Clustering piecewise stationary processes
The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in non-parametric statistics and allow for arbitrary long-range dependence between variables. Piecewise stationary processes studied here for the first time in the context of clustering, relax the last remaining assumption in this model: stationarity. A natural formulation is proposed for this problem and a notion of consistency is introduced which requires the samples to be placed in the same cluster if and only if the piecewise stationary distributions that generate them have the same set of stationary distributions. Simple, computationally efficient algorithms are proposed and are shown to be consistent without any additional assumptions beyond piecewise stationarity.
Code (0)
등록된 구현이 없습니다.
Tasks
ClusteringTime SeriesTime Series AnalysisTime Series ClusteringSimilar Papers 제목 키워드 기반
Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes
We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotically consistent algorithms is designed for…
ClusteringBootstrap-Assisted Unit Root Testing With Piecewise Locally Stationary Errors
In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the li…
Locally Linear Continual Learning for Time Series based on VC-Theoretical Generalization Bounds
Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely…
Time Series ForecastingContinual LearningA Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Bandits
We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-s…
Change DetectionMulti-Armed BanditsDetection Is All You Need: A Feasible Optimal Prior-Free Black-Box Approach For Piecewise Stationary Bandits
We study the problem of piecewise stationary bandits without prior knowledge of the underlying non-stationarity. We propose the first $\textit{feasible}$ black-box algorithm applicable to most common parametric bandit va…
All