We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditiona…
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48 results for “unknown noise rates”
Bayes classifier cannot be learned from noisy labels without knowing noise distribution.
problem Learning a Bayes classifier from noisy labels when the noise distribution is unknown.
method Demonstrates the identifiability issues and proposes a simple algorithm for learning the Bayes decision rule.
result The Bayes decision rule is generally unidentified and cannot be learned without knowing the noise distribution.
We consider classification in the presence of class-dependent asymmetric label noise with unknown noise probabilities. In this setting, identifiability conditions are known, but additional assumptions were shown to be required for finite sample rates, and so far only the parametric rate has been obtained. Assuming thes…
This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common \textit{noise conditions}. These rates display interesting transitions -- due to the inte…
Study online linear regression with paid noise reduction.
problem Online linear regression with noisy features and the ability to pay for reduced noise.
method Analyzes regret against optimal predictor, uses matrix martingale concentration.
result Optimal regret rates for known and unknown noise covariance.
Improved SGD with AdaGrad stepsizes adapts to unknown parameters and unbounded gradients.
problem Adaptive optimization with unknown parameters and unbounded gradients.
method Stochastic Gradient Descent with AdaGrad stepsizes, without assuming problem parameters or strong global Lipschitz conditions.
result Sharp rates of convergence in both low-noise and high-noise regimes, supporting an affine variance noise model.
When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We pro…
The paper tackles learning to control systems with unknown parameters using Brownian noise.
problem Learning to control systems with unknown parameters.
method Proposes algorithms based on moving empirical averages and integrates statistical methods with stochastic control theory.
result Achieves a logarithmic expected regret rate.
Study uncovers statistical optimality of nonconvex tensor completion methods.
problem Estimating a low-rank tensor from incomplete and corrupted observations.
method Two-stage estimation algorithm for nonconvex optimization.
result Nonconvex tensor completion achieves optimal accuracy.
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.
The paper develops adaptive confidence intervals for Efron's Gaussian two-groups model with unknown contamination.
problem Developing robust uncertainty quantification for Efron's Gaussian two-groups model with unknown contamination fraction.
method The approach involves Fourier-based certification procedures to find minimax-optimal adaptive confidence intervals.
result The minimax-optimal length of adaptive confidence intervals is polynomially worse than when contamination fraction is known.
Safety filter for unknown discrete-time systems with learned models and noise covariance.
problem Ensuring safety for unknown discrete-time linear systems with Gaussian noise.
method Develops a learning-based safety filter using empirical model and noise covariance, optimizing control actions to stay within safety constraints.
result Minimally modifies nominal control actions to ensure safety with high probability, tightening constraints as more data is collected.
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 and losses.
result Squared loss is robust in Sy-De model but not in Asy-In model.
We consider a statistical inverse learning problem, where we observe the image of a function through a linear operator at i.i.d. random design points , superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimati…
Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time …
We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsyb…
We study the problem of learning an unknown mixture of rankings over elements, given access to noisy samples drawn from the unknown mixture. We consider a range of different noise models, including natural variants of the "heat kernel" noise framework and the Mallows model. For each of these noise models we giv…
Distributed estimation and learning with privacy preserved.
problem Privacy-preserving distributed estimation and learning in a networked environment.
method Linear aggregation schemes with differential privacy constraints.
result Noise minimizes convergence time to best estimates, using Laplace noise.
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…
Unsupervised nonparametric detection of unknown objects in noisy images based on percolation theorymath.ST
We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametri…
We investigate multiple testing and variable selection using the Least Angle Regression (LARS) algorithm in high dimensions under the assumption of Gaussian noise. LARS is known to produce a piecewise affine solution path with change points referred to as the knots of the LARS path. The key to our results is an express…
Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the stochastic noise (the difference between the stochastic and true gradient) is con…
New theory explains why normalization is preferred in SGD under heavy-tailed noise.
problem Understanding why normalization is preferred in stochastic gradient descent (SGD) under heavy-tailed noise.
method Developed a worst-case complexity theory for stochastically preconditioned SGD and its variants.
result Normalization guarantees convergence at optimal rates, while clipping may fail in the worst 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.
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.
