“Both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity” – Vaupel & Yashin

Big Data is daily topic of conversation among data analysts, with much said and written about its promises and pitfalls. The issue of heterogeneity, however, has received scant attention. This is unfortunate, since failing to take heterogeneity into account can easily derail the discoveries one makes using these data.

This issue, which some may recognize as an example of ecological fallacy, first came to my attention via a paper elegantly titled “Heterogeneity’s ruses: some Surprising Effects of Selection on Population Dynamics” (Vaupel and Yashin, 1985). Authors discuss a variety of examples where the aggregated behavior of a heterogeneous population, composed of two homogeneous but differently behaving subpopulations, will differ from the behavior of any single individual. Consider the following example. It has been observed that the recidivism rate of convicts released from prison declines with time. A natural conclusion one may reach from this observation is that former convicts are less likely to commit crime as they age. However, this is false. In reality, there may be two groups of individuals “reformed” and “incorrigible” with constant – but different – recidivism rates. With time, there will be more “reformed” individuals left in the population, as the “incorrigibles” are sent back to prison, resulting in decreasing recidivism rate for the population as a whole. This simple example shows that “the patterns observed [at population level] may be surprisingly different from the underlying patterns on the individual level. Researchers interested in uncovering these individual patterns, perhaps to help develop or test theories or to make predictions, might benefit from an “understanding of heterogeneity’s ruses.” (Vaupel & Yashin)

My colleagues and I have been tricked by heterogeneity time and again. As one example, our study of information spread on the follower graphs of Twitter and Digg revealed that it was surprisingly different from the simple epidemics that are often used to model information spread. In a simple epidemic, described, for example, as an independent cascade model, the probability of infection increases monotonically with the number of exposures to infected friends. This probability is measured by the exposure response function. The figure below shows the exposure response function we measured on Twitter: the probability for becoming infected (i.e., retweet) information (a URL) on Twitter as a function of how many friends had previously tweeted this information. In contrast to epidemics, it appears as though repeated exposure to information suppresses infection probability. We measured an even more pronounced suppression of infection on Digg [Ver Steeg et al, 2011], and a similar exposure response was observed for hashtag adoption following friends’ use of them [Romero et al, 2011].

Figure: Exposure response on Twitter. Probability a user will retweet a message containing a URL after a number of friends have tweeted about it. Retweet probability is averaged over all users.

It is easy to draw wrong conclusions from this finding. In “What stops social epidemics?” [Ver Steeg et al, 2011], we reported that information spread on Digg is quickly extinguished, and attributed this to the exposure response function. We speculated that initial exposures “inoculate” users to information, so that they will not become infected (i.e., propagate it) despite multiple exposures. Now we know this explanation was completely wrong.

Figure: Exposure response of subpopulations of Twitter users, differentiated according to the number of friends they follow.

The exposure response function, while aggregated over all users, does not describe the behavior of any individual Digg or Twitter user – even the hypothetical “typical” user. In fact, there is no “typical” Twitter (or Digg) user. Twitter users are extremely heterogeneous. Separating them into more homogeneous sub-populations reveals a more regular pattern. Figure 2 shows the exposure response function for different populations of Twitter users, separated according to the number of friends they follow (large fluctuations are the result of small sample size). Why number of friends? This is explained in more detail in our papers [Hodas & Lerman 2012, 2013], but in short, we found it useful to separate users according to their cognitive load, i.e., the volume of information they receive, which is (on average) proportional to the number of friends they follow [Hodas et al, 2013]. Now, the probability that a user within each population will become infected increases monotonically with the number of infected, very similar to the predictions of the independent cascade model.

Figure 2 has a different, more significant interpretation, with consequences for information diffusion. It suggests that highly connected users, i.e., those who follow many others, are less susceptible to becoming infected. Their decreased susceptibility in fact explains Figure 1: as one moves to the right of the exposure response curve, only the better connected, and less sensitive, users contribute to that portion of the response. However, despite their reduced susceptibility, highly connected users respond positively to repeated exposures, like all other users. You do not inhibit response by repeatedly exposing people to information. Instead, the reason that these users are less susceptible hinges on the human brain’s limited bandwidth. There are only so many tweets any one can read, the more tweets you receive (on average proportional to the number of friends you follow), the less likely you are to see – and retweet – any specific tweet. If it was not for recognizing heterogeneity, we would not have found this far more interesting explanation.

References

• Vaupel, J. W. and Yashin, A. I. (1985). Heterogeneity’s ruses: some surprising effects of selection on population dynamics. The American Statistician, 39(3):176-185.
• Hodas, N. O. and Lerman, K. (2013). The simple rules of social contagion.
• Hodas, N. O., Kooti, F., and Lerman, K. (2013). Friendship paradox redux: Your friends are more interesting than you. In Proceedings of 7th International Conference on Weblogs and Social Media.
• Steeg, G. V., Ghosh, R., and Lerman, K. (2011). What stops social epidemics? In Proceedings of the 5th International AAAI Conference on Weblogs and Social Media.
• Romero, D. M., Meeder, B., and Kleinberg, J. (2011). Differences in the mechanics of information Diffusion Across topics: Idioms, political hashtags, and Complex Contagion on twitter. In Proceedings of World Wide Web Conference.

I was recently approached by an entrepreneur who had an interesting way to correlate short term performance of a stock with news reports about the stock. Needless to say, there are many places from which one can get the news, and what results one gets from this sort of analysis does depend on the input news sources. Surprisingly, within two minutes the conversation had drifted from characteristics of news sources to the challenges of running SVM on Hadoop. The reason for this is not that Hadoop is the right infrastructure for this problem. But rather that the problem can legitimately be considered a Big Data problem. In consequence, in the minds of many, it must be addressed by running analytics in the cloud.

