arXiv subjects

Reihaneh Malekian

Publications and source records attributed to Reihaneh Malekian.

3 recordsLinked to original sources

arXiv2026

LDP for Tensor Forms

In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of the "bad" cut norm. Using the LDP, we analyze a Gibbs measure with a tensor-valued Hamiltonian, and characterize the optimizers of the limiting variational problem in terms of a functional fixed point equation. As applications, we focus on several concrete examples, which include monochromatic subgraph counts in sparse random graphs, Erdős-Rényi hypergraphs, and a generalized Potts statistic of order $v\ge 2$. Studying the optimization problem, we give sufficient conditions for uniqueness of the optimizer, as well as for existence of constant optimizers (replica symmetry). Our results demonstrate universal weak laws for a large class of tensor Gibbs models with approximately regular tensors.

math.PR↗

arXiv2025

Is speckle noise more challenging to mitigate than additive noise?

We study the problem of estimating a function in the presence of both speckle and additive noises, commonly referred to as the de-speckling problem. Although additive noise has been thoroughly explored in nonparametric estimation, speckle noise, prevalent in applications such as synthetic aperture radar, ultrasound imaging, and digital holography, has not received as much attention. Consequently, there is a lack of theoretical investigations into the fundamental limits of mitigating the speckle noise.This paper is the first step in filling this gap. Our focus is on investigating the minimax estimation error for estimating a $β$-Hölder continuous function and determining the rate of the minimax risk. Specifically, if $n$ represents the number of data points, $f$ denotes the underlying function to be estimated, $\hatν_n$ is an estimate of $f$, and $σ_n$ is the standard deviation of the additive Gaussian noise, then $\inf_{\hatν_n} \sup_f \mathbb{E}_f\| \hatν_n - f \|^2_2$ decays at the rate $(\max(1,σ_n^4)/n)^{\frac{2β}{2β+1}}$. Note that the rate achieved under purely additive noise is $({σ_n^2/n})^{\frac{2β}{2β+1}}$. We will provide a detailed comparison of this rate with the one obtained in the presence of both noise types across different regimes of their relative magnitudes, and discuss the insights that emerge from these comparisons.

math.ST↗

arXiv2024

Matrix Concentration: Order versus Anti-order

The matrix Markov inequality by Ahlswede was stated using the Loewner anti-order between positive definite matrices. Wang use this to derive several other Chebyshev and Chernoff-type inequalities (Hoeffding, Bernstein, empirical Bernstein) in the Loewner anti-order, including self-normalized matrix martingale inequalities. These imply upper tail bounds on the maximum eigenvalue, such as those developed by Tropp and howard et al. The current paper develops analogs of all these inequalities in the Loewner order, rather than anti-order, by deriving a new matrix Markov inequality. These yield upper tail bounds on the minimum eigenvalue that are a factor of d tighter than the above bounds on the maximum eigenvalue.

math.PR↗