Robert R. Tucci

Robert R. Tucci

Determining a causal DAG (directed acyclic graph) for a problem under consideration, is a major roadblock when doing Judea Pearl's Causal Inference (CI) in Statistics. The same problem arises when doing CI in Artificial Intelligence (AI) and Machine Learning (ML). As with many problems in Science, we think Nature has found an effective solution to this problem. We argue that human and animal brains contain an explicit engine for doing CI, and that such an engine uses as input an atlas (i.e., collection) of causal DAGs. We propose a simple algorithm for constructing such an atlas from a library of books or videos/movies. We illustrate our method by applying it to a database of randomly generated Tic-Tac-Toe games. The software used to generate this Tic-Tac-Toe example is open source and available at GitHub.

Robert R. Tucci

We propose a Goodness of Causal Fit (GCF) measure which depends on Judea Pearl's ``do" interventions. This is different from Goodness of Fit (GF) measures, which do not use interventions. Given a set ${\cal G}$ of DAGs with the same nodes, to find a good $G\in {\cal G}$, we propose plotting $GCF(G)$ versus $GF(G)$ for all $G\in {\cal G}$, and finding a graph $G\in {\cal G}$ with a large amount of both types of goodness.

Robert R. Tucci

The goal of this paper is to generalize classical d-separation and classical Belief Propagation (BP) to the quantum realm. Classical d-separation is an essential ingredient of most of Judea Pearl's work. It is crucial to all 3 rungs of what Pearl calls the 3 rungs of Causation. So having a quantum version of d-separation and BP probably implies that most of Pearl's Bayesian networks work, including his theory of causality, can be translated in a straightforward manner to the quantum realm.

Robert R. Tucci

In this paper, we define a new information theoretic measure that we call the "uprooted information". We show that a necessary and sufficient condition for a probability $P(s|do(t))$ to be "identifiable" (in the sense of Pearl) in a graph $G$ is that its uprooted information be non-negative for all models of the graph $G$. In this paper, we also give a new algorithm for deciding, for a Bayesian net that is semi-Markovian, whether a probability $P(s|do(t))$ is identifiable, and, if it is identifiable, for expressing it without allusions to confounding variables. Our algorithm is closely based on a previous algorithm by Tian and Pearl, but seems to correct a small flaw in theirs. In this paper, we also find a {\it necessary and sufficient graphical condition} for a probability $P(s|do(t))$ to be identifiable when $t$ is a singleton set. So far, in the prior literature, it appears that only a {\it sufficient graphical condition} has been given for this. By "graphical" we mean that it is directly based on Judea Pearl's 3 rules of do-calculus.

Robert R. Tucci

This is a purely pedagogical paper with no new results. The goal of the paper is to give a fairly self-contained introduction to Judea Pearl's do-calculus, including proofs of his 3 rules.