Also available on the web as HTML (takes a few seconds to open because it’s a 30 MB single file) (IMPORTANT: Open the HTML in an INCOGNITO tab. If you open the HTML in a regular tab, you are likely to get an old version residing in cache.) https://www.ar-tiste.com/bayesuvius.html
I’m considering writing a chapter on Causal Genomics (CG) for my book Bayesuvius. Unfortunately, my PhD is in physics so I know approx zero about genomics. Are there any people in this Reddit that work in CG and would care to share their personal opinion on what are the most important papers so far in CG? Also, are there any pedagogical materials intended to teach someone, starting from scratch, all he/she needs to learn to understand a paper in CG?
Just prepared this slide for a presentation. Très magnifique.
How Mappa Mundi (free, open source, MIT license) and all humans distinguish between correlation and causation, said with a single picture that even an 8 year old can understand, and say: “I knew that. I’ve been doing that all my life”.
Probability that ice cream causes sharks is low so no arrow from ice cream to sharks in DAG. Probability that rain causes green sprouts is high. So arrow from rain to green sprouts in DAG.
I was recently asked by someone (let me call him Mr. XXX) on social media, whether I disagree with Judea Pearl about some issue concerning Causal Inference. I felt as if I had been accused of apostasy before the Holy See. This was my reply (after cleaning it up a bit) to Mr. XXX:
Yes, I disagree with Pearl in several ways.
He assumes that all data is presented in the dataset format, with a column for each feature and no notion of time so time independent process. For him, the nodes of a DAG are not events in spacetime. Mappa Mundi assumes data is given in chronological order, and nodes ARE events
I also think Pearl’s Do Calculus is overly complicated and I have produced an alternative technique called NDC (Not Do Calculus) that can be used instead of Do Calculus. (see chapter entitled “Do Calculus proofs” in my book Bayesuvius)
I also think that his large causality book is unreadable. I like my book Bayesuvius much more. Must be because I wrote it. LOL
I also think that Pearl is wrong when he claims that you cannot speak about counterfactuals (CF) if you use Bayesian Networks. He claims that SCM are necessary to speak of CF. The logical conclusion of that is that Donald Rubin’s Potential Outcomes theory is wrong, which he also claims. LOL
In my book Bayesuvius, I show that Rubin’s theory and Pearl’s theory are equivalent. Both of them claim that the other guys theory is wrong. LOL
I did my homework and studied the work of Pearl and Rubin and economists like Imbens. I leaned the good parts of each, and then tried to grow the theory further. It seems that you believe Pearl is never wrong, and it’s a sin to contradict him. That is not Science, Mr. XXX.
A “digital twin” is just a modern term for a “simulation”.
Expecting that a digital twin will be useful for doing Causal Inference is just wishful thinking. A digital twin can only model a small, well understood theoretically, facet of a system, such as the aerodynamics of different shape cars or something. You cannot make a digital twin of a person such that the twin responds like a person to any med for any disease, because to program into a digital twin how to respond to each disease, the programmer first has to understand that disease and what factors influence it. Learning the cause-effect DAG of each disease has to be done before you build the digital twin, not after. That is, unless the digital twin is so elaborate, that it’s almost indistinguishable from a real person.
But a super elaborate digital twin of a person would be like a single human patient. One can’t decide how to treat each strata of an entire population based on a single human patient.
The best digital twin of a person already exists: it’s another person.
The above paper and software by a group at MIT (Álvaro Martínez-Sánchez, Gonzalo Arranz & Adrián Lozano-Durán) proposes a new Causal AI method called SURD. The goal of this blog post is to compare the SURD method with the method used in the Mappa Mundi (MM) Project. Here are some key differences and similarities between the two methods:
For both MM and SURD, the nodes of the DAG are “events”. This is a paradigm shift compared to what the followers of Pearl and Rubin Causal Inference assume. For Pearl cadets, the nodes of a DAG do not occur at a definite time. Rubin cadets like Imbens do not even use DAGs, for political reasons.
SURD does not discover the variables (i.e., nodes) of the DAG. Those are an input. What it tries to discover are the arrows of the DAG. MM discovers both the nodes and the arrows.
SURD requires a time series for each of the nodes of the DAG. MM can extract DAGs from a time series (See CausalFitbit part of MM), but this is only one of its modes of operation. MM can also extract DAGs from plain text, as long as the text tells a story in chronological order (no flash backs or time travel shenanigans)
SURD uses DAGs but does not stress the importance of storing the DAGs it discovers in a directory. I like to call a directory of DAGs, a DAG atlas. MM stores DAGs in a DAG atlas.
