Related papers: An Explicit Conjectured Determinant Evaluation Who…
Many experiments elicit subjects' prior and posterior beliefs about a random variable to assess how information affects one's own actions. However, beliefs are multi-dimensional objects, and experimenters often only elicit a single response…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
By providing explanations for users and system designers to facilitate better understanding and decision making, explainable recommendation has been an important research problem. In this paper, we propose Counterfactual Explainable…
We analyze an extended model of the Iterated Prisoner's Dilemma where agents decide to play based on the data from their limited memory or recommendations. The cooperators can decide whether to play with the matched opponent or not. The…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
Transparency, user trust, and human comprehension are popular ethical motivations for interpretable machine learning. In support of these goals, researchers evaluate model explanation performance using humans and real world applications.…
We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the…
An automated explanation facility for Bayesian conditioning aimed at improving user acceptance of probability-based decision support systems has been developed. The domain-independent facility is based on an information processing…
Recommender systems are central to digital platforms, yet they face a fundamental trade-off between accuracy and explainability. Black-box models achieve strong performance but lack interpretability needed for trust and adoption. Existing…
We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon…
It is known that recommendations of AI-based systems can be incorrect or unfair. Hence, it is often proposed that a human be the final decision-maker. Prior work has argued that explanations are an essential pathway to help human…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
Complete non-ambiguous trees have been studied in various contexts. Recently, a conjecture was made about their determinants, and subsequently proved by Aval. An alternative proof is given here.
It is often argued that one goal of explaining automated decision systems (ADS) is to facilitate positive perceptions (e.g., fairness or trustworthiness) of users towards such systems. This viewpoint, however, makes the implicit assumption…
AI-driven outcomes can be challenging for end-users to understand. Explanations can address two key questions: "Why this outcome?" (factual) and "Why not another?" (counterfactual). While substantial efforts have been made to formalize…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
We state and prove an explicit evaluation of a certain multi-variate integral and use it to furnish a new, and shorter, proof of an elegant determinant identity of Michael Dougherty and Jon McCammond that came up in their study of critical…
We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland…