相关论文: Improvement of two Hungarian bivariate theorems
This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…
The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme…
We study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov…
McDiarmid's inequality has recently been proposed as a tool for setting margin requirements for complex systems. If $F$ is the bounded output of a complex system, depending on a vector of $n$ bounded inputs, this inequality provides a bound…
Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…
Uniform and nonuniform Berry--Esseen (BE) bounds of optimal orders on the closeness to normality for general abstract nonlinear statistics are given, which are then used to obtain optimal bounds on the rate of convergence in the delta…
We present improved numerical approximations to the exact Poissonian confidence limits for small numbers n of observed events following the approach of Gehrels (1986). Analytic descriptions of all parameters used in the approximations are…
A surprising 'converse to the polynomial method' of Aaronson et al. (CCC'16) shows that any bounded quadratic polynomial can be computed exactly in expectation by a 1-query algorithm up to a universal multiplicative factor related to the…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
The quest for an algorithm that solves an $n\times n$ linear system in $O(n^2)$ time complexity, or $O(n^2 \text{poly}(1/\epsilon))$ when solving up to $\epsilon$ relative error, is a long-standing open problem in numerical linear algebra…
We observe a stochastic process $Y$ on $[0,1]^d$ ($d\geq 1$) satisfying $dY(t)=n^{1/2}f(t)dt$ + $dW(t)$, $t \in [0,1]^d$, where $n \geq 1$ is a given scale parameter (`sample size'), $W$ is the standard Brownian sheet on $[0,1]^d$ and $f…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
We present an algorithm to efficiently sample first-passage times for fractional Brownian motion. To increase the resolution, an initial coarse lattice is successively refined close to the target, by adding exactly sampled midpoints, where…
Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…