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We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…

Probability · Mathematics 2015-09-03 Erik Ekström , Juozas Vaicenavicius

We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…

Probability · Mathematics 2020-07-28 Mikhail Zhitlukhin

Computer programs often behave differently under different compilers or in different computing environments. Relative debugging is a collection of techniques by which these differences are analysed. Differences may arise because of…

Software Engineering · Computer Science 2013-04-12 John Collins , Brian Farrimond , David Flower , Mark Anderson , David Gill

Drifting models are capable one-step generative models trained to follow a drifting field. The field combines attractive and repulsive softmax-weighted centroids over the data and current-generator distributions. In practice, only a…

Machine Learning · Computer Science 2026-05-01 Jiaru Zhang , Zeyun Deng , Juanwu Lu , Ziran Wang , Ruqi Zhang

National statistical institutes currently investigate how to improve the output quality of official statistics based on machine learning algorithms. A key obstacle is concept drift, i.e., when the joint distribution of independent variables…

Methodology · Statistics 2021-03-02 Quinten Meertens , Cees Diks , Jaap van den Herik , Frank Takes

The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…

Machine Learning · Computer Science 2019-12-05 Fabian Hinder , André Artelt , Barbara Hammer

In safety-critical domains such as autonomous driving and medical diagnosis, the reliability of machine learning models is crucial. One significant challenge to reliability is concept drift, which can cause model deterioration over time.…

Machine Learning · Computer Science 2023-11-23 Anton Winter , Nicolas Jourdan , Tristan Wirth , Volker Knauthe , Arjan Kuijper

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they…

Statistical Mechanics · Physics 2018-02-12 L. Bertini , P. Buttà

Drift in machine learning refers to the phenomenon where the statistical properties of data or context, in which the model operates, change over time leading to a decrease in its performance. Therefore, maintaining a constant monitoring…

Computation and Language · Computer Science 2023-09-08 Saeed Khaki , Akhouri Abhinav Aditya , Zohar Karnin , Lan Ma , Olivia Pan , Samarth Marudheri Chandrashekar

In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential…

Probability · Mathematics 2015-05-29 Robert C. Dalang , Albert N. Shiryaev

While many real-world data streams imply that they change frequently in a nonstationary way, most of deep learning methods optimize neural networks on training data, and this leads to severe performance degradation when dataset shift…

Machine Learning · Computer Science 2021-07-02 Wonju Lee , Seok-Yong Byun , Jooeun Kim , Minje Park , Kirill Chechil

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial…

Methodology · Statistics 2010-01-13 Ansgar Steland , Ewaryst Rafalowicz

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively…

Information Theory · Computer Science 2012-06-19 Swarnendu Kar , Pramod K. Varshney , Marimuthu Palaniswami

Classifiers and other statistics-based machine learning (ML) techniques generalize, or learn, based on various statistical properties of the training data. The assumption underlying statistical ML resulting in theoretical or empirical…

Machine Learning · Computer Science 2021-11-11 Samuel Ackerman , Orna Raz , Marcel Zalmanovici , Aviad Zlotnick

A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect…

Methodology · Statistics 2021-06-23 Michael Messer

Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…

Probability · Mathematics 2020-07-30 Philip A. Ernst , Goran Peskir

This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…

Numerical Analysis · Mathematics 2025-10-14 Dakang Cen , Wenlong Zhang , Zhidong Zhang

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…

Statistics Theory · Mathematics 2014-07-15 Shota Gugushvili , Peter Spreij

We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it…

Statistics Theory · Mathematics 2026-01-14 Alexey Muravlev , Mikhail Zhitlukhin

We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…

Optimization and Control · Mathematics 2026-02-24 Tiziano De Angelis , Jhanvi Garg , Quan Zhou
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