A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
SONIG algorithm improves system identification with noisy data.
problem System identification with noisy input data and online updates.
method Sparse Online Noisy Input Gaussian Process (SONIG) regression.
result SONIG outperforms existing methods in accuracy and runtime.
Develops methods for statistical inference on matrix linear forms from noisy data.
problem Statistical inference on linear forms of a large matrix from noisy observations.
method Double-sample debiasing and low-rank projection for constructing asymptotically normal estimators.
result Asymptotically normal estimators of linear forms allow for confidence intervals and hypothesis testing.
Bayesian analysis reveals significant deviations from underlying function in noisy linear bandits.
problem Contextual linear bandits with noisy features and missing entries.
method Bayesian analysis and proposed algorithm to approximate the oracle.
result Achieves i l d e O ( d T ) ilde{O}(d\sqrt{T}) i l d e O ( d T ) regret bound under noisy conditions. Neural networks can interpolate noisy data and still generalize well.
problem Generalization of neural networks trained on noisy data.
method Two-layer neural networks trained to interpolation by gradient descent on corrupted labels.
result Neural networks can achieve zero training error and optimal test error.
Estimates linear model from noisy covariates and instruments using spectral regularization.
problem Estimating a linear model from many noisy covariates and instruments.
method Two-stage least squares with spectral regularization of canonical correlations.
result Upper and lower bounds on estimation error, proving optimality of the method with noisy data.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
Deep neural networks can generalize well even with perfect fits to noisy data.
problem Understanding the conditions under which deep neural networks generalize well in the presence of noise.
method Comprehensive study of linear maximum margin classifiers, focusing on noisy and noiseless cases.
result Discovery of a phase transition in test error bounds for the noisy model.
Deep learning with noisy gradient descent outperforms linear estimators in high dimensions.
problem Theoretical explanation of deep learning's superiority over linear methods.
method Theoretical analysis of excess risk of a deep learning estimator trained by noisy gradient descent.
result Deep learning achieves a faster learning rate than linear estimators, especially in high dimensions.
The paper tackles noisy labels in high-dimensional data, showing low-dimensional intuitions fail and proposing an optimized method.
problem Noisy labels in high-dimensional data classification.
method Linear classifier with a label noisiness aware loss function, using random matrix theory and Gaussian mixture data model.
result The performance of the linear classifier in high-dimension converges to a limit involving scalar statistics of the data, and the optimal classifier in low-dimension fails.
Permutation recovery in noisy linear models is studied with Gaussian noise and permutation matrix.
problem Permutation recovery in noisy linear models with unknown permutation and Gaussian noise.
method Random design setting with Gaussian matrix entries; NP-hardness of maximum likelihood estimation; polynomial time algorithm for d=1.
result Sharp conditions on SNR, sample size, and dimension for exact and approximate permutation recovery.
Machine learning finds linear equations from noisy data.
problem Discovering conservation laws from noisy data.
method Gaussian process priors modified for differential operators.
result Parameters of linear equations inferred from data.
INGB improves oversampling for noisy imbalanced datasets.
problem Imbalanced, noisy, and complex datasets in classification problems.
method INGB uses granular balls to simulate spatial distribution and informed entropy for optimization, followed by nonlinear oversampling.
result INGB outperforms traditional linear sampling frameworks and algorithms on complex datasets.
Gradient descent finds linear systems from noisy data.
problem Identifying unknown linear dynamical systems from noisy observations.
method Stochastic gradient descent on maximum likelihood objective.
result Gradient descent efficiently converges to global optimizer in polynomial time and sample complexity.
Develops goodness-of-fit tests for noisy submanifold samples.
problem Testing non-linear models on noisy submanifold samples.
method Non-linear least-square problem solution and χ 2 χ^2 χ 2 distribution application. result Residual follows χ 2 χ^2 χ 2 distribution with parameters related to model order and dimension. Learning theory for linear systems with compositional inputs.
problem Training linear system operators with unknown variables constrained to non-negativity and unity.
method Bayesian inversion method for inferring unknown variable from noisy linear system output.
result Quantified uncertainty in trained operator and convergence rates for various cases.
