Related papers: Minimum Error Entropy Rauch-Tung-Striebel Smoother
The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage…
Synthetic aperture radar (SAR) images are subject to prominent speckle noise, which is generally considered a purely multiplicative noise process. In theory, this multiplicative noise is that the ratio of the standard deviation to the…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
Recent advances in dynamic scene reconstruction have significantly benefited from 3D Gaussian Splatting, yet existing methods show inconsistent performance across diverse scenes, indicating no single approach effectively handles all dynamic…
In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…
Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on $L^2$ whose multi-point correlations satisfy an infinite hierarchy of weak identities. Modern generative samplers for PDE forecasting…
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We…
Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against $\ell_p$ adversaries,…
The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate…
Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$;…
We study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves a collection of…
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned…
For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte…