Time and time again, Judea Pearl makes the point on Twitter to neural net advocates that they are trying to do a provably impossible task, to derive a model from data. I could be wrong, but this is what I think he means.

When Pearl says “data”, he is referring to what is commonly called a dataset. A dataset is a table of data, where all the entries of each column have the same units, and measure a single feature, and each row refers to one particular sample or individual. Datasets are particularly useful for estimating probability distributions and for training neural nets. When Pearl says a “model“, he is referring to a DAG (directed acyclic graph) or a bnet (Bayesian Network= DAG + probability table for each node of DAG).

Sure, you can try to derive a model from a dataset, but you’ll soon find out that you can only go so far.

The process of finding a partial model from a dataset is called structure learning (SL).  SL can be done quite nicely with Marco Scutari’s open source program bnlearn. There are 2 main types of SL algorithms: score-based and constraint based. The first and still very competitive constraint-based SL algorithm was the Inductive Causation (IC) algorithm proposed by Pearl and Verma in 1991. So Pearl is quite aware of SL. The problem is that SL often cannot narrow down the model to a single one. It finds an undirected graph (UG), and it can determine the direction of some of the arrows in the UG, but it is often incapable, for well understood fundamental –not just technical– reasons, of finding the direction of ALL the arrows of the UG. So it often fails to fully specify a DAG model.

Let’s call the ordered pair (dataset, model) a data SeMo . Then what I believe Pearl is saying is that a dataset is model-free or model-less (although sometimes one can find a partial model hidden in there). A dataset is not a data SeMo.

Sample usage of term data SeMo: The vast library of data SeMo’s in our heads allows us to solve CAPTCHAs quickly and effortlessly. What fun!