New algorithm reduces MFGs with common noise complexity.
problem Prohibitive computational cost in solving MFGs with common noise.
method Signatured deep fictitious play based on rough path theory.
result Significantly reduced computational complexity and improved efficiency.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
Framework for robust control in cooperative systems with uncertain common noise.
problem Optimizing collective behavior of agents in the presence of uncertain common noise.
method Proposes a robust mean-field control framework and proves existence of optimal controls.
result Existence of optimal open-loop controls linked to a lifted robust Markov decision problem.
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results…
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.
Study on PG learning for LQ MFC problems with common noise, proving convergence and sample complexity.
problem Optimal policy learning in LQ MFC problems with common noise and entropy regularization.
method Comprehensive error analysis of PG algorithms in both model-based and model-free settings.
result Global linear convergence and sample complexity of PG algorithms in model-free setting.
Study on optimal bubble riding with price-dependent entry times in a mean field game model.
problem Optimal bubble riding with price-dependent entry times.
method Mean field game of controls with common noise and random entry time, existence result obtained through discretization and limit analysis.
result Existence of equilibrium in the mean field game model.
Study optimizes interbank lending and borrowing to reduce systemic risk.
problem Optimizing lending and borrowing in interbank markets to mitigate systemic risk.
method Risk-sensitive mean field games with common noise, convex analysis, Fokker-Planck equations, first hitting time method.
result Risk-averse behavior reduces individual and systemic bank risks.
Method combines deep learning and elicitability for solving complex stochastic equations.
problem Solving McKean-Vlasov FBSDEs with common noise.
method Combines Picard iterations, elicitability, and deep learning.
result Validated on systemic-risk model and extended to quantile-mediated interactions.
The paper develops a method to model high-dimensional data with many variables and weak signals.
problem Modeling high-dimensional dependent data with many explanatory variables and low signal-to-noise ratio.
method Penalized regression for high-dimensional data, factor modeling of residuals, high-dimensional white noise testing, projected Principal Component Analysis.
result Established asymptotic properties of the proposed method for high-dimensional data.
Multi-view subspace learning (MSL) aims to find a low-dimensional subspace of the data obtained from multiple views. Different from single view case, MSL should take both common and specific knowledge among different views into consideration. To enhance the robustness of model, the complexity, non-consistency and simil…
Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable charac…
Proposes GRAB-MDM for robust multiview data fusion.
problem Limited theoretical guarantees for multiview fusion methods in noisy high-dimensional data.
method Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM) with adaptive bandwidth selection.
result Adaptive bandwidths lead to robust recovery of shared intrinsic structure in noisy multiview data.
Improved privacy-preserving statistical estimates with customizable noise reduction.
problem Balancing privacy and accuracy in statistical estimation.
method Introducing the Brownian mechanism, which adds Gaussian noise to a sequence of estimates, gradually reducing it based on the practitioner's needs.
result The Brownian mechanism produces more accurate estimates while maintaining strong privacy guarantees, outperforming existing methods.
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.
A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix corresponding to each dataset, and an additive noise matrix. Existing decomposition …
The paper analyzes arbitrage opportunities in a large investor market with common stock noises.
problem Identifying arbitrage opportunities in a market with many competitive investors.
method Stochastic differential games and mean-field systems to study market dynamics and optimal arbitrage.
result Optimal arbitrage is characterized by a solution to a Cauchy PDE involving volatility terms.
It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly accurate. If this input noise is not taken into account, a supervised machine learn…
Enhanced consistency bounds derived for classification under a new noise condition.
problem Enhanced consistency bounds for classification under a new noise condition.
method Model Margin Noise (MM noise) assumption, derived enhanced H-consistency bounds.
result Enhanced H-consistency bounds under MM noise condition, interpolates between linear and square-root regimes.
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 examines noise sensitivity of DNNs for binary classification.
problem Understanding non-robustness of DNN classifiers under noise.
method Defined and extended noise sensitivity and stability concepts for Boolean functions, applied to DNN models.
result Sorted out the relation between definitions and properties of DNN architectures under noise.
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.
The problem of multi-speaker localization is formulated as a multi-class multi-label classification problem, which is solved using a convolutional neural network (CNN) based source localization method. Utilizing the common assumption of disjoint speaker activities, we propose a novel method to train the CNN using synth…
Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most…
Colored noise improves neural network robustness against adversarial attacks.
problem Vulnerability of neural networks to adversarial perturbations.
method Injection of colored noise into network weights and activations during adversarial training.
result Our approach outperforms previous methods in terms of adversarial accuracy on CIFAR-10 and CIFAR-100 datasets.
