Related papers: Using Kolmogorov-Smirnov Distance for Measuring Di…
We study the problem of distribution shift generally arising in machine-learning augmented hybrid simulation, where parts of simulation algorithms are replaced by data-driven surrogates. We first establish a mathematical framework to…
KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence…
Machine Learning~(ML) has provided promising results in recent years across different applications and domains. However, in many cases, qualities such as reliability or even safety need to be ensured. To this end, one important aspect is to…
Kolmogorov-Smirnov (K-S) test-a non-parametric method to measure the goodness of fit, is applied for automatic modulation classification (AMC) in this paper. The basic procedure involves computing the empirical cumulative distribution…
Statistical distances quantifies the difference between two statistical constructs. In this article, we describe reference values for a distance between samples derived from the Kolmogorov-Smirnov statistic $D_{F,F'}$. Each measure of the…
The fidelity of financial market simulation is restricted by the so-called "non-identifiability" difficulty when calibrating high-frequency data. This paper first analyzes the inherent loss of data information in this difficulty, and…
This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…
The advent of high dimensional single cell data in the biomedical sciences has necessitated the development of dimensionality-reduction tools. t-SNE and UMAP are the two most frequently used approaches, allowing clear visualisation of…
We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate,…
Goodness-of-fit tests gauge whether a given set of observations is consistent (up to expected random fluctuations) with arising as independent and identically distributed (i.i.d.) draws from a user-specified probability distribution known…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
In this work we propose a methodology for assessment of pedestrian models continuous in space. With respect to the Kolmogorov-Smirnov distance between two data clouds, representing for instance simulated and the corresponding empirical…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
Estimating the test performance of software AI-based medical devices under distribution shifts is crucial for evaluating the safety, efficiency, and usability prior to clinical deployment. Due to the nature of regulated medical device…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
We establish inequalities that compare the p-Wasserstein distance to distances which are built as suprema of box measures. More precisely, when the measures are supported on $[0,1]^d$, we obtain sharp upper-bounds of the $p$-Wasserstein…
Transfer learning is an increasingly common approach for developing performant RL agents. However, it is not well understood how to define the relationship between the source and target tasks, and how this relationship contributes to…
We present a novel modulation level classification (MLC) method based on probability distribution distance functions. The proposed method uses modified Kuiper and Kolmogorov-Smirnov distances to achieve low computational complexity and…
Measuring distances of cosmological sources such as galaxies, stars and quasars plays an increasingly critical role in modern cosmology. Obtaining the optical spectrum and consequently calculating the redshift as a distance indicator could…