The study investigates noise effects on parameter estimation for Ornstein-Uhlenbeck processes.
problem Impact of noise on parameter fitting for Ornstein-Uhlenbeck processes.
method Proposed algorithms to distinguish between thermal and multiplicative noise.
result Effective methods to estimate parameters even when multiplicative noise dominates.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
problem Distorted pairwise Euclidean distances due to heteroskedastic noise.
method Developed a hyperparameter-free approach to jointly estimate noise magnitudes and correct distances.
result Our method provides accurate noise magnitude estimates and corrected distances in high-dimensional settings.
Paper estimates noise covariance in correlated multi-task linear models.
problem Estimating noise covariance in multi-task high-dimensional linear models with correlated noise.
method Uses multi-task elastic-net and lasso estimators to estimate noise covariance, correcting bias in squared residual matrix.
result Develops a novel estimator of noise covariance that converges at rate n−1/2, matching oracle estimator under suitable conditions. Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.
problem Estimating rank-one spikes from heavy-tailed noise.
method Self-avoiding walks to count and estimate the spikes.
result Optimal estimation up to the BBP threshold for heavy-tailed noise.
AVICA estimates noise levels for better group ICA source recovery.
problem Estimating shared independent sources from multiple noisy views.
method AVICA models each view as a linear mixture of shared sources with additive noise, optimizing noise levels alongside sources.
result AVICA yields better source estimates than other methods, especially in real-world applications like MEG and fMRI.
Noise-resilient method improves Hurst exponent estimation accuracy in noisy data.
problem Noise degrades accuracy of Hurst exponent estimation methods.
method Noise-Controlled ALPHEE (NC-ALPHEE) using wavelet multi-scale analysis and neural network combination.
result NC-ALPHEE consistently outperforms existing techniques in noisy conditions.
Paper presents a robust Kalman filter for state estimation.
problem Robust state estimation under process and measurement noise.
method Generalized Bayesian approach to a Weighted Observation Likelihood Filter (WoLF) framework.
result Achieved robust state estimation against both process and measurement noise.
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.
New insights into noise distribution for self-supervised learning.
problem Challenges the assumption that optimal noise should match data distribution.
method Turns to Noise-Contrastive Estimation (NCE) to define optimality of noise distribution.
result Optimal noise distribution is different from data distribution, challenging GANs assumption.
This paper analyzes M-estimators under infinite-variance noise in high dimensions.
problem High-dimensional M-estimation with infinite-variance noise.
method Study of the Fenchel conjugate domain and its impact on risk.
result Exact risk of M-estimators under infinite-variance noise is derived.
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterat…
Characterizes uncertainty in low-rank matrix completion with noisy data.
problem Uncertainty quantification in low-rank matrix completion with heterogeneous sub-exponential noise.
method Characterizes the distribution of estimated matrix entries under low-rank estimators with heterogeneous sub-exponential noise.
result Explicit formulas for the distribution of estimated matrix entries under Poisson and Binary noise.
HeMPPCAT improves PCA for data with varying noise.
problem PCA's suboptimal performance on data with heterogeneous noise.
method HeMPPCAT uses a GEM algorithm to estimate factors, means, and noise variances.
result Improved factor estimates and clustering accuracy compared to MPPCA.
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.
Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametr…
Study improves parameter estimation for SDEs driven by Levy noise.
problem Challenges in estimating parameters of SDEs with non-Gaussian noises.
method Introduces PEnet, a CNN-LSTM model for efficient parameter estimation.
result PEnet offers superior accuracy and adaptability for various SDE scenarios.
We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resul…
A new framework for PPLS combines noise estimation, optimization, and calibration.
problem Probabilistic PLS models need interpretable latent factors and calibrated uncertainty.
method End-to-end pipeline combining noise estimation, constrained optimization, and prediction calibration.
result Achieves near-nominal coverage and native calibrated uncertainty across benchmarks.
We develop a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The microstructure noise is a parametric function of the limit order book. The noise-robust estimators are constructed as plug-in versions of their counterparts, where we replace the e…
Study on deep learning for speckle noise reduction in imaging modalities.
problem Multiplicative speckle noise challenges conventional deep learning methods for speckle denoising.
method Likelihood-based deep neural network (DNN) estimators for nonparametric regression under speckle noise.
result Established minimax rates for speckle denoising, matching those for additive Gaussian noise alone.
In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in practice. A possible remedy is to consider estimators, such as the Concomitant/Scale…
Examines WENDy-IRLS algorithm's noise robustness and efficiency in various differential equations.
problem Noise robustness and efficiency of WENDy-IRLS algorithm.
method Studied coverage and bias properties of WENDy-IRLS algorithm's estimators in various differential equations and noise distributions.
result WENDy-IRLS algorithm shows notable noise robustness and computational efficiency.
