Related papers: Standardization of Weighted Ranking Correlation Co…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
We treat the problem of testing for association between a functional variable belonging to Hilbert space and a scalar variable. Particularly, we propose a distribution-free test statistic based on Kendall's Tau which is one of the most…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
We study the cross-correlations in stock price changes between the S&P 500 companies by introducing a weighted random graph, where all vertices (companies) are fully connected, and each edge is weighted. The weight assigned to each edge is…
Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure…
Canonicalization provides an architecture-agnostic method for enforcing equivariance, with generalizations such as frame-averaging recently gaining prominence as a lightweight and flexible alternative to equivariant architectures. Recent…
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…
We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/\mu)^2$ (where $L$ is a bound on…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
Sphericity test plays a key role in many statistical problems. We propose Spearman's rho-type rank test and Kendall's tau-type rank test for sphericity in the high dimensional settings. We show that these two tests are equivalent. Thanks to…
In his groundbreaking work on pair correlation, Montgomery analyzed the distribution of the differences $\gamma'-\gamma$ between ordinates $\gamma$ of the nontrivial zeros of the Riemann zeta function, assuming the Riemann Hypothesis. In…
We consider the composition optimization with two expected-value functions in the form of $\frac{1}{n}\sum\nolimits_{i = 1}^n F_i(\frac{1}{m}\sum\nolimits_{j = 1}^m G_j(x))+R(x)$, { which formulates many important problems in statistical…
Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…
This paper studies ordered weighted L1 (OWL) norm regularization for sparse estimation problems with strongly correlated variables. We prove sufficient conditions for clustering based on the correlation/colinearity of variables using the…
Clustered and longitudinal data are pervasive in scientific studies, from prenatal health programs to clinical trials and public health surveillance. Such data often involve non-Gaussian responses--including binary, categorical, and count…
Kemeny (1959) introduced a topologically complete metric space to study ordinal random variables, particularly in the context of Condorcet's paradox and the measurability of ties. Building on this, Emond & Mason (2002) reformulated Kemeny's…
Generalized correlation analysis (GCA) is concerned with uncovering linear relationships across multiple datasets. It generalizes canonical correlation analysis that is designed for two datasets. We study sparse GCA when there are…