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Modeling Topic Distance Over Time, Initial Thoughts

I am always inspired by Ted Underwood’s work and his research notes are no exception. “Do topic models wrap time?” he asks in a recent blog entry. At stake is a curious and somewhat troubling phenomenon, whereby all distributions of topics over time seem to show aberrations at the temporal edges of the sampled data. Please read his post before continuing, because what I am about to say only makes in the context of his observations. Ted and others responding to his post suggest a few statistical methods to deal with the discrepancy, but I think this edge thing is also indicative of a deeper problem with using topic modeling to track cultural changes over time.

Once you return from Ted’s blog, consider what a topic is. Roughly, a topic is a collection of words representative of a particular textual grouping. The words like gun and murder are perhaps more often found in detective fiction rather than erotica, for example. So remember this: topics are bags of words. Crucially, unsupervised1 topic modelling involves logic for the discovery of arbitrary word groupings. We are asking a machine to organize a pile of texts into stacks by “the difference that makes the largest difference.” From the many ways of grouping or classifying a collection of texts, we want those groups that are most starkly different from each other. Often these machine-generated “topics” track human-derived, social categories such as authors or genres. And sometimes these “topics” don’t make any (human) sense. They can indicate a difference for which no social, cultural category can exist—which is kind of fun to explore in any case.

With these pleasantries out of the way, let’s take a look at Ted’s outliers. The problem in a nutshell is this: our picture of the topic timeline changes depending on the window of time we take into consideration. Underwood writes:

The two models provide significantly different pictures of the period where they overlap. 1978, which was a period of relatively slow change in the first model, is now a peak of rapid change. On the other hand, 1920, which was a point of relatively rapid change, is now a trough of sluggishness.

A quick way to fix this, as Ted suggests, would be to “pad” the window of time under consideration and then discard the padding, because we know that it is susceptible to time aberrations. This makes good sense too. The texts in the beginning of our timeline represent a collection of topics derived from the entirety of the corpus. Yet these initial texts are also likely to contain topics not in the sample. The texts from the 1890s at the left-most edge contain past topics prominent in the 1880s, beyond the scope of our sample. The same is true for the last segment, which contains future topics again not included in the sample. Thus the decline in similarity at the edges.

But wait, how did we get here? Like the authors of the music styles paper Ted cites, we took the distribution of topics in the whole corpus as a measuring stick for change between periods!2 The weirdness at edges is indicative of that decision. First, our measuring stick changes depending on our sample. Second, our sample is itself not a stable culture. And finally, even our medium has not be stabilized for long-historical observation.

Imagine you are a scientist measuring the growth of bacterial in a Petri dish. You fill it with nutritious agar and measure the diameter of the mold colony every day to track its progress. In this case you are guaranteed three things: your measurements (in centimeters) are universal, in that they do not in themselves change from day to day. Biologically, your bacteria is the same on first and the last day of your observation. Agar—the medium of your culture—is relatively stable as well. You can be sure that the changes that you measure are changes in the bacterial culture, and not in the shape or the composition of the dish.

As textual scholars we have none of these assurances:

  1. Does it make sense to measure local “synchronic” differences using arbitrarily derived diachronic measures? I am not prepared to answer that question without more experimentation, but intuitively I would say not. Whatever our view of the topics in the century is clearly different from the view of the topics in the decade. For this reason, the study of change is more immediately convincing when we use simpler, more stable measures. Although language changes, it is less volatile than literary fashion. For this reason, something like “the usage of definite particles over time” is a more robust marker than complex, derivative metrics such as “topics.” (A strategy that has been successful in authorship attribution.) Overall “topic proportions” as a measure of distance between localized texts is suspect at the least. The unit of measure itself depends on our sample.

  2. Something like “agar” and “bacteria” have precise definitions in the world of biology. Not so with human culture. Because there is no precision as to what literature is, it is very difficult for us to address “the pace of change in fiction.” We are extremely susceptible to sample bias. How do we go about “randomly selecting 750 works in each decade”? Will this “total population” from which we sample include works of genre literature such as sci-fi, young adult, and pornography? (Studies in our field usually do not). Should we include film scripts? Historical novels? Autobiographies? What counts as “literature” changes with time and point of view.

  3. Finally, the petri dish itself is not stable. In other words, changes in topics cannot be reduced to the formal features of the text, much less to words alone. One way to deal with sample bias is to rely on external, socially constructed markers of distinction. Rather than argue about what “fiction” is, we can use the “The New York Times Best Sellers” list in the fiction category, which has been around since the 1930s. Stability at last: We have found a sample with “natural” boundaries, not dependant on the bias of the researcher. Fiction published in a particular journal forms similarly “naturalized” boundaries. Better. The petri dish of The New Yorker is more stable than that of “literature” in general. Still, we understand that changes in formatting or editorial leadership will have a dramatic effect on the kinds of fiction published in The New Yorker or selected for The New York Times Best Sellers List. What looks like changes in topic distance—a bag of words—may really illustrate second order institutional effects. Clustering topics by words alone will always miss such meta-literary changes. Adding social features for classification, the way Bamman and Underwood have done in their “Mixed Effects Model of Literary Character” paper for example, again more closely tracks our theories of literary formation.

None of these are insurmountable obstacles for computational literary studies. I suspect the temporal weirdness at the edges of historical topic modeling is indicative of deeper methodological problems and of the excitement of working at the intersection between qualitative and quantitative analysis.

  1. A supervised approach involves teaching the machine based on human categories. In other words: “computer, give me texts most similar to this pile I call ‘detective fiction’.” 

  2. Ted writes: “For instance, suppose we want to understand the pace of change in fiction between 1885 and 1984. To make sure that there is exactly the same amount of evidence in each decade, we might randomly select 750 works in each decade, and reduce each work to 10,000 randomly sampled words. We topic-model this corpus. Now, suppose we measure change across every year in the timeline by calculating the average cosine distance between the two previous years and the next two years. So, for instance, we measure change across the year 1911 by taking each work published in 1909 or 1910, and comparing its topic proportions (individually) to every work published in 1912 or 1913. Then we’ll calculate the average of all those distances.” 

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