Related papers: Counterexamples to "The Blessings of Multiple Caus…
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an…
Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…
Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon…
This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof…
Proximal causal inference (PCI) has emerged as a promising framework for identifying and estimating causal effects in the presence of unobserved confounders. While many traditional causal inference methods rely on the assumption of no…
In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
Combining evidence from different sources can be achieved with Bayesian or Dempster-Shafer methods. The first requires an estimate of the priors and likelihoods while the second only needs an estimate of the posterior probabilities and…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Counterfactuals answer questions of what would have been observed under altered circumstances and can therefore offer valuable insights. Whereas the classical interventional interpretation of counterfactuals has been studied extensively,…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
Inferring causal effects of a treatment, intervention or policy from observational data is central to many applications. However, state-of-the-art methods for causal inference seldom consider the possibility that covariates have missing…
It is often asserted that to control for the effects of confounders, one should include the confounding variables of concern in a statistical model as a covariate. Conversely, it is also asserted that control can only be concluded by…
One of the most pressing issues in AI in recent years has been the need to address the lack of explainability of many of its models. We focus on explanations for discrete Bayesian network classifiers (BCs), targeting greater transparency of…
We establish the independence of multipliers for polynomial endomorphisms of $\mathbb C^n$ and endomorphisms of $\mathbb P^n.$ This allows us to extend results about the bifurcation measure and the critical height obtained in…
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…