Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. Th…
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48 results for “additive/multiplicative noise”
The study investigates noise effects on parameter estimation for Ornstein-Uhlenbeck processes.
problem Impact of noise on parameter fitting for Ornstein-Uhlenbeck processes.
method Proposed algorithms to distinguish between thermal and multiplicative noise.
result Effective methods to estimate parameters even when multiplicative noise dominates.
The paper identifies generators of linear SDEs with noise types.
problem Identifying the generator of linear SDEs from their solution distribution.
method Deriving sufficient and necessary conditions for additive noise, and sufficient conditions for multiplicative noise.
result Generic conditions for identifying the generator of linear SDEs with both types of noise.
Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative…
Study on deep learning for speckle noise reduction in imaging modalities.
problem Multiplicative speckle noise challenges conventional deep learning methods for speckle denoising.
method Likelihood-based deep neural network (DNN) estimators for nonparametric regression under speckle noise.
result Established minimax rates for speckle denoising, matching those for additive Gaussian noise alone.
Optimizes control of noisy discrete systems without system matrix knowledge.
problem Optimal control of discrete-time systems with additive and multiplicative noises.
method Stochastic Lyapunov and Riccati equations, model-free reinforcement learning.
result Model-free reinforcement learning algorithm converges to optimal control policy.
Bayesian method improves forecasting of nonseparable Hamiltonian systems with noise.
problem Forecasting nonseparable Hamiltonian systems with multiplicative noise.
method Bayesian approach using deep learning and reduced-order modeling.
result Bayesian method yields up to 724 times improvement in forecasting accuracy.
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
SGD's escape rate depends on log loss barrier, not linear loss barrier.
problem Understanding the escape rate of SGD from local minima.
method Derived a stochastic differential equation (SDE) with additive noise from SGD's multiplicative noise property.
result The log loss barrier determines the escape rate of SGD, not the linear loss barrier.
We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local…
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio of the number o…
Stochastic regularisation is an important weapon in the arsenal of a deep learning practitioner. However, despite recent theoretical advances, our understanding of how noise influences signal propagation in deep neural networks remains limited. By extending recent work based on mean field theory, we develop a new frame…
Deep learning based numerical approximation algorithms for stochastic partial differential equationsmath.NA
Deep learning approximates SPDE solutions from noise trajectories.
problem Approximating solutions to stochastic partial differential equations (SPDEs).
method Uses neural networks to approximate SPDE solutions based on noise realizations.
result Accurately estimates SPDE solutions and functionals like mean and variance.
Proposes a new video attack method that multiplies perturbation to improve model robustness.
problem Challenges existing defense methods for video recognition models against additive adversarial attacks.
method Introduces Multiplicative Adversarial Videos (MultAV) to impose perturbation by multiplication.
result Model trained against additive attacks is less robust to MultAV.
Stochastic optimization's success linked to heavy-tailed noise.
problem Understanding stochastic optimization's success mechanisms.
method Modeling stochastic optimization as random recurrence relations, analyzing multiplicative noise and heavy-tailed behavior.
result Multiplicative noise leads to heavy-tailed stationary behavior in optimization parameters.
It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive noise and recover convergence. We show new sufficient conditions for the converge…
Algorithm identifies and corrects noisy labels using Gaussian process regression.
problem Detecting and correcting real-valued noisy labels from mixed data.
method Gaussian process regression with heteroscedastic noise model and leave-one-out cross-validation.
result The method can pinpoint corrupted sample points and improve regression models.
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.
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…
Estimates shared linear subspace from noisy data with multiple users.
problem Recovering shared linear subspace from noisy data with non-isotropic noise.
method Estimates shared subspace using at least two data points per user, avoiding restrictive assumptions.
result Upper and lower bounds for estimation error match, showing no additional error due to noise irregularity.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…
Dropout is a regularisation technique in neural network training where unit activations are randomly set to zero with a given probability \emph{independently}. In this work, we propose a generalisation of dropout and other multiplicative noise injection schemes for shallow and deep neural networks, where the random noi…
New method identifies causal graphs with limited data and noise.
problem Identifying causal graphs from observational data is generally impossible.
method Using additional data from two environments with different noise statistics, and assuming Gaussian noise.
result The entire causal graph can be uniquely identified with a constant number of environments.
A new method combines synthetic data analysis and DP generation to produce accurate uncertainty estimates.
problem Invalid inferences from DP synthetic data analysis.
method Combining synthetic data analysis techniques from MI and NA Bayesian modeling with a novel noise-aware synthetic data generation algorithm.
result Accurate confidence intervals from DP synthetic data are produced, wider with tighter privacy.
