一种求解噪声复指数逼近问题的新变换

近似Wonham滤波器的指数收缩性与鲁棒性

Exponential contractions and robustness for approximate Wonham filters

该研究针对连续时间马尔可夫链的含噪状态估计问题，证明最优滤波器在希尔伯特投影空间的路径严格收缩性并给出收敛速率，改进了最优滤波器鲁棒性的误差估计，推导了近似滤波器的可计算严格误差界。

Adaptive estimation of a function from its Exponential Radon Transform in presence of noise

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric kernel type estimator and show that for a class of functions comprising a wide Sobolev regularity scale, our proposed strategy follows the minimax optimal rate up to a $\log{n}$ factor. We also show that there does not exist an optimal adaptive estimator on the Sobolev scale when the pointwise risk is used and in fact the rate achieved by the proposed estimator…

Consistent Inversion of Noisy Non-Abelian X-Ray Transforms

For $M$ a simple surface, the non-linear statistical inverse problem of recovering a matrix field $Φ: M \to \mathfrak{so}(n)$ from discrete, noisy measurements of the $SO(n)$-valued scattering data $C_Φ$ of a solution of a matrix ODE is considered ($n\geq 2$). Injectivity of the map $Φ\mapsto C_Φ$ was established by [Paternain, Salo, Uhlmann; Geom.Funct.Anal. 2012]. A statistical algorithm for the solution of this inverse problem based on Gaussian process priors is proposed, and it is shown how it can be implemented by infinite-dimensional MCMC methods. It is further shown that as the number $…

一种具备强收敛性质的指数平均过程

An Exponential Averaging Process with Strong Convergence Properties

针对传统指数移动平均（EMA）因最新观测权重恒定而缺乏强随机收敛性的问题，提出权重以次谐波速率衰减的$p$-EMA方法，给出温和假设下的收敛保证，并探讨其在SGD自适应步长控制中的应用意义。

Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform

In this article, we consider the problem of inverting the exponential Radon transform of a function in the presence of noise. We propose a kernel estimator to estimate the true function, analogous to the one proposed by Korostelëv and Tsybakov in their article `Optimal rates of convergence of estimators in a probabilistic setup of tomography problem', Problems of Information Transmission, 27:73-81,1991. For the estimator proposed in this article, we then show that it converges to the true function at a minimax optimal rate.

动态团队理论：通过Girsanov测度变换的随机微分决策系统的去中心化噪声信息结构

Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noisy Information Structures via Girsanov's Measure Transformation

本文提出两种方法，将静态团队理论推广到动态团队理论，通过连续时间随机非线性微分去中心化决策系统，利用Girsanov测度变换获得等价动态团队问题，研究团队最优条件和放松策略的存在性。