A Glimpse into The Possibilistic Mindset

Contrary to the probabilistic approach to data analytics, which relies on probabilities and ways to model them, usually through a statistical framework, the possibilistic approach focuses on what’s actually there, not what could be there, in an effort to model uncertainty. Although not officially a paradigm (yet), it has what it takes to form a certain mindset, highly congruent with that of a competent data scientist. 

If you haven’t heard of the possibilistic approach to things, that’s normal. Most people have already jumped on the bandwagon of the probabilistic dogma, so someone seriously thinking of things possibilistically would be considered eccentric at best. After all, the last successful possibilistic systems are often considered obsolete, due to their inherent limitations when it came to higher dimensionality datasets. I’m referring to the Fuzzy Logic systems, which are part of the the GOFAI family of A.I. systems (in these systems the possibilities are expressed as membership levels, through corresponding functions). These systems are still useful, of course, but not the go-to choice when it comes to building an AI solution to most modern data science problems. 

Possibilistic reasoning is that which relies on concrete facts and observable relationships in the data at hand. It doesn’t assume anything, nor does it opt for shortcuts by summarizing a variable with a handful of parameters corresponding to a distribution. So, if something is predicted with a possibilistic model, you know all the how’s and why’s of that prediction. This is directly opposite to the black-box predictions of most modern AI systems.

Working with possibilities isn’t easy though. Oftentimes it requires a lot of computational resources, while an abundance of creativity is also needed, when the data is complex. For example, you may need to do some clever dimensionality reduction before you can start looking at the data, while unbiased sampling may be a prerequisite also, particularly in transduction-related systems. So, if you are looking for a quick-and-easy way of doing things, you may want to stick with MXNet, TensorFlow, or whatever A.I. framework takes your fancy.

If on the other hand you are up for a challenge, then you need to start thinking in terms of possibilities, forgetting about probabilities for the time being. Some questions that may help in that are the following:
* How much does each data point contribute to a metric (e.g. one of central tendency or one of spread)?
* Which factors / features influence the similarity between two data points and by how much?
* What do the fundamental components of a dataset look like, if they are defined by both linear and non-linear relationships among the original features?
* How can we generate new data without any knowledge of the shape or form of the original dataset?
* How can we engineer the best possible centroids in a K-means-like clustering framework?
* What is an outlier or inlier essentially and how does it relate to the rest of the dataset?

For all of these cases, assume that there is no knowledge of the statistical distributions of the corresponding variables. In fact, you are better off disregarding any knowledge of Stats whatsoever, as it’s easy to be tempted to use a probability-based approach. 

Finally, although this new way of thinking about data is fairly superior to the probabilistic one, the latter has its uses too. So, I’m not advocating that you shouldn’t learn Stats. In fact, I’d argue that only after you’ve learned Stats quite well, will you be able to appreciate the possibilistic approach to data in full. So, if you are looking into A.I., Machine Learning, or both, you may want to consider a possibilistic way of tackling uncertainty, instead of blindly following those who have vested interests in the currently dominant paradigm.