Meaningful and meaningless variables (and correlations)

A number of data scientists I know like to go about their business in a domain-free manner. They make a conscious choice to not know anything about the domain in which they are solving the problem, and instead treat a dataset as just a set of anonymised data, and attack it with the usual methods.

I used to be like this as well a long time ago. I remember in my very first job I had pissed off some clients by claiming that “I don’t care if this is a nut or a screw. As far as I’m concerned this is just a part number”.

Over time, though, I’ve come to realise that even a little bit of domain knowledge or intuition can help build significantly superior models. To use a framework I had introduced a few months back, your domain knowledge can be used to restrict the degrees of freedom in your model, thus increasing how much the machine can learn with the available data.

Then again, some problems lend themselves better to domain-based intuition than others, and this has to do with the meaning of a data point.

Consider two fairly popular problem statements from data science – determining whether a borrower will pay back a loan, and determining whether there is a cat in a given picture. While at the surface level, both are binary decisions, to be made by looking at large dimensional data (the number of data points that can be used for credit scoring can be immense), there is an important distinction between the two problems.

In the cat picture case, a single data point is basically the colour of a single pixel in an image, and it doesn’t really mean anything. If we were to try and build a cat recognition algorithm based on a single pre-chosen pixel in an image, it is unlikely we can do better than noise. Instead, the information is encoded in groups of pixels near each other – a bunch of pixels that look like cat ears, for example. In this case, whether you are training to model to identify cats or cinnamon buns is immaterial, and the domain-free approach works well.

With the credit scoring problem, the amount of information in each explanatory variable is significant. Unless we are looking at some extremely esoteric or insignificant variables (trust me, these get used fairly often in credit scoring models), it is possible to build a decision model based on just one explanatory variable and still have significant predictive power. There is definitely information in correlation between explanatory variables, but that pales compared to the information in the variables themselves.

And the amount of information captured by each explanatory variable means that it makes sense in these cases to invest some human effort to understand the variables and the impact it is having. In some cases, you might decide to use a mathematical transformation of a variable (square or log or inverse) instead of the variable itself. In other cases, you might determine based on logic that some correlations are spurious and drop the variables altogether. You might see a few explanatory variables with largely similar information and decide to drop some of them or use dimension reduction algorithms. And you can do a much better job of this if you have some experience or intuition about the domain, and care to understand what each variable means. Because variables have meanings.

Unlike in the image recognition problem, where most of the intuition is in the correlation term, because of which the “variables” don’t have any meaning, where domain doesn’t matter that much (though it can – in that some kinds of algorithms are superior at some kinds of images. I don’t have much experience in this domain to comment 🙂 ).

Again like in all the two-by-twos that I produce (and there are many, though this is arguably the most famous one), the problem is where you take people from one side and put them in a situation from the other side.

If you come from a background where you’ve mostly dealt with datasets where each individual variable is meaningless, but there is information in the collective, you are likely to “stir the pile” rather than using intuition to build better models.

If you are used to dealing with datasets with “meaning”, where variables hold the information, you might waste time doing your jiggery-pokery when you should be looking to apply models that get information in the collective.

The problem is this is a rather esoteric classification, so there is plenty of chance for people to be thrown into the wrong end.

Simplicity and improvisation

While writing my previous post on the film game, I was thinking about simplicity and improvisation. About how if you seek to improvise, in order to improvise well, you would rather choose a simple base. Like how the simplicity of film aata allows you to improvise so much and create so much fun. I was thinking about this in several contexts.

This concept first entered my mind back in class 11, when a mridangist classmate told me that for all music competitions, he would choose to play the aadi taaLa. His funda was that the simple and intuitive 8-beat cycle in this taaLa let his mind free of conforming to the base and allowed him to use all his energy in improvisation.

Thinking about it, though I have little domain knowledge, I would consider it very unlikely that a Carnatic performer would choose a vakra raaga for the “main piece” of a concert. The main piece requires one to do extensive alaap and then taaLa and requires a lot of improvisation and creative thinking on the part of the performer. Now, a vakra raaga (one where there are strict rules governing the order to notes) would impose a lot of constraints on the performer and he would be spending a large part of his energy just keeping track of the raaga and making sure he isn’t straying from the strict scales.

Starting from a simple easy base allows you to do that much more. It gives you that many more degrees of freedom to experiment, that many more directions to take your product in. If you build a sundae with vanilla ice cream, you can do pretty much what you want with it. However, if you use butterscotch, you will need to make sure that every additive blends in well with the butterscotch flavour, thus constraining your choices.

When the base for your innovation is itself fairly complicated, it leaves you with little room to manouever, and I’m afraid this is what occasionally happens when you are into research. You specialize so much and start working on such a narrow field that you will be forced to build upon already existing work in the field, which is already at a high level of sophistication. This leaves you with little choice in terms of further work, and you end up publishing “delta papers”.

Similarly in the management context, if you start off by using something complicated as your “base framework”, there aren’t too many things you can put on top of it, and that constrains the possibilities. There is even the chance that you might miss out on the most optimal solution to the problem because your base framework didn’t allow you to pursue that direction.

It is all good to borrow. It is all good to not reinvent the wheel. It is all good to stand on the shoulders of giants. However, make sure you pick your bases carefully, and not start on complicated ground. You will produce your best work when you give yourself the maximum choice.