相关论文: "Proper" Shift Rules for Derivatives of Perturbed-…
The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
We propose a robust parameter estimation method for dynamical systems based on Statistical Learning techniques which aims to estimate a set of parameters that well fit the dynamics in order to obtain robust evidences about the qualitative…
Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…
Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the…
Many important applications in biochemistry, materials science, and catalysis sit squarely at the interface between quantum and statistical mechanics: coherent evolution is interrupted by discrete events, such as binding of a substrate or…
In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem…
In this work, we establish the maximal $\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time. These schemes include…
Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…
We consider estimation of a single unknown parameter embedded in a quantum state. Quantum Cram\'er-Rao bound (QCRB) is the ultimate limit of the mean squared error for any unbiased estimator. While it can be achieved asymptotically for a…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion,…
We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process) in the presence of jumps extending the seminal work…
Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…
We obtain sharp large deviation estimates for exceedance probabilities in dependent triangular array threshold models with a diverging number of latent factors. The prefactors quantify how latent-factor dependence and tail geometry enter at…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…