This paper identifies and estimates the label noise transition matrix without ground truth labels.
problem Learning with noisy labels and identifying the noise transition matrix.
method Building on Kruskal's identifiability results, the paper characterizes the identifiability of the label noise transition matrix for the generic case at the instance level.
result The necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level.
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.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
A method to learn transition matrices without anchor points improves classifier performance.
problem Learning transition matrices in label-noise learning without anchor points.
method Transition-revision (T-Revision) method to learn transition matrices. result The proposed method leads to better classifiers without anchor points.
Proposes a new method to handle noisy labels without needing accurate noise transition estimation.
problem Learning with noisy labels in the presence of class-conditional noise.
method Introduces a Latent Class-Conditional Noise (LCCN) model that embeds noise transition in a Bayesian framework and iteratively infers latent labels.
result Demonstrates superior performance compared to state-of-the-art methods on various noisy label datasets.
Paper tackles instance-dependent label noise by approximating it with part-dependent noise.
problem Learning with instance-dependent label noise is challenging.
method Approximate instance-dependent label noise with part-dependent noise. Use transition matrices for parts to model noise.
result Method outperforms state-of-the-art approaches for instance-dependent label noise.
New method improves robustness of deep learning with noisy labels.
problem Robust deep learning on corrupted labels with noisy samples.
method Meta-transition adaptation through clean meta data guidance.
result More accurate estimation of noise transition matrix and classifier parameters.
It is important to learn various types of classifiers given training data with noisy labels. Noisy labels, in the most popular noise model hitherto, are corrupted from ground-truth labels by an unknown noise transition matrix. Thus, by estimating this matrix, classifiers can escape from overfitting those noisy labels. …
A method uses confidence scores to handle noisy labels for each instance.
problem Learning with noisy labels where each instance's label can randomly change.
method Introduces confidence-scored instance-dependent noise (CSIDN) to estimate transition distributions for each instance.
result Demonstrates the utility and effectiveness of CSIDN through experiments with synthetic and real-world noise.
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
Missing data reduces signal-to-noise ratio, not sample size, for PCA.
problem Effect of missing data on PCA signal structure learning.
method Analytic and simulation studies of probabilistic PCA with missing data.
result Missing data effectively reduces signal-to-noise ratio, not sample size.
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 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.
Deep heteroskedastic models overfit, showing a phase transition with regularization strength.
problem Overfitting in deep heteroskedastic regression models.
method Theoretical framework based on statistical field theory, empirical verification, and hyperparameter simplification.
result A phase transition in model behavior with varying regularization strength.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.
problem Signal-to-noise ambiguity in overparameterized mean-variance models.
method Statistical field theory framework to explain phase transition.
result Regularization reduces variability and improves predictive uncertainty quantification.
Proposes an alternative probabilistic interpretation of Huber loss.
problem Lack of intuitive understanding of Huber loss transition point.
method Relates Huber loss to Kullback-Leibler divergence between Laplace distributions.
result Identifies optimal transition point intuitively based on data noise.
New method improves variational inference for dynamical systems without extra computational cost.
problem Inexact variational inference leading to overconfident posterior and overestimation of process noise.
method Proposes a non-factorised posterior distribution for Gaussian process transition functions.
result Improves accuracy of posterior over transition function and process noise estimation.
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.
New insights show stochastic initialization prevents token clustering in deep Transformers.
problem Understanding token dynamics in deep stochastic Transformers.
method Analysis of deep Transformers with random initialization noise, proving convergence to an interacting-particle system on the sphere.
result Initialization noise prevents token clustering, leading to antipodal formations.
Paper tackles noisy similarity labels for multi-class classification.
problem Learning multi-class classifiers from noisy similarity-labeled data.
method Proposes a method using a noise transition matrix to learn from noisy data.
result Demonstrates superior performance compared to state-of-the-art methods.
Study on estimating signals from shifted and noisy copies in high dimensions, revealing a phase transition.
problem Estimating a signal in high-dimensional space from its circularly-shifted and noisy copies.
method Analysis of sample complexity in the high-dimensional regime, focusing on the parameter α.
result A phase transition phenomenon governed by α, with different sample complexities based on α values.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
problem Recovering a planted signal in spiked matrix models.
method Path-wise characterization of overlap using integro-differential equations and explicit formula derivation.
result Sharp phase transition in limiting overlap: positive in one regime, zero in another due to injected noise.
Free lunch from noise reveals linear spectral features for RL.
problem Trade-off between expressiveness and tractability in RL.
method Noise assumption and Spectral Dynamics Embedding (SPEDE).
result SPEDE breaks the trade-off and completes optimistic exploration.
