Noise Sensitivity Exponent controls statistical-computational gaps in learning.
problem Understanding when learning is statistically possible yet computationally hard in high-dimensional statistics.
method Investigating statistical-computational gaps in single- and multi-index models using Noise Sensitivity Exponent.
result Noise Sensitivity Exponent governs statistical-computational gaps in high-dimensional learning.
Noise-resilient method improves Hurst exponent estimation accuracy in noisy data.
problem Noise degrades accuracy of Hurst exponent estimation methods.
method Noise-Controlled ALPHEE (NC-ALPHEE) using wavelet multi-scale analysis and neural network combination.
result NC-ALPHEE consistently outperforms existing techniques in noisy conditions.
Python package for estimating Hurst exponent in fBm.
problem Estimating Hurst exponent in fractional Brownian motion.
method Whittle's likelihood method applied to fractional Gaussian noise.
result Implementation achieves state-of-the-art accuracy and speed.
New convergence bounds for online learning with heavy-tailed noise.
problem Learning on streaming data with heavy-tailed noise.
method Nonlinear stochastic gradient descent (SGD) for non-convex and strongly convex costs.
result Strong convergence rates for various nonlinearities and noise distributions.
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…
In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can …
Optimizer memory affects learning rate sensitivity in shuffle order, impacting fine-tuning noise.
problem Optimizer memory affects the learning rate sensitivity in shuffle order, leading to fine-tuning noise.
method Isolated the mechanism of fixed-clock optimizer memory affecting the learning rate sensitivity in shuffle order, deriving a fit-free way to size the noise.
result Fixed-clock optimizers like AdamW produce a larger first-order noise channel compared to memoryless optimizers, affecting fine-tuning comparisons.
Proposes a differentially private bandit algorithm reducing noise over time.
problem Privacy concerns in interactive recommendation systems.
method Tree-based mechanism to add Laplace or Gaussian noise to model parameters, focusing on dynamic global sensitivity.
result Demonstrates (ε,δ)-differential privacy with reduced noise and improved regret. This study generalizes an econophysics model to account for trader heterogeneity, finding robust power-law exponents but sensitive prefactors.
problem The original Lillo-Mike-Farmer model assumed homogeneity in traders' order-splitting strategies, which this study generalizes.
method The study proposes a generalised Lillo-Mike-Farmer model and solves it exactly without heuristic assumptions.
result The power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions, but the prefactor is sensitive to heterogeneity.
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.
New method for certified unlearning reduces noise injection.
problem Achieving formal unlearning guarantees with adaptive noise calibration.
method Adaptive per-instance noise calibration based on individual data point sensitivities.
result Derivation of high-probability per-instance sensitivity bounds for ridge regression.
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample of asset returns. We find that the existence of the optimum is a probabilistic …
The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more s…
Deep Convolutional Networks (DCNs) have been shown to be sensitive to Universal Adversarial Perturbations (UAPs): input-agnostic perturbations that fool a model on large portions of a dataset. These UAPs exhibit interesting visual patterns, but this phenomena is, as yet, poorly understood. Our work shows that visually …
In binary classification framework, we are interested in making cost sensitive label predictions in the presence of uniform/symmetric label noise. We first observe that 0-1 Bayes classifiers are not (uniform) noise robust in cost sensitive setting. To circumvent this impossibility result, we present two schemes; un…
Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender). Existing work on the problem operates under the assumption that the sensitive feature available in one's training sample is perfectly reliable. This assumption may be violated in…
Study on financial systems using perturbed unimodal maps with heteroscedastic noise.
problem Analyzing systemic risk in financial systems using mathematical models.
method Investigation of one-dimensional unimodal maps perturbed by heteroscedastic noise, proving stability, convergence, and Lyapunov exponent continuity.
result Continuous dependence of average Lyapunov exponent on Markov chain parameters, and Gumbel's law for extreme values.
Study finds roughness in volatility despite diffusive instantaneous volatility.
problem Determining the roughness of volatility in financial assets.
method Non-parametric method based on normalized p-th variation for estimating roughness of sample paths. result Realized volatility exhibits rough behavior with a significantly smaller Hurst exponent than instantaneous volatility.
Diffusion models accurately recover mixture weights from generated samples despite score function insensitivity.
problem Score-based generative models often fail to learn correct relative mode amplitudes (mixture weights) from generated samples.
method Relate diffusion score matching (DSM) loss to mixture weight estimation error, define diffusion score sensitivity index (DSSI), and prove its governing role in mixture weight recovery.
result Generated samples can accurately recover mixture weights from the DSM loss, even when the target score is insensitive to mixture weights.
Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3-5. We show how to use Friedrich et al.'s formalism to predict that…
edPLS adds Gaussian noise to PLS regression to protect data privacy.
problem Protecting sensitive data in PLS regression models.
method Integrates Gaussian noise into PLS algorithm based on global sensitivity.
result Effective at preserving privacy while maintaining competitive prediction accuracy.
With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known inputs", these NNs can fail absurdly on the "unseen inputs", especially if these real…
New method calibrates noise for attack risk, improving ML model accuracy.
problem Improving accuracy of privacy-preserving ML models while maintaining privacy.
method Directly calibrates noise scale to a desired attack risk level, bypassing the standard ε-calibration. result Significantly decreases noise scale, leading to increased utility at the same risk level.
