Related papers: Probabilistic Analysis of Scalogram Ridges in Sign…

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…

We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…

In this paper, we study the convergence of the Adaptive Moment Estimation (Adam) algorithm under unconstrained non-convex smooth stochastic optimizations. Despite the widespread usage in machine learning areas, its theoretical properties…

Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that the noise of stochastic gradient descent improves…

Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or…

Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically…

Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of…

Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…

We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large…

We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimising a penalised ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical…

Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…

In quantum computing, characterizing the full noise profile of qubits can aid in increasing coherence times and fidelities by developing error-mitigating techniques specific to the noise present. This characterization also supports efforts…

The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex…

It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Inference about a scalar parameter of interest is a core statistical task that has attracted immense research in statistics. The Wald statistic is a prime candidate for the task, on the grounds of the asymptotic validity of the standard…

Machine learning algorithms aim to find patterns from observations, which may include some noise, especially in robotics domain. To perform well even with such noise, we expect them to be able to detect outliers and discard them when…