Related papers: Interval Spacing
Transit agencies have been removing a large number of bus stops, but discussions around the bus stop spacings exhibit a lack of clarity and data for comparison. This paper proposes new terminology and concepts for statistical consideration…
The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation…
The aim of ordinal classification is to predict the ordered labels of the output from a set of observed inputs. Interval-valued data refers to data in the form of intervals. For the first time, interval-valued data and interval-valued…
In pattern recognition, learning, and data mining one obtains information from information-carrying objects. This involves an objective definition of the information in a single object, the information to go from one object to another…
This note addresses the input and output of intervals in the sense of interval arithmetic and interval constraints. The most obvious, and so far most widely used notation, for intervals has drawbacks that we remedy with a new notation that…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
In this short technical report, we define on the sample space R^D a distance between data points which depends on their correlation. We also derive an expression for the center of mass of a set of points with respect to this distance.
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…
Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing.…
The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…
Comparing the top $k$ elements between two or more ranked results is a common task in many contexts and settings. A few measures have been proposed to compare top $k$ lists with attractive mathematical properties, but they face a number of…
Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
To analyse the significance of the digits used for interval bounds, we clarify the philosophical presuppositions of various interval notations. We use information theory to determine the information content of the last digit of the numeral…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…
Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…