Deep learning approximates SPDE solutions from noise trajectories.
problem Approximating solutions to stochastic partial differential equations (SPDEs).
method Uses neural networks to approximate SPDE solutions based on noise realizations.
result Accurately estimates SPDE solutions and functionals like mean and variance.
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.
Gradient descent with noise converges to a unique optimum in nonconvex matrix factorization.
problem Gradient descent with noise converges to a unique optimum in nonconvex matrix factorization.
method A perturbed form of gradient descent with arbitrary initialization.
result Gradient descent with noise converges to a unique optimum.
Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem through training a simple two-layer convolutional neural network model. Although trai…
Researchers establish bounds for SGMs' KL and Wasserstein divergences under various noise schedules.
problem Estimating the error between target and estimated distributions in SGMs.
method Established upper bounds for KL divergence and Wasserstein distance, incorporating target distribution properties and SGM hyperparameters.
result Optimal noise schedules identified for SGMs, improving generative quality.
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.
Optimizes control of noisy discrete systems without system matrix knowledge.
problem Optimal control of discrete-time systems with additive and multiplicative noises.
method Stochastic Lyapunov and Riccati equations, model-free reinforcement learning.
result Model-free reinforcement learning algorithm converges to optimal control policy.
Recently, several data analytic techniques based on connection graph laplacian (CGL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is observed without noise. We study the impact of additive noise on these methods, and sh…
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.
We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology is very flexible: adapting to different signal and noise models only requires m…
Method extracts stochastic systems with Lévy noise from data.
problem Identifying stochastic dynamical systems with Lévy noise from short data.
method Estimate Lévy jump measure and noise intensity, approximate drift coefficient.
result Accurate and effective method for discovering stochastic laws.
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary time, and we applie…
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
Generative models learn better with data-adaptive noise.
problem Learning heavy-tailed distributions in flow-based models.
method Data-adaptive latent noise using 1D quantile functions optimized via Wasserstein distance.
result Flexibility and effectiveness in learning heavy-tailed and compactly supported distributions.
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
Simultaneous orthogonal matching pursuit (SOMP) and block OMP (BOMP) are two widely used techniques for sparse support recovery in multiple measurement vector (MMV) and block sparse (BS) models respectively. For optimal performance, both SOMP and BOMP require \textit{a priori} knowledge of signal sparsity or noise vari…
New convergence bounds for online learning with heavy-tailed noise.
problem Learning on streaming data with heavy-tailed noise.
method Nonlinear stochastic gradient descent (SGD) for non-convex and strongly convex costs.
result Strong convergence rates for various nonlinearities and noise distributions.
Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.
problem Analyzing stochastic approximation under heavy-tailed and LRD noise.
method Noise-averaging argument to regularize impact of non-classical noise.
result Established first finite-time moment bounds for SA under heavy-tailed and LRD noise.
Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most…
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary mechanism responsible for the observed long-range dependence and statistical propertie…
Locally private algorithm improves online federated learning with correlated noise.
problem Privacy-preserving online federated learning with non-IID data.
method Locally differentially private algorithm using temporally correlated noise.
result Established dynamic regret bound for nonconvex loss functions.
Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain circumstances, namely when the covariance matrix of the nonlinearly expanded data does not …
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
problem Nonlinear spiked random matrix models with rank-one signal and noise.
method Signal-plus-noise decomposition and phase transition analysis.
result Identified precise phase transitions in signal components at critical thresholds.
Proposes a new method for efficient manifold denoising robust to high dimensional noise.
problem Efficiently denoise manifolds in high dimensional spaces with complicated noise.
method Landmark diffusion and optimal shrinkage under high dimensional noise and compact manifold setup.
result Systematic comparison with other algorithms on simulated and real datasets shows superior performance.
A new method for support vector regression using a data-driven insensitive parameter.
problem Determining an optimal insensitive parameter in support vector regression.
method A data-driven approach to approximate the insensitive parameter by minimizing a generalized loss function based on the likelihood principle.
result The proposed method outperforms traditional support vector regression methods and has lower computational costs.
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.