SURD does not use LLMs or rdf triples (“semantic triples”). MM uses both of these. Note that MM does not use prompt driven LLM (yuck). An LLM, a.k.a. transformer, consists of two parts, an encoder and a decoder. MM only uses the encoder half of an LLM. In particular, MM uses BERT, the first ever transformer encoder. MM uses BERT in two ways: First (using the Openie6 algo), to extract rdf triples (subject, verb, object) from text. These rdf triples are the nodes/events of the DAG. Second (using the popular sBERT software), to measure the similarity between two events. MM distinguishes between correlation and causation using a simple idea explained with a picture of event “bridges” that appears in the white paper that is included with the MM software.
#4 might sound like a trivial quibble but it isn’t, IMHO. Most attempts to date to do Causal AI do not compile a DAG atlas. Many of them don’t even use DAGs. For example, the Causal AI methods (“Flow Networks”) proposed by Bengio et al use Reinforcement Learning (RL) to do CI. It might be argued that in RL, a DAG is discovered, but it is implicit in the weights of a NN. But an explicit DAG that is stored in a DAG atlas, is definitely not produced by RL.
As I have explained in previous blog posts, the benefits of using DAGs and a DAG atlas are yuge:
DAGs can be stored in a DAG atlas for future re-use, so you don’t have to discover them over and over again
A DAG atlas is portable between models
DAGs are explainable. Neural Nets aren’t.
Most Causal Inference (CI) theory (by Pearl and Rubin) is based on DAGs or is greatly clarified by them. So any Causal AI method that does not use DAGs must forgo the rich toolset of CI.
Mappa Mundi (MM) is the part of my Mappa Mundi Project that extracts causal DAGs from text. More generally, MM can be described as Causal_AI/Causal_DAG_Discovery software.
Having received a Ph.D. in physics, I am well informed on the subjects of thermodynamics, the physics of phase transitions and the Renormalization Group (RG) technique. Hence, I could not help but notice and find remarkable that my MM algorithm requires a parameter, call it , that controls the complexity of the DAG that it extracts from text. This parameter seems very similar to the energy scale parameter that is used in a RG equation. This begs the question, is MM performing a RG transformation? That would not be too hard to believe, since anybody that knows about Bayesian Networks (bnets) and RG has probably told him or her self, gee, summing over the values of a node of a bnet is like the perfect RG transformation that leads from a bnet with nodes to one with nodes.
As you might know, RG is an approximation that is valid only in the vicinity of a second order phase transition (2PT). At a first order phase transition (1PT), the first derivative of the free energy is discontinuous. At a 2PT, the first derivative of the free energy is continuous but its second derivative is discontinuous. For example, in the phase diagram for water shown below, the boundary lines and the triple point are 1PT, whereas the critical point is a 2PT. In general, any critical point is a 2PT but not all 2PT are critical points. For example, the Curie Temperature of a ferromagnet is a 2PT but not a critical point. The critical point of water is the highest temperature at which gas and liquid phases coexist. The triple point of water is the point at which gas/liquid/solid coexist.
RG can be used to map out the phase diagram in the vicinity of a 2PT such as the critical point of water. Note that the phase diagram exists whether you use the RG approximation or not. Using the RG approximation just facilitates the approximate calculation of its phase boundaries.
All this begs the question that is the title of this blog post. My opinion is that we should expect them. Given nodes, the transition from when there are no arrows between them to one or more arrows between them, seems like a phase transition. Also when a bunch of disconnected DAGs merge to form a single giant DAG, seems like a phase transition.
The idea of a causal phase transition is not new in physics. It arises in quantum gravity, for example in this paper: https://arxiv.org/abs/1205.1229 But causality and phase transitions are not strongly wedded to such esoterica as quantum gravity. They play a fundamental role in all kinds of everyday physics. And perhaps AI too.
Sorry for not posting much in 2024. Witnessing the Gaza genocide and the sheer evilness of the Zio-Nazi Israelis and the American gov that funds them, has drained me emotionally during 2024. It has been a daily gut-punch and shedding of tears. It has totally transformed, irrevocably and forever, my opinion of the governments of the US, Israel, UK, France, and Germany, and of many people who have supported the genocide or did not speak against it. For the rest of my life, the first question I will ask when judging a scientist, or a politician or a corporation, or a journalist, or a news outlet, or an actor or a musician, will be: did they support (actively or passively, by staying quiet) the Palestinian Holocaust? If you did, I will shun you and boycott you as if you had the plague, and I will encourage my progeny and friends to do the same.