Privacy preserving machine learning algorithms are crucial for learning models over user data to protect sensitive information. Motivated by this, differentially private stochastic gradient descent (SGD) algorithms for training machine learning models have been proposed. At each step, these algorithms modify the gradie…
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.
Study reveals investor heterogeneity in Korean equity market cash flows.
problem Investor heterogeneity and its impact on market dynamics.
method Detrended fluctuation analysis (DFA) on aggregated cash flows.
result Persistence in cash flows varies by investor type, with retail flows showing strong persistence.
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.
Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. We show how to extract and decompose uncertainty into epistemic and…
Noise injection improves inference privacy in DNN models.
problem Malicious servers can infer sensitive attributes from input data.
method Adaptive Noise Injection (ANI) using a lightweight DNN on the client.
result Significant improvement in privacy (up to 48.5% degradation in sensitive-task accuracy with <1% degradation in primary accuracy).
Lyapunov exponents help understand RNN stability.
problem Optimizing RNNs is sensitive to various parameters.
method Use Lyapunov exponents as dynamical system tools.
result Lyapunov spectrum measures training stability.
Paper develops methods for fair insurance pricing without direct access to sensitive attributes.
problem Fairness in insurance pricing with restricted access to sensitive attributes.
method Develops statistical methods for estimating discrimination-free premiums using privatized sensitive attributes.
result The proposed methods enable fair insurance pricing while respecting privacy and regulatory constraints.
Proposes a text perturbation method using a Mahalanobis metric to balance privacy and utility.
problem Low utility of text analysis when using spherical noise for privacy-preserving text embedding.
method Regularized Mahalanobis metric to add elliptical noise, accounting for embedding space density.
result Improves privacy statistics while maintaining utility, outperforming Laplace mechanism.
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%.
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of the…
Improved saliency maps for deep neural networks with reduced noise.
problem Noisy explanations in Integrated Gradients for deep neural networks.
method SmoothTaylor, adaptive noising, and SmoothGrad techniques.
result SmoothTaylor and adaptive noising generate better quality saliency maps.
Existence of solutions to the Heath-Jarrow-Morton equation of the bond market with linear volatility and general Lévy random factor is studied. Conditions for existence and non-existence of solutions in the class of bounded fields are presented. For the existence of solutions the Lévy process should necessarily be with…
Gradient-based methods introduce noise that penalizes models sensitive to weight perturbations.
problem Noise in gradient-based optimization methods.
method Analysis of Gradient Descent (GD) and Stochastic Gradient Descent (SGD) updating all parameters simultaneously.
result Noise introduced by simultaneous parameter updates penalizes models sensitive to weight perturbations.
Discrete Gaussian noise preserves privacy and accuracy in differential privacy.
problem Finite computers cannot represent continuous Gaussian noise, leading to privacy breaches and loss of interpretability.
method Introduced and analyzed discrete Gaussian noise, providing privacy and accuracy guarantees similar to continuous Gaussian noise.
result Discrete Gaussian noise offers the same privacy and accuracy as continuous Gaussian noise, with efficient sampling algorithms.
New methods for calculating credit valuation adjustment with reduced noise and faster computation.
problem High statistical noise in computing sensitivities of CVA due to non-differentiable default intensities.
method Ad hoc analytical estimators to overcome non-differentiability and finite differences.
result Low statistical noise and fast computation of sensitivities to market quotes.
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…
How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as n−β where n is the number of training examples and β an exponent that depends on both data and algorithm. In this work we measure β when applying kernel methods to real datasets. For …
Bayesian approach improves AdaLoRA's performance and efficiency.
problem Improving the efficiency and performance of adaptive low-rank adaptation.
method Utilized Bayesian metrics and the Improved Variational Online Newton (IVON) optimizer for adaptive parameter budget allocation.
result Bayesian counterpart outperforms sensitivity-based importance metric and is faster than AdaLoRA.
Boosting is known to be sensitive to label noise. We studied two approaches to improve AdaBoost's robustness against labelling errors. One is to employ a label-noise robust classifier as a base learner, while the other is to modify the AdaBoost algorithm to be more robust. Empirical evaluation shows that a committee of…
Diffusion models explained via cognitive science.
problem Weak sensitivity to noise family and noise level scheduling.
method Correspondence with serial reproduction in cognitive science.
result Properties of diffusion models explained by cognitive science.
Paper relaxes symmetry conditions for universal feature selection in noisy data.
problem Feature selection in noisy data with weak symmetry.
method Developed a universal feature selection framework using singular value decomposition of canonical dependence matrix.
result Selected features achieve asymptotically optimal error exponents up to a residual term.
We propose Absum, which is a regularization method for improving adversarial robustness of convolutional neural networks (CNNs). Although CNNs can accurately recognize images, recent studies have shown that the convolution operations in CNNs commonly have structural sensitivity to specific noise composed of Fourier bas…
Noise can affect the overparametrization of QNNs, enabling new directions but also suppressing sensitivity.
problem The overparametrization of QNNs in the presence of noise.
method Analyzing the Quantum Fisher Information Matrix (QFIM) to understand how noise affects the rank of QFIM.
result Noise can turn previously-zero eigenvalues of the QFIM to non-zero, enabling exploration of new directions.
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…