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振荡型非平稳时间序列的高效分段AI 解读

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model,…

带不确定性量化的贝叶斯变点检测框架AI 解读

We introduce a novel Bayesian method that can detect multiple structural breaks in the mean and variance of a length $T$ time-series. Our method quantifies uncertainty by returning $α$-level credible sets around the estimated locations of the breaks. In the case of a single change in the mean and/or the variance of an independent sub-Gaussian sequence, we prove that our method attains a localization rate that is minimax optimal up to a $\log T$ factor. For an $α$-mixing…