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Agent-Based Models of the Blogosphere

My upcoming dissertation will be focused on building mathematical models of bloggers in an effort to understand the social dynamics of the individuals themselves. There are a number of reasons for why this is a useful strategy. By building agent-based (i.e. blogger-based) models, we can test to see if certain social strategies actually play a role in forming the blog network itself. Furthermore, if the models are very good, it might be possible to make predictions about the bloggers themselves.

One of the biggest challenges with building mathematical models is defining a scope for the model. First, one should decide what one is trying to predict. Next, one should decide how to go about making those predictions. This post focuses specifically on agent-based models, where each individual blogger or post is modeled. One assumes this agent makes its own decisions, such as who he or she will link to, or what he or she will write about. Using this information, we can start to get an idea of how the blogosphere in our model will work.

The difficulty with building such models is the validation portion of the process. We can build a simple model that simply states: "Every blogger will post once a day at noon, and will not link to anyone else." This model is obviously incorrect, but how incorrect is it? What is our measure of error? In other words, what are we trying to predict and how good are our predictions?

While this list is by no means extensive, there are three areas I've been exploring for defining error in models of the blogosphere: the macro, meso, and micro levels.

The Micro Level

At one end of the spectrum, we can try to predict the most minute details of the blogosphere. We can try to predict specific links (i.e. that "The Huffington Post" will link to "Wonkette" tomorrow), new posts (i.e. "Daily Kos" will post about Iraq next week), or new entrants (i.e. 30 new political blogs will be created in the next 12 hours). Such predictions are clearly useful, and error is easy to calculate as we simply need to check if our predictions were correct. In Topic-Link LDA: Joint Models of Topic and Author Community, the authors attempt to do this with interblog linking.

The biggest drawback with such specific predictions is the accuracy. Yes, predictions are easy to validate, but the accuracy of such predictions is extremely small. The models have a long way to go before one can actually trust them. Indeed, it might be that such models of blogger behaviour will never be trustworthy to a practical extent.

The Macro Level

At the opposite end of the spectrum, one looks at global properties of the blogosphere. Since predicting what individual bloggers will be doing is so difficult, why not try to predict larger-scale properties? For example, we might predict the number of blog posts likely to be posted on a given day, or the distribution of links in the blog network. While not blog-focused, a good example of such work is provided in Team Assembly Mechanisms Determine Collaboration Network Structure and Team Performance. In this paper, the authors predict the distribution of collaborations between Broadway actors. The actors themselves have specific agendas and make choices about who to work with, and the authors validate their model by seeing how their model predicts "aggregate collaboration" -- in other words, the distribution of collaboration counts on the Broadway scene.

While error rates for such models tend to be lower, a good question to ask is whether such models provide practical information. For example, if we know that only 5 Broadway actors will collaborate with more than 100 actors during their careers, how can we actually use this information? A similar analogy can be used in the blogosphere. If our model predicts that next month, only three blogs will receive more than 100 hyperlinks to their posts, what do we really know? Can we act on this information?

The Meso Level

If the micro level provides too little accuracy and the macro level doesn't provide enough "practical" (your mileage will vary) information, let's make a compromise. Specifically, what about making predictions about subgroups in the blogosphere? Can we predict that certain communities of bloggers will do certain things? Imagine if you knew that a certain community of bloggers will likely be more active than another community. If this community is the pro-life movement in the political blogosphere, then you certainly have useful information.

Two papers in this area are Correlation Profiles and Motifs in Complex Networks and Patterns of Cascading Behavior in Large Blog Graphs. In each case, the authors look at small subgraphs in the networks they model and try to see what happens with those subgraphs. Do they appear more often than is expected? Can one predict how often they appear?

I believe that such an approach has a great deal to offer those modeling political blogs and other networked data sets. While it might be very difficult to predict whether a specific edge will form, if one can instead predict what a group of 3 or 4 bloggers is likely to do, one still has a great deal of practical information. Whether such models have higher error rates has (according to my research) yet to be seen.