Proposes Gaussian Processes for more accurate time-correlated measurement noise in robotics.
problem Time-correlated measurement noise in robotics applications.
method Gaussian Processes as a non-parametric model for correlated measurement noise.
result Improved performance of Kalman filtering with Gaussian Processes.
The chapter compares Gaussian process models for stochastic simulators with varying noise.
problem Modeling stochastic simulators with varying noise.
method Various Gaussian process models are compared, including input varying noise variance, non-Gaussian noise, and quantile modeling.
result Sequential design procedures are adapted for these models.
Noise in SGD affects overparameterized models, favoring sparse solutions.
problem Understanding and mitigating implicit bias in SGD with parameter-dependent noise.
method Theoretical analysis of a quadratically-parameterized model with label noise and Gaussian noise.
result SGD with label noise recovers sparse ground-truth solutions, while SGD with Gaussian noise overfits dense solutions.
New method models multi-view noise as Mixture of Gaussians for robust MSL.
problem Robust multi-view subspace learning with complex noise.
method Model multi-view noise as Mixture of Gaussians, regularize across views.
result Method outperforms existing models in robustness and interpretability.
We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under non- Gaussian environment. The noises can naturally be non-Gaussian (skewed and/or heavy tailed) or to accommodate spurious observations, noises can be modeled as heavy tailed. However, at the cost of such noise robustness, the…
WS diffusion models handle anisotropic Gaussian noise better than conventional methods.
problem Handling anisotropic Gaussian noise in imaging inverse problems.
method Whitened Score (WS) diffusion models based on stochastic differential equations.
result WS DMs outperform conventional DMs on anisotropic Gaussian noise.
New algorithm for estimating MLR parameters with non-Gaussian noise.
problem Estimating MLR parameters with non-Gaussian noise.
method Combining ADMM with EM algorithm idea.
result Our method outperforms EM algorithm in non-Gaussian noise case.
Improved PINNs for solving PDEs with unknown measurement noise.
problem Handling non-Gaussian noise in physics-informed neural networks.
method Jointly train an EBM to learn the correct noise distribution.
result Improved performance in solving PDEs with non-Gaussian noise.
Improved self-supervised denoising for Poisson-Gaussian noise.
problem Handling Poisson-Gaussian noise in self-supervised denoising.
method Extended blindspot model, improved training scheme without hyperparameters.
result Improved denoising performance on microscope image benchmarks.
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the statistical learning context, is still limited. In this study, within the…
DLPM replaces Gaussian noise with α-stable noise in DDPM, improving data distribution coverage and robustness.
problem Handling mode collapse and class imbalance in datasets with heavy-tailed noise.
method Extending DDPM to use α-stable noise, simplifying the process with elementary proof techniques.
result DLPM yields better coverage of data distribution tails, improved robustness to unbalanced datasets, and faster computation times.
Noise regularisation in deep nets makes them behave like Gaussian processes.
problem Understanding the behavior of noise-regularized deep neural networks as Gaussian processes.
method Analyzing the impact of noise regularisation on neural network Gaussian processes (NNGPs) and relating their behavior to signal propagation theory.
result Best performing NNGPs have kernel parameters corresponding to a specific initialisation scheme.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
GNIs induce asymmetric heavy-tailed noise in SGD, affecting network performance.
problem The effect of Gaussian noise injections on SGD dynamics and network performance.
method Developed a Langevin-like SDE driven by asymmetric heavy-tailed noise to model the modified SGD dynamics.
result GNIs induce an implicit bias that varies with noise heaviness and asymmetry, affecting network performance.
Echo noise improves compression in autoencoders with exact rate-distortion.
problem Limitations of Gaussian noise in lossy compression and VAEs.
method Introduces Echo noise, a data-driven noise channel with exact mutual information.
result Echo noise leads to improved bounds on log-likelihood and dominates VAEs.
Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between n economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter ε. We demonstrate, that within Gaussian noise,…
Method estimates noise variance in Gaussian process regression.
problem Estimating noise variance in Gaussian process regression models.
method Reduces hyperparameter space, uses marginal likelihood function, derives bounds and asymptotes.
result Computational advantages and robustness compared to traditional methods.
We propose a robust method to estimate heteroscedastic noise models using Student's t-distribution.
problem Identifying cause and effect from bivariate observational data with non-Gaussian noise.
method We propose a novel approach using Student's t-distribution to estimate heteroscedastic noise models, which is more robust and achieves better performance.
result Our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.
Study of asymmetric rank-one tensor models with non-Gaussian noise.
problem Analyzing maximum-likelihood estimators for asymmetric rank-one tensor models.
method Spectrally separated branch analysis, resolvent methods, cumulant expansions, Efron-Stein-type variance bounds.
result Asymptotic singular value and mode-wise alignments are robust to non-Gaussian noise.
Algorithm identifies and corrects noisy labels using Gaussian process regression.
problem Detecting and correcting real-valued noisy labels from mixed data.
method Gaussian process regression with heteroscedastic noise model and leave-one-out cross-validation.
result The method can pinpoint corrupted sample points and improve regression models.
New method designs joint initial noises for diffusion models to improve diversity and alignment.
problem Independent initial noises limit diversity in generated images.
method Coupling of initial noises, maintaining Gaussian distribution while allowing dependence.
result Repulsive Gaussian coupling improves diversity without increasing sampling cost.
New method distinguishes data noise from GP uncertainty.
problem Uncertainty in kernel regression with non-Gaussian noise.
method Wiener chaos expansions for non-Gaussian noise.
result Can distinguish aleatoric from epistemic uncertainty.
