Related papers: On the detection of superdiffusive behaviour in ti…

Stochastic resetting has emerged as a useful strategy to reduce the completion time for a broad class of first passage processes. In the canonical setup, one intermittently resets a given system to its initial configuration only to start…

Time-series anomaly detection, which detects errors and failures in a workflow, is one of the most important topics in real-world applications. The purpose of time-series anomaly detection is to reduce potential damages or losses. However,…

The scale and quality of a dataset significantly impact the performance of deep models. However, acquiring large-scale annotated datasets is both a costly and time-consuming endeavor. To address this challenge, dataset expansion…

Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders…

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to…

We seek to characterize the motility of mouse fibroblasts on 2D substrates. Utilizing automated tracking techniques, we find that cell trajectories are super-diffusive, where displacements scale faster than t^(1/2) in all directions. Two…

We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…

Machine learning models are being increasingly used to automate decisions in almost every domain, and ensuring the performance of these models is crucial for ensuring high quality machine learning enabled services. Ensuring concept drift is…

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

Human behavior has the nature of indeterminacy, which requires the pedestrian trajectory prediction system to model the multi-modality of future motion states. Unlike existing stochastic trajectory prediction methods which usually use a…

The notion of concept drift refers to the phenomenon that the data generating distribution changes over time; as a consequence machine learning models may become inaccurate and need adjustment. In this paper we consider the problem of…

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal…

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…

Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…