Related papers: Generalizing the Mean and Variance to Categorical …

We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider a class of generalized coarsened procedures for confounding. At a…

Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…

Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…

We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of…

Multi-modal learning has achieved remarkable success by integrating information from various modalities, achieving superior performance in tasks like recognition and retrieval compared to uni-modal approaches. However, real-world scenarios…

We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are…

Visualization as a discipline often grapples with generalization by reasoning about how study results on the efficacy of a tool in one context might apply to another context. This work offers an account of the logic of generalization in…

This paper evaluates global-scale dialect identification for 14 national varieties of English as a means for studying syntactic variation. The paper makes three main contributions: (i) introducing data-driven language mapping as a method…

This paper demonstrates how to use generative models trained for image synthesis as tools for visual data mining. Our insight is that since contemporary generative models learn an accurate representation of their training data, we can use…

Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…

Quantifying the similarity between datasets has widespread applications in statistics and machine learning. The performance of a predictive model on novel datasets, referred to as generalizability, depends on how similar the training and…

In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution…

We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of…

Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial…

Search engine results pages are usually abstracted as binary relevance vectors and hence are categorical data, meaning that only a limited set of operations is permitted, most notably tabulation of occurrence frequencies, with determination…

We describe new datasets for studying generalization from easy to hard examples.

An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…