Related papers: Einstein from Noise: Statistical Analysis
Inferring networks from observed time series data presents a clear glimpse into the interconnections among nodes. Network inference models, when dealing with real-world open cases, especially in the presence of observational noise,…
In the electronic measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densities of thermal noise across a resistor at the triple point of water, and pseudo-random noise synthetically…
Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself -- a notable example being the inherent voltage fluctuations that exist across any resistor…
The origin of the low-frequency noise with power spectrum $1/f^\beta$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^\beta$ noise have…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…
The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90 (1999) 5-43],…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
Fine-grained annotations---e.g. dense image labels, image segmentation and text tagging---are useful in many ML applications but they are labor-intensive to generate. Moreover there are often systematic, structured errors in these…
Reconstructing the electric field from the measured voltages in an antenna, unfolding the antenna response, comes with several problems. Due to the noisiness of the signal it is often necessary to disregard part of the bandwidth of the…
Benign overfitting is a phenomenon in machine learning where a model perfectly fits (interpolates) the training data, including noisy examples, yet still generalizes well to unseen data. Understanding this phenomenon has attracted…
Variational quantum algorithms have received substantial theoretical and empirical attention. As the underlying variational quantum circuit (VQC) can be represented by Fourier series that contain an exponentially large spectrum in the…
We study the multi-reference alignment (MRA) problem of recovering a signal from noisy observations acted on by unknown random circular shifts. While the information-theoretic limits of MRA are well characterized in many settings, the…
In coherent optical communication systems the laser phase noise is commonly modeled as a Wiener process. We propose a sliding-window based linearization of the phase noise, enabling a novel description. We show that, by stochastically…
Recent experiments by F. Yoshihara et al. [Phys. Rev. Lett. 97, 167001 (2006)] and by K. Kakuyanagi et al. (cond-mat/0609564) provided information on decoherence of the echo signal in Josephson-junction flux qubits at various bias…
The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of $n$subjects provides $T$ responses to a vector of…
In this article, a general information-plus-noise transmission model is assumed, the receiver end of which is composed of a large number of sensors and is unaware of the noise pattern. For this model, and under reasonable assumptions, a set…
Electroencephalographic (EEG) signals are fundamental to neuroscience research and clinical applications such as brain-computer interfaces and neurological disorder diagnosis. These signals are typically a combination of neurological…
Discovering the mechanism underlying the ubiquity of $"1/f^{\alpha}"$ noise has been a long--standing problem. The wide range of systems in which the fluctuations show the implied long--time correlations suggests the existence of some…
Attenuation bias -- the systematic underestimation of regression coefficients due to measurement errors in input variables -- affects astronomical data-driven models. For linear regression, this problem was solved by treating the true input…