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Text-to-3D, known for its efficient generation methods and expansive creative potential, has garnered significant attention in the AIGC domain. However, the pixel-wise rendering of NeRF and its ray marching light sampling constrain the…

This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…

Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed…

The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each…

This paper aims at distributed algorithms for solving a system of linear algebraic equations. Different from most existing formulations for this problem, we assume that the local data at each node is not accurately measured but subject to…

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

In fiber-optic distributed sensing, vibration signals are mostly assumed to follow Gaussian distribution for the simplicity of signal processing. However, in real applications, vibration signals often behave as non-Gaussian processes, which…

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…

In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…

This paper introduces a noise-tolerant computing method for over-the-air computation (AirComp) aimed at weighted averaging, which is critical in various Internet of Things (IoT) applications such as environmental monitoring. Traditional…

Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling…

Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…

We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…

We consider stochastic model based on the linear stochastic differential equation with the linear relaxation and with the diffusion-like fluctuations of the relaxation rate. The model generates monofractal signals with the non-Gaussian…

The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing…

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…