Related papers: Speeding up lower bound estimation in powerlaw dis…
This paper considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating…
A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
We obtain estimates for the weighted $L^1$-norm of the difference of two probability solutions to Kolmogorov equations in terms of the difference of the diffusion matrices and the drifts. Unlike the previously known results, our estimate…
A novel method for computing exact p-values of one-sided statistics from the Kolmogorov-Smirnov family is presented. It covers the Higher Criticism statistic, one-sided weighted Kolmogorov-Smirnov statistics, and the one-sided Berk-Jones…
We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data)…
After reviewing unnormalized and normalized information distances based on incomputable notions of Kolmogorov complexity, we discuss how Kolmogorov complexity can be approximated by data compression algorithms. We argue that optimal…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their…
We present an efficient algorithm that, given a discrete random variable $X$ and a number $m$, computes a random variable whose support is of size at most $m$ and whose Kolmogorov distance from $X$ is minimal, also for the one-sided…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight…
Recently, we have proposed a maximum likelihood iterative algorithm for estimation of the parameters of the Nakagami-m distribution. This technique performs better than state of art estimation techniques for this distribution. This could be…
Higher-order Markov chains play a very important role in many fields, ranging from multilinear PageRank to financial modeling. In this paper, we propose three accelerated higher-order power methods for computing the limiting probability…
One of the major problems in Machine Learning (ML) and Artificial Intelligence (AI) is the fact that the probability distribution of the test data in the real world could deviate substantially from the probability distribution of the…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
The cumulative distribution and quantile functions for the two-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. The CDF is notoriously difficult to explicitly describe and to compute, and…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…