New bounds for kernel regression under non-Gaussian noise.
problem Uncertainty quantification for function estimates from noisy observations.
method Novel non-asymptotic probabilistic uniform error bounds for kernel-based regression.
result Proposed bounds apply to a broad class of non-Gaussian noise distributions.
Generative models improve for multiscale scientific data with new noise and interpolation techniques.
problem Numerical challenges in generating high-fidelity samples for multiscale scientific data.
method Design of noise distributions and interpolation schedules in function space to ensure Lipschitz regularity and finite noise roughness.
result Scale-adaptive noise and interpolation schedules improve numerical efficiency and fidelity of generated samples.
Proposes a new CSC model for handling unknown noise.
problem Existing CSC methods can only model Gaussian noise, which is restrictive.
method Uses Gaussian mixture model for unknown noise and EM algorithm for optimization.
result Effective modeling of complicated unknown noise with high-quality filters and representation.
GaussDetect-LiNGAM eliminates Gaussianity tests for causal discovery.
problem Causal direction identification without Gaussianity assumptions.
method Leverages the equivalence between noise Gaussianity and residual independence in reverse regression.
result Gaussianity tests replaced with robust kernel-based independence tests.
Exact recovery method for community detection in Gaussian mixtures with dependent noise.
problem Community detection in Gaussian mixtures with dependent and heterogeneous noise.
method Maximum likelihood estimator (MLE) for constrained quadratic optimization problem, using Σ-whitened separation and local inequalities. result Sharp exact-recovery threshold and no-gap mechanism in the unknown-size setting.
Generalized R2R handles non-Gaussian noise for deep network training.
problem Training deep networks from noisy data alone.
method Extending R2R to handle various noise distributions.
result GR2R loss is an unbiased estimator of supervised loss.
A system for federated learning with private data, adding discrete Gaussian noise and secure aggregation.
problem Training models on private data distributed across devices while ensuring privacy.
method Discretizes data, adds discrete Gaussian noise, and uses secure aggregation to protect privacy.
result Matches the accuracy of central differential privacy with less than 16 bits of precision per value.
We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the ℓ_p ball for p∈[1,∞] and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decisio…
Improves generative models by using heavy-tailed noise in score matching.
problem High-dimensional limitations of Gaussian noise in generative models.
method Extended DSM to generalised normal distribution, relaxed key assumptions, developed iterative noise scaling algorithm.
result Heavy-tailed DSM leads to improved generative performance.
Study shows short rate can explode to infinity in HJM model, impacting Eurodollar futures.
problem Exploding short rate in HJM model affecting Eurodollar futures.
method Small-noise deterministic limit analysis.
result Explicit explosion criteria derived for short rate under mild assumptions.
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
Study examines noise sensitivity of DNNs for binary classification.
problem Understanding non-robustness of DNN classifiers under noise.
method Defined and extended noise sensitivity and stability concepts for Boolean functions, applied to DNN models.
result Sorted out the relation between definitions and properties of DNN architectures under noise.
New algorithms recover signals robustly against outliers and heavy-tailed noise.
problem Estimating signals in the presence of heavy-tailed noise and outliers.
method Sum-of-squares relaxations for robust estimation.
result Recovery of signals in polynomial/quasipolynomial time for specific problems.
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
Optimal test for detecting signal in noisy matrix model.
problem Signal detection in noisy matrix models with unknown rank.
method Hypothesis test based on linear spectral statistics, optimal under Gaussian noise.
result Optimal test under Gaussian noise, improved with non-Gaussian noise.
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
The paper examines how SGD noise deviates from Gaussian distribution.
problem Understanding why SGD outperforms GD in neural networks.
method Analysis of SGN vectors' distribution during training.
result For large batch sizes, SGN vectors are mostly Gaussian in early phases.
Study analyzes perturbations in singular subspaces under random noise.
problem Understanding singular vector and subspace changes in signal-plus-noise models.
method Generalized Davis-Kahan-Wedin theorem for any unitarily invariant norm, considering ℓ∞ and ℓ2,∞ bounds. result Fine-grained insights into singular vector and subspace perturbations, including ℓ∞ and ℓ2,∞ bounds. Polynomial-time algorithm for learning halfspaces with Gaussian-distributed data and adversarial noise.
problem Learning halfspaces in the presence of adversarial label noise.
method Iterative soft localization technique enhanced with appropriate testers.
result Output a halfspace with misclassification error $O(\opt)+\eps$.
New approach to neural networks by incorporating observation noise and arbitrary prior means.
problem Misspecification on noisy data and limitations of NTK-GP equivalence.
method Introducing a regularizer for observation noise and proposing a shifted network for arbitrary prior means.
result Removes key obstacles to practical Gaussian process modeling in neural networks.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
problem Improving state-space radio interferometric imaging in the presence of heavy-tailed noise
method Stochastic Approximation Expectation Maximization
result Significant improvement in reconstruction fidelity and robustness to radio-frequency interference
Improves generative models by adding jump-diffusion noise.
problem Limited performance of diffusion models in generating samples from unknown distributions.
method Generalizes diffusion processes to include jump-diffusion noise, deriving closed-form generalized score functions.
result Jump-diffusion models outperform Gaussian models in specific parameter regimes.
Discrete Gaussian noise preserves privacy and accuracy in differential privacy.
problem Finite computers cannot represent continuous Gaussian noise, leading to privacy breaches and loss of interpretability.
method Introduced and analyzed discrete Gaussian noise, providing privacy and accuracy guarantees similar to continuous Gaussian noise.
result Discrete Gaussian noise offers the same privacy and accuracy as continuous Gaussian noise, with efficient sampling algorithms.
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.