Related papers: Characterization of Hida Measures in white noise a…
Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
In this work, we consider an estimation method in sparse Poisson models inspired by [1] and provide novel sign consistency results under mild conditions.
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…
In this paper, we prove a central limit theorem and a moderate deviation principle for a perturbed stochastic Cahn-Hilliard equation defined on [0, T]x [0, \pi]^d, with d \in {1,2,3}. This equation is driven by a space-time white noise. The…
We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…
In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of "generic stability" in arbitrary theories. Among other things, we show that the standard definition of generic…
This work studies properties of the conditional mean estimator in vector Poisson noise. The main emphasis is to study conditions on prior distributions that induce linearity of the conditional mean estimator. The paper consists of two main…
We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for…
We study the noise, in the sense of Tsirelson, generated by Harris flows. A criterion is given for the noise to be non-white, and in this case we study the associated spectral sets.
We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…
We consider fine-tuning a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which has often been observed (e.g., when the target dataset is small…
This paper introduces a novel ridgelet transform-based method for Poisson image denoising. Our work focuses on harnessing the Poisson noise's unique non-additive and signal-dependent properties, distinguishing it from Gaussian noise. The…
White noise measurement can provide very useful information in addition to normal transport measurements. For example thermal noise measurement can be used at sub Kelvin temperature to determine the absolute electron temperature without…
Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering, learning systems. However, this paper aims to investigate whether the conventional proposition always holds. It begins with the definition of task…
A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and…
We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries…
We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling and…