Confidence bands for time series data

Korpela, Jussi; Puolamäki, Kai; Gionis, Aristides

doi:10.1007/s10618-014-0371-0

Cited by 17 publications

(44 citation statements)

References 16 publications

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“…The proposed solution is not to report p-values at all, but use confidence intervals instead [14]. Simultaneous confidence intervals for time series data have been proposed [9,11]. These correspond to the confidence areas in this paper when l = 0.…”

Section: Related Workmentioning

confidence: 80%

“…This formulation preserves easy interpretability: the user knows that any observation within the confidence area is guaranteed to violate at most l variable-specific confidence intervals. In the special case l = 0, this new definition coincides with the MWE problem [11]. The following examples illustrate further properties and uses of the new definition.…”

Section: Introductionmentioning

confidence: 78%

“…In Fig. 1 (left) the confidence area based on MWE [11], is shown by the green lines; recall the MWE interval corresponds to setting l = 0. While it is unaffected by the outlier, it strongly reacts to local fluctuations.…”

Section: Example 1: Local Anomalies In Time Seriesmentioning

confidence: 99%

“…Confidence areas for time series data have been defined [9,11] in terms of the minimum width envelope (MWE) problem: a time series is within a confidence area if it is within the confidence interval of every variable. While this has desirable properties, it can, however, result in very conservative confidence areas if there are local deviations from what constitutes "normal" behavior.…”

Section: Introductionmentioning

confidence: 99%

“…While this has desirable properties, it can, however, result in very conservative confidence areas if there are local deviations from what constitutes "normal" behavior. The definition in [11] is in fact too strict by requiring an observation to be contained in all variable-specific intervals.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multivariate Confidence Intervals

Korpela

Oikarinen

Puolamäki

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence intervals for multivariate data that extend the one-dimensional definition in a natural way. In our definition every variable is associated with its own confidence interval as usual, but a data vector can be outside of a few of these, and still be considered to be within the confidence area. We analyze the problem and show that the resulting confidence areas retain the good qualities of their onedimensional counterparts: they are informative and easy to interpret. Furthermore, we show that the problem of finding multivariate confidence intervals is hard, but provide efficient approximate algorithms to solve the problem.

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Section: Related Workmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 78%

Section: Example 1: Local Anomalies In Time Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multivariate Confidence Intervals

Korpela

Oikarinen

Puolamäki

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

Self Cite

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Efficient Local Search for Pseudo Boolean Optimization

Lei

Luo

Hoos

2021

Theory and Applications of Satisfiability Testing – SAT 2021

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Approximation Algorithms for Confidence Bands for Time Series

Tatti

2021

Machine Learning and Knowledge Discovery in Databases. Research Track

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Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find the smallest area enveloping k time series, where k is a user parameter. Confidence bands can be then used to detect abnormal time series, not just individual observations within the time series. We will show that despite being an NP-hard problem it is possible to find optimal confidence band for some k. We do this by considering a different problem: discovering regularized bands, where we minimize the envelope area minus the number of included time series weighted by a parameter α. Unlike normal confidence bands we can solve the problem exactly by using a minimum cut. By varying α we can obtain solutions for various k. If we have a constraint k for which we cannot find appropriate α, we demonstrate a simple algorithm that yields O( √ n) approximation guarantee by connecting the problem to a minimum k-union problem. This connection also implies that we cannot approximate the problem better than O n 1/4 under some (mild) assumptions. Finally, we consider a variant where instead of minimizing the area we minimize the maximum width. Here, we demonstrate a simple 2-approximation algorithm and show that we cannot achieve better approximation guarantee.

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Confidence bands for time series data

Cited by 17 publications

References 16 publications

Multivariate Confidence Intervals

Multivariate Confidence Intervals

Efficient Local Search for Pseudo Boolean Optimization

Approximation Algorithms for Confidence Bands for Time Series

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