Related papers: Metrics for matrix-valued measures via test functi…
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
We prove a sharp general inequality estimating the distance of two probability measures on a compact Lie group in the Wasserstein metric in terms of their Fourier transforms. We use a generalized form of the Wasserstein metric, related by…
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…
In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…
The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every pre-and-post-selected ensemble. They also extend the applicability and valid…
We consider the continuous quantum measurement of a two-level system, for example, a single-Cooper-pair box measured by a single-electron transistor or a double-quantum dot measured by a quantum point contact. While the approach most…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with…
In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient…
We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distributions with finite second moment. It derives a class of…
The quadratic Wasserstein metric has shown its power in measuring the difference between probability densities, which benefits optimization objective function with better convexity and is insensitive to data noise. Nevertheless, it is…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…
Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these…
Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein distances between this empirical measure and…