Related papers: Better Gaussian Mechanism using Correlated Noise

Recent diffusion models have achieved promising performances in audio-denoising tasks. The unique property of the reverse process could recover clean signals. However, the distribution of real-world noises does not comply with a single…

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…

Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…

Differential privacy for the 2020 census required an estimated 90 terabytes of randomness [GL20], an amount which may be prohibitively expensive or entirely infeasible to generate. Motivated by these practical concerns, [CSV25] initiated…

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

Newtonian noise limits the low-frequency sensitivity of ground-based gravitational wave detectors. While seismometers and geophones are commonly employed to monitor ground motion for Newtonian noise cancellation, their limited spatial…

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…

This work proposes a class of differentially private mechanisms for linear queries, in particular range queries, that leverages correlated input perturbation to simultaneously achieve unbiasedness, consistency, statistical transparency, and…

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

Differentially private noise mechanisms commonly use symmetric noise distributions. This is attractive both for achieving the differential privacy definition, and for unbiased expectations in the noised answers. However, there are contexts…

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…

In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a…

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…

Excess noise is a major obstacle to high-performance continuous-variable quantum key distribution (CVQKD), which is mainly derived from the amplitude attenuation and phase fluctuation of quantum signals caused by channel instability. Here,…

We compute the expected randomized benchmarking sequence fidelity for a system subject to Gaussian time-correlated noise. For single qubit benchmarking we show that the expected sequence fidelity is given by the partition function of a…

We propose a novel theoretical and methodological framework for Gaussian process regression subject to privacy constraints. The proposed method can be used when a data owner is unwilling to share a high-fidelity supervised learning model…