Related papers: How To Overcome Richness Axiom Fallacy

This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate…

Determining the quality of the results obtained by clustering techniques is a key issue in unsupervised machine learning. Many authors have discussed the desirable features of good clustering algorithms. However, Jon Kleinberg established…

The widespread use of machine learning has raised the question of quantum supremacy for supervised learning as compared to quantum computational advantage. In fact, a recent work shows that computational and learning advantage are, in…

In 2002, Kleinberg proposed three axioms for distance-based clustering, and proved that it was impossible for a clustering method to satisfy all three. While there has been much subsequent work examining and modifying these axioms for…

Machine learning tasks may admit multiple competing models that achieve similar performance yet produce conflicting outputs for individual samples -- a phenomenon known as predictive multiplicity. We demonstrate that fairness interventions…

Learning classifiers using skewed or imbalanced datasets can occasionally lead to classification issues; this is a serious issue. In some cases, one class contains the majority of examples while the other, which is frequently the more…

At the zero lower bound, the New Keynesian model predicts that output and inflation collapse to implausibly low levels, and that government spending and forward guidance have implausibly large effects. To resolve these anomalies, we…

Ranking individuals based on their performance in different coalitions is a problem emerging in various domains (teams sports, scientific evaluation, argumentation, etc.). Often, for practical reasons, the number of comparable coalitions is…

In the context of a large class of stochastic processes used to describe the dynamics of wealth growth, we prove a set of inequalities establishing necessary and sufficient conditions in order to avoid infinite wealth concentration. These…

Logarithmic score and information divergence appear in both information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to the use…

Logarithmic score and information divergence appear in information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to regret…

Consider a binary decision making process where a single machine learning classifier replaces a multitude of humans. We raise questions about the resulting loss of diversity in the decision making process. We study the potential benefits of…

Stability issues with reinforcement learning methods persist. To better understand some of these stability and convergence issues involving deep reinforcement learning methods, we examine a simple linear quadratic example. We interpret the…

Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…

Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting…

We explain that the difficulties of training deep neural networks come from a syndrome of three consistency issues. This paper describes our efforts in their analysis and treatment. The first issue is the training speed inconsistency in…

Empirical risk minimization, a cornerstone in machine learning, is often hindered by the Optimizer's Curse stemming from discrepancies between the empirical and true data-generating distributions.To address this challenge, the robust…

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…

Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results…

A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…