A new PCA method using Tℓ1-norm outperforms existing methods.
problem Outliers and noise sensitivity in classical PCA.
method PCA based on Tℓ1-norm maximization. result The method outperforms PCA-ℓp, ℓpSPCA, and PCA in numerical experiments. Optimized method tackles convex optimization with heavy-tailed noise.
problem Convex optimization problems with noisy gradients.
method Vanilla stochastic proximal subgradient method without gradient clipping or normalization.
result Achieves optimal complexity for various convex optimization types under heavy-tailed noise.
Interpolation hurts robust generalization even without noise.
problem The challenge of robust generalization in the absence of noise.
method Avoiding interpolation through ridge regularization.
result Ridge regularization improves robust generalization.
In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing popular volatility estim…
R2T hybrid model improves robust regression for asymmetric noise.
problem Least-squares regression fails with asymmetric structured noise.
method Transformer encoder, compression NN, fixed symbolic equation.
result Median regression MSE of 6e-6 to 3.5e-5 on synthetic data.
Large datasets often have unreliable labels-such as those obtained from Amazon's Mechanical Turk or social media platforms-and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment…
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…
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
Study on signal recovery from low-rank matrix with sparse noise.
problem Inference of a rank-one signal in the presence of sparse noise.
method Replica method from statistical physics, recursive distributional equations, population dynamics algorithm.
result Critical signal strength for recovery via top eigenvector identified.
Deep-neural-network (DNN) based noise suppression systems yield significant improvements over conventional approaches such as spectral subtraction and non-negative matrix factorization, but do not generalize well to noise conditions they were not trained for. In comparison to DNNs, humans show remarkable noise suppress…
New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.
problem Removing noise or artifacts from measurements in physics experiments.
method Alternative formulation using Wasserstein loss, developing a convergent algorithm.
result Optimal transport approach offers robust, accurate performance compared to classical techniques, especially in cases with significant binning artifacts.
This paper proves a central limit theorem for differential privacy in high dimensions.
problem Understanding optimal noise distributions for privacy-accuracy trade-offs in high-dimensional settings.
method Developed a central limit theorem approach to analyze differential privacy mechanisms.
result Gaussian mechanisms achieve the optimal privacy-accuracy trade-off in high dimensions.
Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a p…
New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.
problem Optimization problems with heavy-tailed noise and weakly average smoothness.
method Normalized stochastic first-order methods with Polyak, multi-extrapolated, and recursive momentum.
result First-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise.
Paper tackles SMPC for linear systems with unknown noise distribution.
problem Stochastic MPC for linear systems with chance state constraints and unknown noise distribution.
method Reformulate chance constraints, design robust benchmark SMPC, and develop adaptive SMPC with online noise statistics learning.
result Adaptive SMPC guarantees time-uniform satisfaction of unknown reformulated state constraints with high probability.
In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the Rényi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datas…
This work introduces a noise-adaptive conformal inference method for better prediction sets in noisy data.
problem Real-world complications like random label noise limit the effectiveness of conformal inference.
method An adaptive conformal inference method capable of handling deviations from exchangeability.
result Informative prediction sets with tight marginal coverage guarantees in noisy data.
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a priori. Therefore, we propose learning arbitrary noise distributions. To do so, th…
Develops statistical confidence sets for multidimensional scaling.
problem Statistical uncertainty in multidimensional scaling of noisy data.
method Formal statistical framework, distributional convergence results, uniform confidence sets, bootstrap procedures.
result Construction of reliable confidence sets for latent configurations in multidimensional scaling.
Automatically detects and down-weights noisy samples in machine learning training.
problem Numerical noise in reference data hampers the accuracy of machine learning models.
method On-the-fly outlier detection using exponential moving average to identify and down-weight noisy samples.
result The method prevents overfitting and matches the performance of iterative refinement with reduced overhead.
We propose a novel receiver for orthogonal frequency division multiplexing (OFDM) transmissions in impulsive noise environments. Impulsive noise arises in many modern wireless and wireline communication systems, such as Wi-Fi and powerline communications, due to uncoordinated interference that is much stronger than the…