Related papers: The P versus NP Brief

This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…

In order to build reliable and trustworthy NLP applications, models need to be both fair across different demographics and explainable. Usually these two objectives, fairness and explainability, are optimized and/or examined independently…

If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

We compare a traditional and non-traditional view on the subject of P-partitions, leading to formulas counting linear extensions of certain posets.

In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…

This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.

For each type of number, structures that differ by arbitrary scaling factors and are isomorphic to one another are described. The scaling of number values in one structure, relative to the values in another structure, must be compensated…

In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (1998).

We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…

Reconciliation of frequentist and Bayesian approaches to elementary treatment of data in nuclear and particle physics is attempted. Unique procedure to express the significance of a small count in presence of background is henceforth…

We discuss the nature and a general formulation of the relativity principle and we show that it can be justified starting from a strictly operational point of view. We give some remark on the connection with the spacetime symmetry groups.…

The purpose of the paper is to present an short proof of the Chuang's inequality.

Fairness assumptions are a valuable tool when reasoning about systems. In this paper, we classify several fairness properties found in the literature and argue that most of them are too restrictive for many applications. As an alternative…

After a very brief review of twentieth century elementary particle physics, prospects for the next century are discussed. First and most important are technological limits of opportunities; next, the future experimental program, and finally…

This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…

A growing effort in NLP aims to build datasets of human explanations. However, the term explanation encompasses a broad range of notions, each with different properties and ramifications. Our goal is to provide an overview of diverse types…

Blanket statements of equivalence between causal concepts and purely probabilistic concepts should be approached with care. In this short note, I examine a recent claim that counterfactual fairness is equivalent to demographic parity. The…

The rise of concern around Natural Language Processing (NLP) technologies containing and perpetuating social biases has led to a rich and rapidly growing area of research. Gender bias is one of the central biases being analyzed, but to date…