Related papers: Stein Estimation for Infinitely Divisible Laws
We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective…
By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical…
Penalized Least Squares are widely used in signal and image processing. Yet, it suffers from a major limitation since it requires fine-tuning of the regularization parameters. Under assumptions on the noise probability distribution,…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
We introduce a simple iterative technique for bounding derivatives of solutions of Stein equations $Lf=h-\mathbb{E}h(Z)$, where $L$ is a linear differential operator and $Z$ is the limit random variable. Given bounds on just the solutions…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either…
We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present…
The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics.…
We study the entanglement detection by using mutually unbiased measurements and provide a quantum separability criterion that can be experimentally implemented for arbitrary $d$-dimensional bipartite systems. We show that this criterion is…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…
Accuracy and interpretability are two essential properties for a crime prediction model. Because of the adverse effects that the crimes can have on human life, economy and safety, we need a model that can predict future occurrence of crime…
We investigate the role of reinsurance in maximizing the wealth of an insurance company. We use Liu's uncertainty theory (B. Liu, 2007) for the problem modeling and follow-up computations. The uncertainty measure of ruin for the insurance…
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…