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We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
The advent of high-throughput sequencing technologies has lead to vast comparative genome sequences. The construction of gene-gene interaction networks or dependence graphs on the genome scale is vital for understanding the regulation of…
The probability distribution, $p(\mathrm{DM})$ of cosmic dispersion measures (DM) measured in fast radio bursts (FRBs) encodes information about both cosmology and galaxy feedback. In this work, we study the effect of feedback parameters in…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
Neural networks are suggested for learning a map from $d$-dimensional samples with any underlying dependence structure to multivariate uniformity in $d'$ dimensions. This map, termed DecoupleNet, is used for dependence model assessment and…
Independence screening methods such as the two sample $t$-test and the marginal correlation based ranking are among the most widely used techniques for variable selection in ultrahigh dimensional data sets. In this short note, simple…
Recently, researches related to unsupervised disentanglement learning with deep generative models have gained substantial popularity. However, without introducing supervision, there is no guarantee that the factors of interest can be…
We study the effect of positive correlations on the critical threshold of site and bond percolation in a square lattice with d = 2. We propose two algorithms for generating dependent lattices with minimal correlation length and non-negative…
This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Negative sampling schemes enable efficient training given a large number of classes, by offering a means to approximate a computationally expensive loss function that takes all labels into account. In this paper, we present a new connection…
Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective of many computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluating f at a finite number of points in [0,1)^d. There is a design issue in the choice of…
Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower…
Detecting dependence between variables is a crucial issue in statistical science. In this paper, we propose a novel metric called label projection correlation to measure the dependence between numerical and categorical variables. The…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning…
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Let $f:[0,1]^d\to\mathbb{R}$ be a completely monotone integrand as defined by Aistleitner and Dick (2015) and let points $\boldsymbol{x}_0,\dots,\boldsymbol{x}_{n-1}\in[0,1]^d$ have a non-negative local discrepancy (NNLD) everywhere in…