Related papers: Class Density and Dataset Quality in High-Dimensio…

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…

Density Based Clustering are a type of Clustering methods using in data mining for extracting previously unknown patterns from data sets. There are a number of density based clustering methods such as DBSCAN, OPTICS, DENCLUE, VDBSCAN,…

Data-oriented applications, their users, and even the law require data of high quality. Research has divided the rather vague notion of data quality into various dimensions, such as accuracy, consistency, and reputation. To achieve the goal…

Density-based Out-of-distribution (OOD) detection has recently been shown unreliable for the task of detecting OOD images. Various density ratio based approaches achieve good empirical performance, however methods typically lack a…

In this paper, we use a probabilistic model to estimate the number of uncorrelated features in a large dataset. Our model allows for both pairwise feature correlation (collinearity) and interdependency of multiple features…

Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…

We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…

Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be…

Data diversity is crucial for the instruction tuning of large language models. Existing studies have explored various diversity-aware data selection methods to construct high-quality datasets and enhance model performance. However, the…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…

We aim to select data subsets for the fine-tuning of large language models to more effectively follow instructions. Prior work has emphasized the importance of diversity in dataset curation but relied on heuristics such as the number of…

We introduce the concept of a class of equivalence of molecular clouds represented by an abstract spherically symmetric, isotropic object. This object is described by use of abstract scales in respect to a given mass density distribution.…

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…

Anomaly detection is not an easy problem since distribution of anomalous samples is unknown a priori. We explore a novel method that gives a trade-off possibility between one-class and two-class approaches, and leads to a better performance…

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

We propose a new method to count objects of specific categories that are significantly smaller than the ground sampling distance of a satellite image. This task is hard due to the cluttered nature of scenes where different object categories…