Related papers: A Baseline $T\log^2 T$ Upper Bound for KL-Regulari…
We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as $T \rightarrow \infty$ for a set of $t \in [T, 2T]$ of…
Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…
This study introduces a novel approach for estimating plane-wave coefficients in sound field reconstruction, specifically addressing challenges posed by error-in-variable phase perturbations. Such systematic errors typically arise from…
This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density $\rho$ and a probability measure $\mu$ on R^d , which we denote T$\mu$. Assuming that the source density $\rho$ is…
The beat time {\tau}_{fpt} associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound {\tau}_{fpt}\sim 1/{\delta}{\omega}. We show, both experimentally and…
In this article, we give explicit bounds of order $\log t$ for $\sigma$ close to $1$, for two quantities: $|\zeta'(\sigma +it)/\zeta(\sigma +it)|$ and $|1/\zeta(\sigma +it)|$. We correct an error in the literature, and especially in the…
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
We prove a near-unconditionality property for the normalized Haar basis of $L_1[0,1]$.
In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…
We study the estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller…
Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is $1/\tau_\text{tr} = 2\pi \lambda T$, where $\lambda$ is a dimensionless strength of…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive novel guarantees for its convergence rate when the involved…
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples and where the goal is to find the closest map to the ground…
We provide an explicit family of pairs $(\alpha, \beta) \in \mathbb{R}^k \times \mathbb{R}^k$ such that for sufficiently regular $f$, there is a constant $C>0$ for which the theta sum bound…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…