Related papers: Roy's largest root under rank-one alternatives:The…
Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario…
We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much…
Reinforcement Learning with Verifiable Rewards (RLVR) has established itself as the dominant paradigm for instilling rigorous reasoning capabilities in Large Language Models. While effective at amplifying dominant behaviors, we identify a…
We develop a framework for spectrum sensing in cooperative amplify-and-forward cognitive radio networks. We consider a stochastic model where relays are assigned in cognitive radio networks to transmit the primary user's signal to a…
The top eigenvalues of rank $r$ spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for…
This article studies a Newton-like method already used by several authors but which has not been thouroughly studied yet. We call it the robust-variance scoring (RVS) algorithm because the main version of the algorithm that we consider…
Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
The statistical behaviour of the smallest eigenvalue has important implications for systems which can be modeled using a Wishart-Laguerre ensemble, the regular one or the fixed trace one. For example, the density of the smallest eigenvalue…
This paper addresses one of the classical problems in random matrix theory-- finding the distribution of the maximum eigenvalue of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative…
This study investigates a robust screening problem under distributional ambiguity, where a seller is uncertain about a buyer's true valuation distribution, knowing only that it lies near a reference distribution measured by the Wasserstein…
A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density…
The r largest order statistics approach is widely used in extreme value analysis because it may use more information from the data than just the block maxima. In practice, the choice of r is critical. If r is too large, bias can occur; if…
Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model.…
In reinforcement learning, two objective functions have been developed extensively in the literature: discounted and averaged rewards. The generalization to an entropy-regularized setting has led to improved robustness and exploration for…
The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…
This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance…
We study the problem of approximating the largest root of a real-rooted polynomial of degree $n$ using its top $k$ coefficients and give nearly matching upper and lower bounds. We present algorithms with running time polynomial in $k$ that…