Private Topic Modelingstat.ML
We develop a privatised stochastic variational inference method for Latent Dirichlet Allocation (LDA). The iterative nature of stochastic variational inference presents challenges: multiple iterations are required to obtain accurate posterior distributions, yet each iteration increases the amount of noise that must be …
Multiplicative noise, including dropout, is widely used to regularize deep neural networks (DNNs), and is shown to be effective in a wide range of architectures and tasks. From an information perspective, we consider injecting multiplicative noise into a DNN as training the network to solve the task with noisy informat…
BNCR-GAN improves GANs to generate clean images from degraded inputs.
problem Generating clean images from blurred, noisy, and compressed degraded inputs.
method Multiple-generator model with image, blur-kernel, noise, and quality-factor generators, using masking architectures and adaptive consistency losses.
result BNCR-GAN effectively learns clean image generators from degraded images without degradation parameters.
GNIs induce asymmetric heavy-tailed noise in SGD, affecting network performance.
problem The effect of Gaussian noise injections on SGD dynamics and network performance.
method Developed a Langevin-like SDE driven by asymmetric heavy-tailed noise to model the modified SGD dynamics.
result GNIs induce an implicit bias that varies with noise heaviness and asymmetry, affecting network performance.
Improved optimization guarantees for deep learning models with Nesterov acceleration.
problem Optimization in non-convex deep learning landscapes.
method Analysis of Nesterov acceleration in benignly non-convex landscapes.
result Identical guarantees can be obtained in optimization problems with weak geometric assumptions, especially in overparametrized deep 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.
The inference of the causal relationship between a pair of observed variables is a fundamental problem in science, and most existing approaches are based on one single causal model. In practice, however, observations are often collected from multiple sources with heterogeneous causal models due to certain uncontrollabl…
Develops efficient inference for noise heterogeneity in machine learning models.
problem Downstream procedures based on residuals can be biased in additive noise models.
method Semiparametrically efficient inference using a novel Hilbert-valued one-step estimator.
result Constructs tests and confidence intervals for residual independence and goodness of fit.
Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian neural networks; several extensions ensued. We show that the log-uniform prior us…
Noise can stabilize systemic risk models with uncertain robustness.
problem Understanding systemic risk in financial systems with uncertain parameters.
method Analyzing a mean-field model of systemic risk with uncertain coefficients and noise.
result Noise can induce stability in systemic risk models, contrary to intuition.
This paper introduces a novel approach to texture synthesis based on generative adversarial networks (GAN) (Goodfellow et al., 2014). We extend the structure of the input noise distribution by constructing tensors with different types of dimensions. We call this technique Periodic Spatial GAN (PSGAN). The PSGAN has sev…
Study on nonsmooth contractive SA with constant stepsize and Q-learning.
problem Understanding convergence and bias in nonsmooth contractive SA with different noise types.
method Proposed prelimit coupling technique for steady-state convergence and derived asymptotic bias.
result Asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize.
Improved Kalman filtering with hierarchical variational approach.
problem Inconsistent process covariance estimation and slow convergence speed in traditional variational Kalman filtering.
method Introducing a surrogate variable for process-noise-free state, reformulating CAVI, and sliding-window hyperparameter estimation.
result Enhanced convergence speed and superior estimation accuracy compared to existing methods.
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCM…
Study quantization effects on high-dimensional linear regression learning.
problem Understanding quantization's impact on learning high-dimensional linear regression models.
method Analyzes stochastic gradient descent for high-dimensional linear regression under various quantization targets.
result Establishes precise bounds on excess risk for different quantization schemes.
Proposes a spectral method for jointly smooth functions on multiple manifolds.
problem Registering measurements from different sensors and rejecting noise.
method Two steps: kernel subspace span and spectral method.
result Guaranteed orthogonal functions that are as jointly smooth as possible.
Paper proposes a robust framework for detecting multiple periodic components in time series.
problem Detecting multiple periodic components in time series with interlaced patterns and external noise.
method Applying maximal overlap discrete wavelet transform to isolate periodic components, ranking them by wavelet variance, and detecting single periodicity robustly.
result The proposed algorithm outperforms other methods for both single and multiple periodicity detection.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
A new graph-based approach for estimating complex data with manifold structure.
problem Regression of large-scale, complex data with underlying geometric structure and noises.
method Constructing a skeleton graph to capture geometric structure, defining metrics, and applying nonparametric regression.
result Statistical guarantees and effectiveness demonstrated through simulations and real data examples.
Limited Attention Allocation in a Stochastic Linear Quadratic System with Multiplicative Noisemath.OC
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
The mean-field approximation model of company's income growthcond-mat.stat-mech
We introduce a mean-field type approximation for description of company's income statistics. Utilizing huge company data we show that a discrete version of Langevin equation with additive and multiplicative noises can appropriately describe the time evolution of a company's income fluctuation in statistical sense. The …
We consider the problem of publicly releasing a dataset for support vector machine classification while not infringing on the privacy of data subjects (i.e., individuals whose private information is stored in the dataset). The dataset is systematically obfuscated using an additive noise for privacy protection. Motivate…
Paper proposes a self-supervised method to denoise autoregressive signals with heavy-tailed noise.
problem Denoising autoregressive signals corrupted by heavy-tailed noise.
method Self-supervised learning approach without requiring full noise distribution knowledge.
result Strong denoising performance compared to baseline methods, especially for impulsive noise.
We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. W…