Study agnostic feature-based dynamic pricing models with linear policies and noisy valuations.
problem Tackles dynamic pricing with unknown noise and no assumptions on data.
method Studies two agnostic models: linear policy and linear noisy valuation, presenting algorithms and regret bounds.
result Demonstrates no-regret learning is possible under weak assumptions, but noisy feedback is not significantly more useful than bandit feedback.
The paper tackles noisy multi-armed bandit problems with improved regret guarantees.
problem Tackling noisy evaluations in multi-armed bandit problems.
method Derives different algorithmic approaches and theoretical guarantees based on the type of observation functions.
result Improved regret guarantees for noisy linear functions of true rewards.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
Deep neural networks solve noisy, complex problems accurately.
problem Reconstructing solutions from noisy, high-dimensional, non-linear inverse problems.
method Restricting infinite-dimensional forward operators to finite-dimensional spaces, training neural networks to approximate these operators robustly to noise.
result Deep neural networks can accurately solve high-dimensional, noisy, non-linear inverse problems.
Bayesian approach learns linear operators from noisy data.
problem Learning linear operators from noisy data in infinite-dimensional spaces.
method Bayesian approach with Gaussian priors.
result Establishes posterior contraction rates and generalization error guarantees.
Paper tackles federated linear bandit learning with AirComp for noisy channels.
problem Minimize cumulative regret in federated linear bandit learning.
method Proposes a federated linear bandits scheme using over-the-air computation (AirComp) over noisy fading channels.
result Determines the regret bound of the proposed scheme.
Interpolating noisy data in linear regression leads to zero training error.
problem Understanding why deep neural networks generalize well with noisy data.
method Investigated overparameterized linear regression, analyzing generalization error and proposing a hybrid scheme.
result Interpolating solutions in noisy data can generalize well, with error decaying to zero with more features.
This research tackles data deletion in linear regression with noisy SGD, finding perfect deleted points.
problem Finding points to delete from a dataset without significantly affecting the training result.
method Signal-to-noise ratio and an algorithm based on it.
result The perfect deleted point is crucial for maintaining model performance and privacy budget.
Paper improves learning mixtures of sparse signals from noisy measurements.
problem Learning mixtures of sparse linear regressions from noisy measurements.
method Improves upon state-of-the-art results using sparse polynomials and error-correcting codes.
result First robust reconstruction algorithm for mixtures of more than two sparse signals.
Study shows squared loss is robust for binary classification with noisy features.
problem Learning binary classifiers with noisy features.
method Sy-De and Asy-In attribute noise models, analyzing l 0 − 1 l_{0-1} l 0 − 1 and l s q l_{sq} l s q losses. result Squared loss is robust in Sy-De model but not in Asy-In model.
This paper approximates Gaussian process emulators with constraints and noisy data.
problem Realistic stochastic emulators with inequality constraints and noisy observations.
method Monte Carlo and Markov Chain Monte Carlo methods with noise term.
result Improved performance of MC and MCMC samplers with noisy observations and constraints.
The paper tackles noisy matrix completion by developing new statistics and controlling false discovery rate.
problem Testing multiple linear forms for noisy matrix completion with low-rank structure.
method Introducing new statistics with sharp asymptotics for individual tests, controlling FDR via data splitting and aggregation.
result Valid FDR control can be achieved with guaranteed power under nearly optimal sample size requirements.
Unified model improves speech enhancement in unseen environments.
problem Robustness against unknown environments in speech enhancement.
method Probabilistic integration of VAE and NMF.
result Outperforms conventional DNN-based method in unseen environments.
New LP method recovers MAP solution from noisy stable instances.
problem MAP inference on noisy stable instances.
method Designing an algorithm to find nearby perturbation stable instances and using LP relaxation.
result LP approximately recovers the MAP solution from noisy stable instances.