Study phase transitions in shuffled regression problems.
problem Phase transitions in shuffled regression problems.
method Transformed permutation recovery into probabilistic graphical model, used message passing (MP) algorithm and branching random walk process.
result Characterized impact of signal-to-noise-ratio ($\snr$) on permutation recovery, proposed Gaussian approximation method.
Noise balance theory explains SGD's behavior in neural networks.
problem Understanding SGD's navigation in neural network loss landscapes.
method Analyzes minibatch noise and loss function symmetries.
result Derives the stationary distribution of SGD for deep networks.
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
New GANs learn clean labels from noisy data.
problem Training GANs with noisy labels.
method Incorporating a noise transition model to learn clean label distributions.
result rGANs can learn clean label distributions from noisy labels.
In this paper, we study the pooled data problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an exact asymptotic threshold on the required number of tests with optimal …
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theo…
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
problem Phase transitions in singular values and vectors of large random matrices.
method Analysis of singular values and vectors of long rectangular random matrices, and tensor unfolding algorithm for asymmetric rank-one spiked tensor models.
result An exact threshold for tensor unfolding to detect signals, independent of unfolding procedure.
Develops a machine learning framework for computing most probable paths in stochastic systems.
problem Computing the most probable paths in stochastic dynamical systems.
method Reformulates the boundary value problem of Hamiltonian systems and uses a neural network to solve the Euler-Lagrange equation for the Onsager-Machlup action functional.
result Demonstrates the efficacy and accuracy of the machine learning approach in computing most probable paths for stochastic systems with various types of noise.
Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.
problem Noisy low-rank-plus-sparse matrix recovery under arbitrary dependence.
method Incoherent-constrained least-square estimator, novel energy spreading result.
result Achieves minimax optimality in estimating structured Markov transition kernels.
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…
New AMP algorithms reveal phase transitions in tensor recovery.
problem Understanding algorithmic behavior of low-rank tensor decompositions.
method Derive Bayesian AMP algorithms and use dynamic mean field theory.
result Reveals phase transitions between easy, hard, and impossible inference regimes.
Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is used to identify the time indices (change points) at which the system transitions …
Model shows phase transitions in asset pricing with market maker incentives.
problem Analyzing asset pricing with market maker profit incentives.
method Stochastic game theory, neural networks.
result Equilibrium experiences three phases: linear pricing, mid-price with spread, and metastable state.
In this work, we investigate a novel training procedure to learn a generative model as the transition operator of a Markov chain, such that, when applied repeatedly on an unstructured random noise sample, it will denoise it into a sample that matches the target distribution from the training set. The novel training pro…
Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.
problem Estimating a rank-one symmetric matrix corrupted by noise.
method Gradient descent on a sphere, using local versions of the semi-circle law.
result Explicit formulas for the time evolution of the estimator and cost function, revealing phase transitions.
SGD transitions between maxima and minima with varying time scales.
problem Understanding SGD's behavior near critical points in noisy landscapes.
method Analyzing SGD convergence and escape dynamics in 1D landscapes with infinite- and finite-variance noise.
result SGD reliably moves to the basin's minimum unless close to a local maximum, where it can linger.
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of n objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …
Study on sample complexity of policy gradient for stabilizing linear systems under multiplicative noise.
problem Learning optimal feedback gain for stabilizing linear systems with multiplicative noise.
method Analyzes the sample complexity of policy gradient methods, addressing the cusp obstruction and using symmetry to control divergent parts of the gradient.
result Proves that projected mini-batch policy gradient attains total sample complexity of O(1/η) when noise density is known and O(η^(-(2s+1)/(2s))) when estimated, for C^s noise densities with s ≥ 2.
Paper learns dynamic generator models for video sequences.
problem Modeling spatial-temporal processes like dynamic textures and actions.
method Alternating back-propagation through time algorithm to learn latent state vectors and generator model.
result Trains realistic models for dynamic textures and actions.
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
A new method handles label noise by leveraging causal information.
problem Label noise degrades deep learning performance.
method Proposes a novel generative approach using a structural causal model.
result Improves classifier performance on label-noise datasets.
Randomized SVD shows phase transitions in noisy data.
problem Noise sensitivity of randomized SVD in large rank matrices.
method Analyzed R-SVD under low-rank signal plus noise model.
result R-SVD exhibits BBP-like phase transition with outliers above detectability threshold.
Improved market state classification for risk assessment.
problem Classifying financial market states for better risk assessment.
method Modified selection criteria for market states, clustering optimization, and visualization of correlation matrices.
result Statistically significant results in SP 500 and Nikkei 225 markets.
New method extracts stochastic laws from data, including Lévy noise.
problem Extracting stochastic laws from data with non-Gaussian noise.
method Using normalizing flows to estimate transition density, then applying nonlocal Kramers-Moyal formulas.
result Can learn stochastic differential equations with Lévy motion.