The electroencephalogram (EEG) is the most popular form of input for brain computer interfaces (BCIs). However, it can be easily contaminated by various artifacts and noise, e.g., eye blink, muscle activities, powerline noise, etc. Therefore, the EEG signals are often filtered both spatially and temporally to increase …
Label noise in adversarial training leads to robust overfitting, explained and mitigated.
problem Label noise in adversarial training causes robust overfitting.
method Proposed a method to automatically calibrate labels.
result Consistent performance improvements across various models and datasets.
The paper studies how noise synchronizes tokens in deep transformer models.
problem Understanding synchronization in deep learning models with noise.
method Proves convergence to a stochastic particle system and identifies the limiting SDE.
result The limiting model displays synchronization by noise and exponential dissipation of interaction energy.
Study shows how market firm capitalization models converge to stochastic PDE solutions.
problem Understanding convergence of rank-based models with common noise to stochastic PDE solutions.
method Analysis of mean field limit, martingale problem, and pathwise entropy solutions.
result Empirical cumulative distribution function converges to solution of a stochastic PDE under certain conditions.
STAG injects noise into graph neural networks to improve performance.
problem Graph neural networks suffer from over-smoothing and limited discrimination.
method Introduces a stochastic aggregation framework (STAG) with adaptive noise injection.
result STAG models correct both over-smoothing and discrimination issues.
Unified framework for isotropic SG noise in posterior sampling.
problem Bayesian posterior sampling with practical and robust methods.
method Designing a novel, isotropic SG noise approach with fixed learning rate.
result Competitive and practical method compared to state-of-the-art.
Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial examples with some perturbations, which are widely known as adversarial examples. A…
Neural Networks have been shown to be sensitive to common perturbations such as blur, Gaussian noise, rotations, etc. They are also vulnerable to some artificial malicious corruptions called adversarial examples. The adversarial examples study has recently become very popular and it sometimes even reduces the term "adv…
The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However, most of these deal only with purely directed causal relationships and cannot det…
RECLAIM discovers causal graphs in cyclic, noisy systems.
problem Discovering causal relationships in cyclic, noisy systems.
method RECLAIM uses EM with residual normalizing flows to handle cycles and noise.
result RECLAIM effectively discovers causal graphs in both synthetic and real-world datasets.
We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to them or completely removing them from the training set. In the first case the model…
Proposes D-CDLF for multi-view data decomposition.
problem Uncorrelatedness between common and distinctive latent factors.
method Decomposes data into common, distinctive, and noise components.
result Effective uncorrelatedness between distinctive latent factors from different views.
While noise is commonly considered a nuisance in computing systems, a number of studies in neuroscience have shown several benefits of noise in the nervous system from enabling the brain to carry out computations such as probabilistic inference as well as carrying additional information about the stimuli. Similarly, no…
NMF and PCC linked, improving data denoising and feature stability.
problem Improving NMF's rank estimation and feature stability.
method Combining NMF and PCC for robust rank estimation and feature stability.
result NMF features are stable against noise and optimization seeds.
We study classification problems where features are corrupted by noise and where the magnitude of the noise in each feature is influenced by the resources allocated to its acquisition. This is the case, for example, when multiple sensors share a common resource (power, bandwidth, attention, etc.). We develop a method f…
Gaussians as noise in NCE lead to exponentially bad conditioning, hindering its efficiency.
problem Exponential conditioning of Hessian in NCE with Gaussian noise.
method Using Gaussian as the noise distribution in NCE.
result Gaussian noise in NCE leads to exponentially bad conditioning of the loss Hessian.
Noise stability improves understanding of Transformer models.
problem Lack of robustness metrics for real-valued domains and junta-like input dependence in modern LLMs.
method Proposed noise stability as a new metric and developed a practical regularization method.
result Noise stability regularization method accelerates training by 35-75%.
Simple method improves deep classifier accuracy under noisy labels.
problem Training deep classifiers with noisy labels.
method Probabilistic approach using temperature parameterized softmax.
result Improves accuracy, log-likelihood and calibration on noisy datasets.
We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.
Noisy labels are very common in real-world training data, which lead to poor generalization on test data because of overfitting to the noisy labels. In this paper, we claim that such overfitting can be avoided by "early stopping" training a deep neural network before the noisy labels are severely memorized. Then, we re…
Study improves model robustness in noisy datasets.
problem Instance-specific label noise in robust classification tasks.
method Coordinated Sparse Recovery (CSR) method introduces a collaboration matrix and confidence weights to reduce generalization error.
result CSR and CSR+ significantly reduce generalization error compared to existing methods.
New model shows neural networks can use noise to improve long-tailed data classification.
problem Understanding overfitting in neural networks with long-tailed data.
method Refined feature-noise data model incorporating class-dependent heterogeneous noise.
result Neural networks can leverage data noise to learn implicit features improving long-tailed data classification.