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In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct…

Applications · Statistics 2021-10-20 Mitchell Krock , Julie Bessac , Michael L. Stein , Adam H. Monahan

Sequential user behavior modeling plays a crucial role in online user-oriented services, such as product purchasing, news feed consumption, and online advertising. The performance of sequential modeling heavily depends on the scale and…

Machine Learning · Computer Science 2020-11-03 Jianwen Yin , Chenghao Liu , Weiqing Wang , Jianling Sun , Steven C. H. Hoi

Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…

Methodology · Statistics 2019-12-06 Shrijita Bhattacharya , Jan Beirlant

We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged…

Statistical Finance · Quantitative Finance 2018-10-30 Ladislav Kristoufek

Feedback controlled ratchets are thermal rectifiers that use information on the state of the system to operate. We study the effects of time delays in the feedback for a protocol that performs an instantaneous maximization of the…

Statistical Mechanics · Physics 2008-04-13 F. J. Cao , M. Feito

We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order…

Probability · Mathematics 2017-01-25 Lev B. Klebanov , Jaromir Antoch , Andrea Karlova , Ashot V. Kakosyan

Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…

Robotics · Computer Science 2019-08-26 Francesco Cursi , Guang-Zhong Yang

Low latency is critical for interactive networked applications. But while we know how to scale systems to increase capacity, reducing latency --- especially the tail of the latency distribution --- can be much more difficult. In this paper,…

Networking and Internet Architecture · Computer Science 2013-06-18 Ashish Vulimiri , P. Brighten Godfrey , Radhika Mittal , Justine Sherry , Sylvia Ratnasamy , Scott Shenker

We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…

Probability · Mathematics 2025-05-09 Xiangyu Huang , Yong Liu , Kainan Xiang

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…

Computation and Language · Computer Science 2025-09-29 Mobina Pournemat , Keivan Rezaei , Gaurang Sriramanan , Arman Zarei , Jiaxiang Fu , Yang Wang , Hamid Eghbalzadeh , Soheil Feizi

Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to…

Machine Learning · Computer Science 2023-01-24 Christian Fröhlich , Robert C. Williamson

Towards safe autonomous driving (AD), we consider the problem of learning models that accurately capture the diversity and tail quantiles of human driver behavior probability distributions, in interaction with an AD vehicle. Such models,…

Machine Learning · Computer Science 2024-10-28 Jia Yu Tee , Oliver De Candido , Wolfgang Utschick , Philipp Geiger

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…

Methodology · Statistics 2026-05-20 Jonas F. Frederiksen , Muneya Matsui , Rasmus S. Pedersen

Single unit recordings in the human medial temporal lobe (MTL) have revealed a population of cells with conceptually based, highly selective activity, indicating the presence of a sparse neural code. Building off previous work by the author…

Neurons and Cognition · Quantitative Biology 2015-08-19 Andrew Magyar

Background: In neurophysiological data, latency refers to a global shift of spikes from one spike train to the next, either caused by response onset fluctuations or by finite propagation speed. Such systematic shifts in spike timing lead to…

Recently, small models with latent recursion have obtained promising results on complex reasoning tasks. These results are typically explained by the theory that such recursion increases a networks depth, allowing it to compactly emulate…

Computation and Language · Computer Science 2026-02-06 Arip Asadulaev , Rayan Banerjee , Fakhri Karray , Martin Takac

Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…

Disordered Systems and Neural Networks · Physics 2017-06-06 Jiajun Luo , M. Grayson

Observations indicate that the distributions of stock returns in financial markets usually do not conform to normal distributions, but rather exhibit characteristics of high peaks, fat tails and biases. In this work, we assume that the…

Statistical Finance · Quantitative Finance 2023-12-06 Bo Li

The focus of the current work concerned the psychological processes that underlie prediction of an events duration. The objective was to push forward existing psychological theory on event duration prediction, something made possible by the…

Human-Computer Interaction · Computer Science 2025-09-19 Mark G Orr

Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…

Data Analysis, Statistics and Probability · Physics 2025-12-10 Robin A. Kopp , Sabine H. L. Klapp , Deepak Gupta