In 2018, when I was on vacation in Kerala, I read the Book of Why by Judea Pearl. I don’t think I’ve fully grasped the details of this book. A lot of the writing seemed to suggest that methods proposed by the authors were the right way to think about causality and I wasn’t able to evaluate this claim. I need to go back and read it again. On a higher level the book is captivating for the most part and made me wonder about what causality is and what are our best efforts as humans to-date to understand causality. The next step that we have already embarked on is to help machines learn causality.

Some of the points that I can still recall are that machine learning currently can learn patterns but cannot reason, for example current machine learning methods are not equipped to handle reasoning situations like counterfactuals(what if X happened instead of Y). Judea talks a lot in this book about Bayesian networks and why they are great to evaluate causal models. I think I’d have to spend some time reading his papers to evaluate this claim, this was not a part of my curriculum and I wasn’t able to figure out the details from the brief mathematical description in this book.

One of the points from the book that I was interested in is that Judea seems to be a great fan of Path Analysis, first introduced by the population geneticist Sewall Wright. Judea considers path analysis as the precursor to lot of the causal analysis methods currently. As a geneticist I wanted to understand why(and if) path analysis is so great and how does it work.

When I was in Don Conrad’s lab we had a journal club called the legends of population genetics. Each member of the lab was assigned one or two population geneticists and each week one person would have to present a blurb about the “legend” they were assigned. I was assigned James Crow and I’ve been a fan of his ever since. Someone else was assigned Sewall Wright. Wright is considered one of the fathers of population genetics, along with Haldane and Fisher, he played an important role in the modern synthesis of the ideas of Darwin and Mendel. Wright invented F-statistics, pioneered fitness landscapes, inbreeding co-efficients, basically a lot of the bread and butter techniques that modern population geneticists use on their shiny new data. I wanted to read up on path analysis and looked it up in my reference textbooks.

Lynch and Walsh has an appendix on Path Analysis (Appendix 2). This section is easy to digest and provides more mathematical detail on path analysis and a few applications. One of the sentences in the introductory passage of the appendix reads as follows “It is not a technique for identifying the actual sources of causality, which can only come from careful experimentation. In response to periodic abuses and criticism of this technique, Wright repeatedly emphasized this point.” I think Judea’s book missed the essence of this point, I came away from the book thinking Path Analysis could be the answer to a lot of questions related to causality. I’ll try to explain path analysis briefly below and I’m sure do a horrible job, do lookup Lynch and Walsh for a good explanation.

In Path Analysis, a path diagram is constructed. The path diagram is constructed not based on observed data but on causal assumptions on how the inputs of the system $z_i$ determine the output $y$. The path coefficients are standardized partial regression coefficients(standardizde using the standard deviations of the variables). The correlation between two nodes on the path are then specified as a product of the path coefficients and correlation coefficients between the nodes the lie on the path. Some of the segments of the path can be bi-directional which specifies that the causal relation can go both ways. Consider the phenotypes of a mom/dad/child trio as an example path diagram. The correlation between the phenotype of an individual can be written as the sum of genetic and environmental contributions. We know the direction of the path-diagram for a trio, the arrows point from the paternal genotypes to the child’s genotype and phenotype. We can thus calculate the correlation between the childs phenotype and the parent’s phenotype using the path coeffecients and correlation coefficients between the parents and the parent and child.

The path diagram is thus extremely useful in this case since the underlying causal structure is known - the direction of effects is from the parents to the child. This makes a huge difference. If we are just looking at a bunch of columns of data with no idea about the direction of effects between them the path analysis will not be of much use. Knowing a bit of prior information, the direction of causality in this case, makes a huge difference.

Wright was so far ahead of his time, there was hardly any genome sequence data when he came up with these ideas. These were all just a product of his thinking about reality.