues, and, after various delays caused by life, a group of us started back on it again. The project seemed to balloon, and we've been working on and off on it for at least a year now. (Some earlier, initial drafts pointing to where we were going are on the arxiv.) Finally, we've reached a stopping point, and we've just put up 3 papers on the arxiv, all of which are now being submitted to various journals. In this post, I'll outline what the papers cover, after the links.

First, people wanted further theoretical foundations for equitability. Our Science paper, being for a general audience, provided an intuitive definition, but we didn't define it as one would in a mathematics paper. (That was, I should be clear, intentional.) We thought our definition was pretty clear in plain English, but for some it was not sufficient; one group, in particular, seemed to ignore our explanations when in their own work they added restrictions to "equitability" and incorrectly ascribed them to us.

So the first paper formalizes this notion of equitability. As is usually the case, formalizing it turns out to be helpful. In particular, it shows that there are (at least) two natural ways of thinking about equitability. One way formalizes our original conception that an equitable statistic is a statistic that gives similar scores to relationships with the same amount of noise, even if the relationships are of different types. But a different way of viewing the formalization shows that equitability can naturally be seen as an extension of statistical power against a null hypothesis of independence (i.e., relationship strength = 0), to power against null hypotheses representing all levels of dependence (i.e. relationship strength <=x for any x). This view clarifies the relationship between equitability and power against independence, showing the former generalizes the latter. In our new papers we have some really nice "heat-map" style visualizations for viewing equitability performance results based on this view that I think are really useful in thinking about and understanding equitability in the paper.

Second, people wanted faster, better versions of our proposed scoring function, MIC. We ended up going back to the theory of MIC, examining further its relation to mutual information, and, perhaps unsurprisingly, doing so allowed us to make tangible practical advances. We ended up with algorithms for computing MIC that are both faster and more accurate. (Our original algorithm in the Science paper used a heuristic approach based on dynamic programming to approximate the MIC score from the data; our new approaches have both improved speed and accuracy.) We're hopeful that people using MIC will be able to switch over time to these improved algorithms. Connecting to the first paper, in re-examining MIC we also developed a variation of MIC (called TIC, for total information coefficient) that is better designed for achieving power against independence as opposed to equitability. We are hopeful that TIC may prove useful to people on its own, as well as in conjunction with MIC.

Third, people just wanted to see more comparisons. Well, really, here I think everyone just has their own favorite measure of dependence, and before they go switching to this new-fangled thing that appeared in Science of all places, they want to see more. Specifically, subsequent to that initial paper, there were people concerned about the power against independence of our methods -- although, again, to be clear, equitability is a larger notion that power against independence, so one might expect a method designed for equitability would not have as high power against independence as methods designed specifically for that purpose. Also, there were some people who claimed, based on very limited experiments, that mutual information estimation would be more equitable than MIC.

So the third paper is a large-scale empirical study. In terms of equitability, we find that MIC still seems to be the current best measure. (Mutual information sometimes does well -- in some very particular circumstances, it can do better than MIC, which is not especially surprising since MIC is a "scaled" version of mutual information -- but MIC still performs much better overall.) In terms of power against independence, we find that MICs power was underrated in previous studies. The discrepancy seemed to be that previous studies used MICs default parameter settings, which were designed for equitability performance, not power against independence; using different default parameters yields substantially better power against independence. (The new algorithms in the second paper that yield more accurate calculations improve the power further.) Finally, the TIC measure described in the second paper does even better, is easily computed when computing MIC scores (and so has negligible overhead if computing MIC scores), and appears to be comparable to other state-of-the-art measures in terms of power against independence. We also find that the new ways of computing MIC are indeed faster and more accurate than previous methods.

We're hoping these works, collectively, move the ball forward on this topic. We like seeing MIC being used, and hope people will start using it more when analyzing their large dimensional data sets. To be clear, perhaps tomorrow we will find that there are better scoring mechanisms than MIC for equitability; perhaps even better mutual information estimators will suffice. That would be great! (I think of it like clustering algorithms; there are lots of good clustering algorithms, different ones may be better suited to different situations. The more the merrier.) We also think equitability continues to be a useful framework, and that there's more to be done with equitability. Though for now our group may again take a breather on this topic, and see what arises from our current work.

One statistical approach is to throw a so-called measure of dependence at the problem, which will tell you whether variables are related or unrelated. But in big data sets, you may expect to have lots of dependent pairs; what you really want is not just a "dependent-independent" test, but a scoring mechanism that ranks the extent of dependence appropriately over a wide range of possible relationships. This methodology seemed underserved by the literature. We dubbed what we were aiming for "equitability", and designed a statistic we dubbed MIC (maximal information coefficient), a "bucketed" version of mutual information, that seemed to be a good ranking mechanism for equitability. The work appeared in Science some years back (the link here will allow you to access it).