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest.…
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
A new method learns noise characteristics for better state estimation in real-time systems.
problem Challenges in accurately estimating states due to uncertainty in process and measurement models.
method Proposes a learning-based approach with different loss functions to identify noise characteristics.
result Demonstrates improved performance in real-time vehicle state estimation.
Develops efficient inference for noise heterogeneity in machine learning models.
problem Downstream procedures based on residuals can be biased in additive noise models.
method Semiparametrically efficient inference using a novel Hilbert-valued one-step estimator.
result Constructs tests and confidence intervals for residual independence and goodness of fit.
Improves score estimation for noised targets using known clean scores.
problem Poor score estimation at low noise levels in Denoising Score Matching.
method Introduces Target Score Identity and Target Score Matching loss.
result Score estimates are more accurate at low noise levels.
The paper analyzes deflation for estimating a low-rank spike in large tensors with noise.
problem Estimating a low-rank symmetric spike in large tensors with additive Gaussian noise.
method Characterization of deflation performance in terms of vector alignments and weights.
result Understanding deflation mechanism in noisy conditions and designing more efficient methods.
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
New method learns from noisy data without knowing noise level.
problem Learning from noisy data without knowing noise level.
method Uses Stein's Unbiased Risk Estimate (SURE) without noise level knowledge.
result Outperforms other self-supervised methods on imaging problems.
Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random fields, and neural network models in unsupervised deep learning. In previous wor…
Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.
problem Efficiently estimating the mean of high-dimensional data while preserving privacy.
method Differential privacy mechanisms with Gaussian noise, focusing on optimal covariance.
result Gaussian noise mechanisms achieve nearly optimal error among all private unbiased mean estimation mechanisms.
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…
Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.
problem Outliers and heavy-tailed noise in linear regression coefficients.
method Sharp concentration inequalities and generic chaining.
result Sharper error bounds under weaker assumptions.
Paper tackles leverage effect estimation from noisy data.
problem Estimating leverage effect from high-frequency data with microstructure noise.
method Holistic multi-scale framework operating directly on leverage effect, using Subsampling-and-Averaging Leverage Effect (SALE) and Multi-Scale Leverage Effect (MSLE) estimators.
result Holistic multi-scale framework achieves substantial efficiency gains over existing benchmarks.
PiNGDA learns beneficial noise for graph augmentation stability.
problem Challenges in generating effective and stable graph augmentations.
method PiNGDA uses positive-incentive noise to scientifically analyze and generate beneficial graph augmentations.
result PiNGDA improves GCL performance by learning beneficial noise on graph topology and attributes.
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price…
New methods improve estimation accuracy in noisy settings.
problem Estimating treatment effects in the presence of treatment noise.
method Developed new structure-agnostic cumulant estimators and practical procedures for higher-order robustness.
result Demonstrated that existing DML estimator is suboptimal for non-Gaussian treatment noise and introduced ACE procedures for improved accuracy.
Estimates shared linear subspace from noisy data with multiple users.
problem Recovering shared linear subspace from noisy data with non-isotropic noise.
method Estimates shared subspace using at least two data points per user, avoiding restrictive assumptions.
result Upper and lower bounds for estimation error match, showing no additional error due to noise irregularity.
Time changes of noise level at Warsaw Stock Market are analyzed using a recently developed method basing on properties of the coarse grained entropy. The condition of the minimal noise level is used to build an efficient portfolio. Our noise level approach seems to be a much better tool for risk estimations than standa…
New findings show optimal noise in contrastive learning is not the same as data distribution.
problem The optimal noise distribution in contrastive learning is not the same as the data distribution.
method Empirical and theoretical analysis of contrastive learning methods.
result Deviation from the assumption of equal noise and data distribution leads to better statistical estimators.
In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual nois…
Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to estimate this noise. To this end, we simulate certain time series and random matr…
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regressi…
New method for spot volatility estimation with reduced microstructure noise.
problem Estimating spot volatility from noisy high-frequency data.
method Pre-averaging/kernel estimator to handle microstructure noise.
result Optimal bandwidth selection and kernel functions for minimal variance.
The paper proves the consistency and efficiency of a volatility estimator in noisy data.
problem Proving the consistency and efficiency of a volatility estimator in the presence of microstructure noise.
method Proves asymptotic normality using Central Limit Theorem for Fourier spot volatility estimator.
result Proves consistency and asymptotic efficiency of the Fourier spot volatility estimator in noisy data.
Improved noise estimation in latent neural SDEs enhances model accuracy.
problem Latent neural SDEs underestimate noise, limiting their stochastic dynamics modeling.
method Explicit additional noise regularization in the loss function.
result Model accurately captures diffusion component of stochastic time series data.
Bayesian consensus improves accuracy of forecasts from miscalibrated sources.
problem Aggregating predictions from miscalibrated and noisy sources.
method Bayesian approach to adjust for bias and noise, using hierarchical models.
result Bayesian consensus estimator is unbiased and more efficient than alternatives.