Related papers: Set Theory and the Analyst
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
The smooth development of large parts of mathematics hinges on the idea that some sets are `small' or `negligible' and can therefore be ignored for a given purpose. The perhaps most famous smallness notion, namely `measure zero', originated…
What makes sets, or more precisely, the category {\bf Set} important in Mathematics are the well known {\it two} specific ways in which arbitrary mappings $f : X \longrightarrow Y$ between any two sets $X, Y$ can {\it fail} to be…
Human evaluation of generated language through pairwise preference judgments is pervasive. However, under common scenarios, such as when generations from a model pair are very similar, or when stochastic decoding results in large variations…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
Recent advances in meta-learning has led to remarkable performances on several few-shot learning benchmarks. However, such success often ignores the similarity between training and testing tasks, resulting in a potential bias evaluation.…
Our study revisits the problem of accuracy-fairness tradeoff in binary classification. We argue that comparison of non-discriminatory classifiers needs to account for different rates of positive predictions, otherwise conclusions about…
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…
This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication…
Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be…
Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…
Existing methods to measure sentence similarity are faced with two challenges: (1) labeled datasets are usually limited in size, making them insufficient to train supervised neural models; (2) there is a training-test gap for unsupervised…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…