Paper studies federated nonparametric testing with privacy constraints, achieving optimal rates and adaptive testing.
problem Federated nonparametric goodness-of-fit testing under distributed differential privacy constraints.
method Establishes matching lower and upper bounds on minimax separation rate, constructs adaptive testing procedure.
result Achieves optimal rates and demonstrates phase transition phenomena in federated testing.
We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification acc…
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected pe…
Adaptive algorithms improve performance in non-convex optimization across various scenarios.
problem Improper handling of noise scales, gradient magnitudes, and smoothness in non-convex optimization.
method Design and analysis of noise-adaptive, scale-free, and generalized algorithms.
result Adaptive algorithms achieve optimal rates and performance in diverse optimization settings.
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
problem Estimating eigenvectors with small eigen-gap and fine-grained statistical reasoning.
method Eigen-decomposition of asymmetric data matrix, distribution-free procedures, adaptive to heteroscedastic noise.
result Minimax optimal under Gaussian noise, confidence intervals for eigenvalues, small eigen-gap handling.
Wavelet-based online learning adapts to noisy Besov spaces with high probability.
problem Minimizing integrated squared error in Besov spaces with noisy observations.
method Adaptive wavelet-based online learning algorithm that dynamically adjusts to gradient noise.
result Achieves minimax-optimal integrated squared error with high probability.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
Method identifies unknown intervention targets in structural causal models from diverse data.
problem Identifying unknown intervention targets in structural causal models from heterogeneous data.
method Two-phase approach: first recovers exogenous noises, second matches with endogenous variables.
result Proposed method uniquely identifies intervention targets under causal sufficiency assumption.
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and ca…
Paper recovers lattice signal partitions efficiently.
problem Estimating lattice partition from noisy data.
method Uses dyadic CART for computationally-efficient partition recovery.
result Consistently estimates partition with optimal error rate.
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic n…
A new method estimates parameters in heavy-tailed corrupted regression with unknown covariance and heterogeneous noise.
problem Estimating parameters in regression with heavy-tailed errors and unknown covariance.
method Near-optimal computationally tractable estimator based on power method and Multiplicative Weight Update algorithm.
result The estimator achieves the optimal statistical rate and breakdown-point under near-optimal sample size.
New algorithm achieves optimal regret in non-stochastic control, showing stochasticity is not beneficial.
problem Achieving optimal control in non-stochastic systems with adversarial noise.
method Novel online Newton step algorithm adapted to adversarial disturbances, using policy regret bounds.
result Optimal regret achieved in unknown dynamics, regret in known dynamics.
In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predict…
The study establishes minimax bounds for estimating operators from noisy samples.
problem Estimating unknown operators between Hilbert spaces from noisy data.
method Developed a minimax theory for uniformly bounded Lipschitz operators, proving lower and upper bounds.
result Sharp characterizations of minimax risk for generic Lipschitz operators, showing a curse of sample complexity.
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required…
Unified framework for structured principal subspace estimation with bounds and rates.
problem Structured principal subspace estimation problems.
method Unified framework, minimax lower and upper bounds, information-geometric complexity.
result Minimax rates of convergence for specific settings, including optimal rates for non-negative PCA/SVD.
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…
New theory for PCA under weak latent factors, improving inference and testing.
problem Statistical inference for PCA with weak latent factors and cross-sectional dependence.
method Comprehensive estimation and inference theory for PCA under nearly minimal factor strength, non-asymptotic.
result Asymptotic normality of PCA-based estimator for with SNR growth rate.
DDPMs are robust to noisy score estimates and achieve optimal convergence rates in Wasserstein-2 distance.
problem Evaluating the quality of DDPMs in Wasserstein distance with noisy score estimates.
method Established finite-sample guarantees in Wasserstein-2 distance for DDPMs, considering noisy score estimates.
result Optimal convergence rates in Wasserstein-2 distance for DDPMs, matching Gaussian case.
Optimal pricing strategy for unknown valuation models with noisy feedback.
problem Minimizing regret in dynamic pricing with unknown valuation functions and noisy feedback.
method Proposes a minimax-optimal algorithm using discretization and data partitioning to handle unknown noise distribution and Lipschitz continuity of valuation functions.
result Achieves minimax-optimal regret bound matching the theoretical lower bound up to logarithmic factors.
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…