We propose a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link (in the sense of implications in mathematical logic) outcomes of specific random variables and extract valuable relations from the data. We also propose an efficient algorithm for computing the model and show its first-order optimality, despite the combinatorial nature of the learning problem. We exemplify our general framework to recommendation systems and gene expression data. We believe that the work is a significant step toward interpretable machine learning.
The paper considers a solution to a statistical association problem. The proposed solution involves a decomposition they call a kolmogorov model (what sort is not justified in any way and confused me a lot). The decomposition has two parts 1) a discrete basis function that needs to be discovered and 2) a discrete distribution over the basis elements. The define an optimization problem (2) which has a data term and some binary and simplex constraints and they propose a relaxation and decomposition of this optimization problem. They go on to claim that (mutual) causal relations can be then inferred by inspecting the representations they have learnt but they give little details on how and what impacts this distinction has in practice.  This may be obvious to a subfield expert but it is not clear to me at all. The paper is locally consistent but I have trouble understanding the contribution and placing in the broad machine learning field. 
I am not an expert in causality so I cannot evaluate the contribution but I can say that what interests me are section 2.2 and sec. 4-5. And they both require a lot better writing. 2.2 made things much more intuitive but i fail to see how the indicator variable annotations (action, scifi, etc.) can possibly come out of the data. I think this is an important point to support the interpretability claim. As for 4 I think there is room for intuition building there as well as limitations (e.g. what sort of inferences can be made and not etc.) Finally for 5 i find that very interesting but i find it difficult to have the right intuition about what the support condition means and how that helps in a practical setting.
pros:
- causality and interpretability are major directions of research
- seems like a valid contribution on an interesting problem
cons:
- the highlevel picture is relatively clear but i find important things very difficult to grasp 
- the kolmogorov model definition i find confusing but i am not an expert in causality (the introduction should give some intuition about what that is and why it is a good idea).
- find it very hard to have a coherent picture of the limitations and assess the contributions of the paper.