Paper analyzes gradient descent with noisy data copies for linear regression, showing regularization and acceleration effects.
problem Improving generalization in machine learning through data augmentation with noise.
method Gradient descent with on-line noisy copies for linear regression analysis.
result Training with on-line noisy copies is equivalent to ridge regularization with a specific regularization parameter.
Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and va…
Proposes a method to create robust linear models with noisy proxies of unobserved variables.
problem Learning robust linear models to handle interventions on unobserved variables with noisy proxies.
method Regularization term that balances in-distribution performance and robustness to interventions.
result Single proxy can create prediction optimal estimators under interventions of bounded strength.
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
Researchers improve tree model recovery from noisy data.
problem Learning tree structured models from corrupted data.
method Linear latent tree models and continuous corruption model.
result Chow-Liu algorithm consistently learns tree from noisy data.
Overparameterized models generalize well despite fitting noisy data.
problem Understanding why overparameterized models generalize well despite fitting noisy data.
method Statistical signal processing perspective.
result Overparameterized models often outperform underparameterized models in test performance.
Theory and method for reducing prediction variance in noisy feature-subsampled ridge ensembles.
problem Reduction of prediction variance in noisy data with feature bagging.
method Developed analytical learning curves for noisy ridge ensembles, introduced heterogeneous feature ensembling.
result Subsampling shifts the double-descent peak, leading to improved performance over a single linear predictor.
Framework prevents deep learning models from memorizing noisy labels.
problem Deep learning models memorize noisy labels during early learning phase.
method Develops a technique that exploits early learning phase via regularization.
result Framework achieves robustness to noisy annotations on benchmarks and real-world datasets.
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…
Detects anomalies in noisy data from linear systems.
problem Identifying samples of noise in a linear dynamical system.
method Robust spectral filtering and anomaly detection method.
result Guaranteed statistical performance in identifying noise samples.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
This work explores how neural network architecture affects robustness to noisy labels.
problem The impact of neural network architecture on robustness to noisy labels.
method Formal framework connecting robustness to architecture alignments, measured by predictive power in representations.
result Network robustness to noisy labels improves when its architecture is more aligned with the target function.
RFMs transition from linear to nonlinear under specific input-label correlation.
problem Understanding the transition from linear to nonlinear behavior in RFMs.
method Analyzing RFMs under spiked covariance designs, characterizing the interaction between anisotropy and input-label correlation.
result The RFM generalization error is governed by the strength of input-label correlation, leading to a clear nonlinear advantage above a specific boundary.
New method models PDEs from noisy, limited data.
problem Modeling PDEs with incomplete, noisy data.
method Learned linear transformation of spatial grid points, followed by dynamics learning in a reduced basis, then back transformation.
result Rapid high-resolution simulations with smaller training data sets.
Framework for fair classification with noisy protected attributes and provable guarantees.
problem Fair classification with noisy protected attributes.
method Optimization framework for linear and linear-fractional fairness constraints, handling multiple non-binary attributes.
result Provably fair classifier with minimal accuracy loss, even with large noise.
New algorithm mitigates bias in subset selection with noisy protected attributes.
problem Mitigating bias in subset selection when protected attributes are noisy.
method Formulated a denoised selection problem and developed a linear-programming based approximation algorithm.
result The approach can produce fairer subsets despite noisy protected attributes.
Thompson Sampling tackles noisy context in stochastic bandits.
problem Designing an action policy for noisy, corrupted contexts in stochastic bandits.
method Introducing a Thompson Sampling algorithm for Gaussian bandits with Gaussian context noise, adopting an information-theoretic analysis.
result Demonstrates the Bayesian regret of the proposed algorithm concerning the oracle's action policy.
Randomized Kaczmarz solves ranking from pairwise comparisons.
problem Inferring overall ranking from pairwise preference data.
method Randomized Kaczmarz method applied to noisy linear system.
result The method is convergent, has good empirical performance.