I have nothing against cloud services. In fact, I think they are an important part of the computational eco-system, permitting organizations to out-source selected aspects of their computational needs, and to provision peak capacity for load bursts. The map-reduce paradigm is a fantastic abstraction with which to handle tasks that are “embarrassingly parallelizable.” In short, there are many circumstances in which cloud services are called for. However, they are not always the solution, and are rarely the complete solution. For the stock price data analysis problem, based solely on the brief outline I’ve given you, one cannot say whether they are appropriate.

I have nothing against Support Vector Machines, or other machine learning techniques. They can be immensely useful, and I have used them myself in many situations. Scaling up these techniques for large data sets can be an issue, and certainly is a Big Data challenge. But for the problem at hand, I would be much more concerned about how it was modeled than how the model was scaled. What should the features be? Do we worry about duplicates in news appearances? Into how many categories should we classify news mentions? These are by far the more important questions to answer, because how we answer them can change what results we get: scaling better will only change how fast we get them.

It is hard to avoid mention of Big Data anywhere we turn today. There is broad recognition of the value of data, and products obtained through analyzing it. Industry is abuzz with the promise of big data. Government agencies have recently announced significant programs towards addressing challenges of big data. Yet, many have a very narrow interpretation of what that means, and we lose track of the fact that there are multiple steps to the data analysis pipeline, whether the data are big or small. At each step, there is work to be done, and there are challenges with Big Data.

The first step is data acquisition. Some data sources, such as sensor networks, can produce staggering amounts of raw data. Much of this data is of no interest, and it can be filtered and compressed by orders of magnitude. One challenge is to define these filters in such a way that they do not discard useful information. For example, in considering news reports, is it enough to retain only those that mention the name of a company of interest? Do we need the full report, or just a snippet around the mentioned name? The second big challenge is to automatically generate the right metadata to describe what data is recorded and how it is recorded and measured. This metadata is likely to be crucial to downstream analysis. For example, we may need to know the source for each report if we wish to examine duplicates.

Frequently, the information collected will not be in a format ready for analysis. The second step is an information extraction process that pulls out the required information from the underlying sources and expresses it in a structured form suitable for analysis. A news report will get reduced to a concrete structure, such as a set of tuples, or even a single class label, to facilitate analysis. Furthermore, we are used to thinking of Big Data as always telling us the truth, but this is actually far from reality. We have to deal with erroneous data: some news reports are inaccurate.

Data analysis is considerably more challenging than simply locating, identifying, understanding, and citing data. For effective large-scale analysis all of this has to happen in a completely automated manner. This requires differences in data structure and semantics to be expressed in forms that are computer understandable, and then “robotically” resolvable. Even for simpler analyses that depend on only one data set, there remains an important question of suitable database design. Usually, there will be many alternative ways in which to store the same information. Certain designs will have advantages over others for certain purposes, and possibly drawbacks for other purposes.

Mining requires integrated, cleaned, trustworthy, and efficiently accessible data, declarative query and mining interfaces, scalable mining algorithms, and big-data computing environments. A problem with current Big Data analysis is the lack of coordination between database systems, which host the data and provide SQL querying, with analytics packages that perform various forms of non-SQL processing, such as data mining and statistical analyses. Today’s analysts are impeded by a tedious process of exporting data from the database, performing a non-SQL process and bringing the data back.

Having the ability to analyze Big Data is of limited value if users cannot understand the analysis. Ultimately, a decision-maker, provided with the result of analysis, has to interpret these results. Usually, this involves examining all the assumptions made and retracing the analysis. Furthermore, as we saw above, there are many possible sources of error: computer systems can have bugs, models almost always have assumptions, and results can be based on erroneous data. For all of these reasons, users will try to understand, and verify, the results produced by the computer. The computer system must make it easy for her to do so by providing supplementary information that explains how each result was derived, and based upon precisely what inputs.

In short, there is a multi-step pipeline required to extract value from data. Heterogeneity, incompleteness, scale, timeliness, privacy and process complexity give rise to challenges at all phases of the pipeline. Furthermore, this pipeline isn’t a simple linear flow – rather there are frequent loops back as downstream steps suggest changes to upstream steps. There is more than enough here that we in the database research community can work on.

To highlight this fact, several of us got together electronically last winter, and wrote a white paper, available at http://cra.org/ccc/docs/init/bigdatawhitepaper.pdf . Please read it, and say what you think. The database community came very late to much of the web. We should make sure not to miss the boat on Big Data.

My post is loosely based on an extract from this white paper, which was created through a distributed conversation among many prominent researchers listed below.

Divyakant Agrawal, UC Santa Barbara
Philip Bernstein, Microsoft
Elisa Bertino, Purdue Univ.
Susan Davidson, Univ. of Pennsylvania
Umeshwar Dayal, HP
Michael Franklin, UC Berkeley
Johannes Gehrke, Cornell Univ.
Laura Haas, IBM
Alon Halevy, Google
Jiawei Han, UIUC
H. V. Jagadish, Univ. of Michigan (Coordinator)
Alexandros Labrinidis, Univ. of Pittsburgh
Sam Madden, MIT
Yannis Papakonstantinou, UC San Diego
Jignesh M. Patel, Univ. of Wisconsin
Raghu Ramakrishnan, Yahoo!
Kenneth Ross, Columbia Univ.
Cyrus Shahabi, Univ. of Southern California
Dan Suciu, Univ. of Washington
Shiv Vaithyanathan, IBM
Jennifer Widom, Stanford Univ.