The work has, I think, been quite successful -- a number of people have used MIC in their research to analyze data sets, and the idea of equitability seems to be catching on. But after it came out, there were some questions and issues raised primarily by statisticians. We had always planned to go back and revisit some of these issues, and, after various delays caused by life, a group of us started back on it again. The project seemed to balloon, and we've been working on and off on it for at least a year now. (Some earlier, initial drafts pointing to where we were going are on the arxiv.) Finally, we've reached a stopping point, and we've just put up 3 papers on the arxiv, all of which are now being submitted to various journals. In this post, I'll outline what the papers cover, after the links.

- Equitability, interval estimation, and statistical power. arXiv

- Measuring dependence powerfully and equitably.
arXiv

- An Empirical Study of Leading Measures of Dependence. arXiv

First, people wanted further theoretical foundations for equitability. Our Science paper, being for a general audience, provided an intuitive definition, but we didn't define it as one would in a mathematics paper. (That was, I should be clear, intentional.) We thought our definition was pretty clear in plain English, but for some it was not sufficient; one group, in particular, seemed to ignore our explanations when in their own work they added restrictions to "equitability" and incorrectly ascribed them to us.

So the first paper formalizes this notion of equitability. As is usually the case, formalizing it turns out to be helpful. In particular, it shows that there are (at least) two natural ways of thinking about equitability. One way formalizes our original conception that an equitable statistic is a statistic that gives similar scores to relationships with the same amount of noise, even if the relationships are of different types. But a different way of viewing the formalization shows that equitability can naturally be seen as an extension of statistical power against a null hypothesis of independence (i.e., relationship strength = 0), to power against null hypotheses representing all levels of dependence (i.e. relationship strength <=x for any x). This view clarifies the relationship between equitability and power against independence, showing the former generalizes the latter. In our new papers we have some really nice "heat-map" style visualizations for viewing equitability performance results based on this view that I think are really useful in thinking about and understanding equitability in the paper.

Second, people wanted faster, better versions of our proposed scoring function, MIC. We ended up going back to the theory of MIC, examining further its relation to mutual information, and, perhaps unsurprisingly, doing so allowed us to make tangible practical advances. We ended up with algorithms for computing MIC that are both faster and more accurate. (Our original algorithm in the Science paper used a heuristic approach based on dynamic programming to approximate the MIC score from the data; our new approaches have both improved speed and accuracy.) We're hopeful that people using MIC will be able to switch over time to these improved algorithms. Connecting to the first paper, in re-examining MIC we also developed a variation of MIC (called TIC, for total information coefficient) that is better designed for achieving power against independence as opposed to equitability. We are hopeful that TIC may prove useful to people on its own, as well as in conjunction with MIC.

Third, people just wanted to see more comparisons. Well, really, here I think everyone just has their own favorite measure of dependence, and before they go switching to this new-fangled thing that appeared in Science of all places, they want to see more. Specifically, subsequent to that initial paper, there were people concerned about the power against independence of our methods -- although, again, to be clear, equitability is a larger notion that power against independence, so one might expect a method designed for equitability would not have as high power against independence as methods designed specifically for that purpose. Also, there were some people who claimed, based on very limited experiments, that mutual information estimation would be more equitable than MIC.

So the third paper is a large-scale empirical study. In terms of equitability, we find that MIC still seems to be the current best measure. (Mutual information sometimes does well -- in some very particular circumstances, it can do better than MIC, which is not especially surprising since MIC is a "scaled" version of mutual information -- but MIC still performs much better overall.) In terms of power against independence, we find that MICs power was underrated in previous studies. The discrepancy seemed to be that previous studies used MICs default parameter settings, which were designed for equitability performance, not power against independence; using different default parameters yields substantially better power against independence. (The new algorithms in the second paper that yield more accurate calculations improve the power further.) Finally, the TIC measure described in the second paper does even better, is easily computed when computing MIC scores (and so has negligible overhead if computing MIC scores), and appears to be comparable to other state-of-the-art measures in terms of power against independence. We also find that the new ways of computing MIC are indeed faster and more accurate than previous methods.

We're hoping these works, collectively, move the ball forward on this topic. We like seeing MIC being used, and hope people will start using it more when analyzing their large dimensional data sets. To be clear, perhaps tomorrow we will find that there are better scoring mechanisms than MIC for equitability; perhaps even better mutual information estimators will suffice. That would be great! (I think of it like clustering algorithms; there are lots of good clustering algorithms, different ones may be better suited to different situations. The more the merrier.) We also think equitability continues to be a useful framework, and that there's more to be done with equitability. Though for now our group may again take a breather on this topic, and see what arises from our current work.

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