I think 2024 was the year that everyone who lives in the West woke up to fact that we are not the good guys…. pic.twitter.com/euiZpZaPEf
In the past few weeks, I revised the chapter entitled “Do Calculus Proofs” of my book Bayesuvius. I started writing this book about 4 years ago, at the height of Covid, and I’ve been continuously adding to it and improving it ever since. From the very beginning of the writing of Bayesuvius, I have aspired to present within its pages a new heuristic graphical technique, call it the Not Do Calculus (NDC) technique, that can be used to prove Pearl identifiability WITHOUT using Pearl’s 3 rules of Do Calculus—using instead only first principles, such as the d-separation theorem and basic principles from Probability Theory.
My NDC technique has been gradually improving, as happens when you practice the sport of Science religiously for a long time. At first, I have to admit, NDC was kind of shaky and handwavy. However, in the past 2 weeks, I had another crack at NDC, and I believe this time, it’s reached a level of rigor and sophistication high enough that it warrants a blog post in my internationally not acclaimed blog.
Below I present a SIMPLE proof of the Front Door Adjustment Formula using NDC. I also present a SIMPLE proof that Pearl’s Napkin Problem is NOT identifiable, despite his claim to the contrary. It’s a very simple proof, so if you can find an error in it, please let me know. The pics below are just meant to pique your interest and challenge you to prove me wrong. If you truly want to understand NDC, the best way is to read the chapter in Bayesuvius entitled “Do Calculus Proofs”.
Mastodon is often disliked by newbie users. I think the reason is because they find it confusing at first. I certainly did. I had to develop a mental model of how it works before I started loving it. In this blog post, I will explain that mental model. It’s an analogy. Consider pairs A–>B, where A is a computer term and B is an analogy.
server –> town
system administrator of a server –> town mayor
Alice’s account on server S –> Alice’s home in town S
mastodon –> a country with many towns
fediverse –> the whole world, many countries, each containing many towns
post on any social network like X, Threads, Mastodon, BlueSky, etc, –> email message
Mastodon is like a country with thousands of towns. For example, @mastodon.social, @mastodon.world and @threads.net are towns. I actually have homes in all 3 of those towns. You are not limited to living in only one town. If you turn ON the “fediverse sharing” switch in your threads account, your emails are all posted publicly at the @threads.net town. Suppose I am currently living (i.e., signed in) in town @my_town and I follow an account called @alice in the town @juneau. Then the mayor of @my_town tells the mayor of @juneau, hey, from now on send me A LINK to every email sent out by @alice. (unfortunately, @alice’s emails are only stored @juneau. If @juneau erases of @alice’s emails, @my_town can no longer see them) The mayor of @juneau starts doing so. But not only are the emails of @alice visible to me, but to everyone else in @my_town. It’s as if they had been posted in @my_town’s bulletin board for everyone in @my_town to see. So basically, each town displays publicly on its bulletin board only a subset of all emails sent by all persons in the country. Different towns display on their bulletin board a different subsets of emails, depending on the tastes of the inhabitants of the town. I can still view @alice’s posts at @juneau from @my_town, even if I don’t follow @alice. It’s just that if I follow @alice, she will appear in my “for you” and in @my_town’s bulletin board.
This paper should mention work that is almost one year old that proposes and implements in the open source software Mappa_Mundi, the same definition of causality between two time series, except in the DISCRETE case. This paper is very creative and novel in the sense that it extends the Mappa Mundi definition of causality to the stochastic differential equations domain, but their definition of causality is not new: it has been enunciated before in the DISCRETE case by Mappa_Mundi.
Este trabajo debiera mencionar un trabajo de casi un año de antigüedad que propone e implementa en el software de código abierto Mappa_Mundi, la misma definición de causalidad entre dos series temporales, excepto en el caso DISCRETO. Este artículo es muy creativo y novedoso en el sentido de que extiende la definición de causalidad de Mappa Mundi al dominio de las ecuaciones diferenciales estocásticas, pero su definición de causalidad no es nueva: ha sido enunciada antes en el caso DISCRETO por Mappa_Mundi. Referencias:
, that controls the complexity of the DAG that it extracts from text. This parameter 
nodes to one with 
nodes.
Quantum Bayesian Networks 