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1. Scalable multiple changepoint detection for functional data sequences

   https://doi.org/10.1002/env.2710  

   Harris, Trevor ; Li, Bo ; Tucker, J. Derek ( November 2021 , Environmetrics)

   We propose the multiple changepoint isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the variability “between” and “within” the functional observations. We then present an augmented fused lasso procedure to split the projections into multiple regions robustly. These regions act to isolate each changepoint away from the others so that the powerful univariate CUSUM statistic can be applied region‐wise to identify the changepoints. Simulations show that our method accurately detects the number and locations of changepoints under many different scenarios. These include light and heavy tailed data, data with symmetric and skewed distributions, sparsely and densely sampled changepoints, and mean and covariance changes. We show that our method outperforms a recent multiple functional changepoint detector and several univariate changepoint detectors applied to our proposed projections. We also show that MCI is more robust than existing approaches and scales linearly with sample size. Finally, we demonstrate our method on a large time series of water vapor mixing ratio profiles from atmospheric emitted radiance interferometer measurements.

    

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2. A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening

   Lin, Kevin ; Sharpnack, James L ; Rinaldo, Alessandro ; Tibshirani, Ryan J ( December 2017 , Advances in neural information processing systems)

   In the 1-dimensional multiple changepoint detection problem, we derive a new fast error rate for the fused lasso estimator, under the assumption that the mean vector has a sparse number of changepoints. This rate is seen to be suboptimal (compared to the minimax rate) by only a factor of loglogn. Our proof technique is centered around a novel construction that we call a lower interpolant. We extend our results to misspecified models and exponential family distributions. We also describe the implications of our error analysis for the approximate screening of changepoints. 

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3. Improved Time-Localization of Power System Forced Oscillations Using Changepoint Detection

   https://doi.org/10.1109/PESGM48719.2022.9916848  

   Dosiek, Luke ; Hosur, Sanjay ( July 2022 , 2022 IEEE Power & Energy Society General Meeting (PESGM))

   This paper explores the use of changepoint detection (CPD) for an improved time-localization of forced oscillations (FOs) in measured power system data. In order for the autoregressive moving average plus sinusoids (ARMA+S) class of electromechanical mode meters to successfully estimate modal frequency and damping from data that contains a FO, accurate estimates of where the FO exists in time series are needed. Compared to the existing correlation-based method, the proposed CPD method is based on upon a maximum likelihood estimator (MLE) for the detection of an unknown number changes in signal mean to unknown levels at unknown times. Using the pruned exact linear time (PELT) dynamic programming algorithm along with a novel refinement technique, the proposed approach is shown to provide a dramatic improvement in FO start/stop time estimation accuracy while being robust to intermittent FOs. These findings were supported though simulations with the minniWECC model. 

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4. An Iterative Algorithm for Accurate Estimation of Power System Forced Oscillation Parameters

   https://doi.org/10.1109/PESGM52003.2023.10253231  

   Dosiek, Luke ; Hosur, Sanjay ( July 2023 , 2023 IEEE Power & Energy Society General Meeting (PESGM))

   This paper proposes an iterative method of estimating power system forced oscillation (FO) amplitude, frequency, phase, and start/stop times from measured data. It combines three algorithms with favorable asymptotic statistical properties: a periodogram-based iterative frequency estimator, a Discrete-Time Fourier Transform (DTFT)-based method of estimating amplitude and phase, and a changepoint detection (CPD) method for estimating the FO start and stop samples. Each of these have been shown in the literature to be approximate maximum likelihood estimators (MLE), meaning that for large enough sample size or signal-to-noise ratio (SNR), they can be unbiased and reach the Cramer-Rao Lower Bound in variance. The proposed method is shown through Monte Carlo simulations of a low-order model of the Western Electricity Coordinating Council (WECC) power system to achieve statistical efficiency for low SNR values. The proposed method is validated with data measured from the January 11, 2019 US Eastern Interconnection (EI) FO event. It is shown to accurately extract the FO parameters and remove electromechanical mode meter bias, even with a time-varying FO amplitude. 

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5. Active multi-fidelity Bayesian online changepoint detection

   Gundersen, Gregory W. ; Cai, Diana ; Zhou, Chuteng ; Engelhardt, Barbara E. ; Adams, Ryan P. ( January 2021 , Uncertainty in artificial intelligence)

   null (Ed.)

   Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it may be beneficial to trade the cost of collecting an environmental measurement against the quality or "fidelity" of this measurement and how the measurement affects changepoint estimation. For instance, one might decide between inertial measurements or GPS to determine changepoints for motion. A Bayesian approach to changepoint detection is particularly appealing because we can represent our posterior uncertainty about changepoints and make active, cost-sensitive decisions about data fidelity to reduce this posterior uncertainty. Moreover, the total cost could be dramatically lowered through active fidelity switching, while remaining robust to changes in data distribution. We propose a multi-fidelity approach that makes cost-sensitive decisions about which data fidelity to collect based on maximizing information gain with respect to changepoints. We evaluate this framework on synthetic, video, and audio data and show that this information-based approach results in accurate predictions while reducing total cost. 

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