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.
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.
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.
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.
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.
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.
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.
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.
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure to construct asymptotically normal estimators of its linear forms through double-…
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.
We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data …
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.
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.
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.
Study shows how over-parameterized classifiers can still perform well on noisy data.
problem Understanding how maximum margin classifiers perform in over-parameterized settings with noisy data.
method Analyzes maximum margin classifiers on sub-Gaussian mixtures, providing risk bounds.
result Characterizes conditions for 'benign overfitting' in linear classification problems.
Transformers can learn noisy linear systems with depth and IID data.
problem Learning noisy linear dynamical systems with transformers.
method Theoretical analysis of multi-layer and single-layer transformers with respect to L2-testing loss. result Single-layer transformers have a non-diminishing lower bound on approximation error, suggesting depth separation.
Study rates of convergence for approximate solutions to linear ill-posed problems in Hilbert scales.
problem Linear ill-posed inverse problems with noisy data.
method Approximate reconstructions from random noisy data using regularization schemes in Hilbert scale.
result Explicitly established error bounds for smooth regression functions.
Adversarial training can lead to overfitting without compromising robustness.
problem Explaining benign overfitting in adversarially robust linear classification.
method Theoretical analysis and numerical experiments on adversarial training.
result Adversarially trained linear classifiers can achieve near-optimal risks despite overfitting noisy data.
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the…
The paper analyzes the maximum margin algorithm's performance on noisy data.
problem Analyzing the performance of maximum margin algorithm on noisy data.
method Finite-sample analysis of maximum margin algorithm applied to noisy data.
result The maximum margin algorithm can achieve nearly optimal population risk with sufficient over-parameterization.
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.
New insights into how linear classifiers and leaky ReLU networks can overfit without harming generalization.
problem Understanding conditions for benign overfitting in linear classifiers and leaky ReLU networks.
method Utilizing Karush--Kuhn--Tucker (KKT) conditions for margin maximization.
result Satisfaction of KKT conditions leads to benign overfitting in linear classifiers and leaky ReLU networks.
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.
This paper presents a statistical method of single-channel speech enhancement that uses a variational autoencoder (VAE) as a prior distribution on clean speech. A standard approach to speech enhancement is to train a deep neural network (DNN) to take noisy speech as input and output clean speech. Although this supervis…
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.
Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MC…
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.
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, with…
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.
New linear denoiser outperforms standard Wiener filter in noisy data.
problem Improving denoising performance for unknown covariance data.
method Synthetically constructed noisy samples to train a linear denoiser using least-squares approximation.
result Optimal denoiser found using the Convex Gaussian Min-Max Theorem (CGMT) for proportional regime.
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.
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.
Paper tackles noisy labels for non-decomposable performance measures.
problem Learning from noisy labels for non-decomposable performance measures.
method Designs algorithms for multiclass non-decomposable performance measures using Frank-Wolfe and Bisection methods, corrected for class-conditional noise.
result Noise-corrected algorithms are Bayes consistent, converging to optimal performance.
Paper introduces a neural network training algorithm for noisy data that achieves optimal parameters and replicates real-world behaviors.
problem Theoretical gap between universal approximation theorems and practical machine learning with noisy data.
method Randomized training algorithm for neural networks trained on noisy data samples.
result Trained neural networks achieve optimal parameters and exhibit real-world behaviors like sub-linear complexity and interpolation.
Accuracy on in-distribution data correlates with out-of-distribution data when data is noisy or contains nuisance features.
problem Correlation between in-distribution and out-of-distribution accuracy in noisy or feature-rich data.
method Analyzes the impact of noise and nuisance features on model performance.
result Accuracy on in-distribution and out-of-distribution data can become negatively correlated in noisy or feature-rich data.
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.
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel…
Study supports recovery of PDEs from noisy data using a specific regularization method.
problem Support recovery of PDEs from a single noisy trajectory.
method Applying ℓ1-regularized Pseudo-Least Squares model to a given data set.
result Support of ℓ1-c coefficients asymptotically converges to the true signed-support of the PDE.
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.
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.
A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solut…
New tensor recovery method uses Riemannian optimization on Segre manifold.
problem Recovering low-rank tensors from noisy measurements.
method Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) algorithms over the Segre manifold.
result Proven convergence rates for RGD and RGN under mild noise assumptions.
DHLNN improves deep hedging for financial derivatives with faster convergence and better stability.
problem Challenges in computational inefficiency, sensitivity to noisy data, and optimization complexity in deep hedging methods.
method Integrates periodic fixed-gradient optimization and linearized training dynamics to stabilize and accelerate deep learning model training.
result Demonstrates faster convergence, improved stability, and superior hedging performance across diverse market scenarios.
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.
Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.
problem Finding frequencies, amplitudes, and phases of sinusoids in noisy data.
method Maximum likelihood approach to estimate tone parameters from contaminated observations. Successively estimates frequencies and jointly optimizes amplitudes and phases.
result Near-linear computational complexity (O(N)) for estimating M number of sinusoidal sources. 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.
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work (4, 19, 24, 20) provided strong theoretical guarantee for s…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are …