Reactive point processes: A new approach to predicting power failures in underground electrical systems

Ertekin, Şeyda; Rudin, Cynthia; McCormick, Tyler H.

doi:10.1214/14-aoas789

Cited by 57 publications

(43 citation statements)

References 35 publications

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“…Our focus with real data experiments is to demonstrate that the models we analyze are sufficiently complex to capture real-world phenomena and enhance prediction performance relative to naive models. Others have successfully used more complex, difficult to analyze models (cf., [39,17]) which are similar in spirit to those analyzed here. Our claim is not that our approach leads to uniformly better empirical performance than previous methods, but rather that our models capture essential elements of all these approaches and hence our theoretical work provides insights into a variety of approaches.…”

Section: Numerical Experimentssupporting

confidence: 82%

Network Estimation From Point Process Data

Mark

Raskutti

Willett

2019

IEEE Trans. Inform. Theory

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Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-exciting point processes, in which the likelihood of future events depends on the past events. This paper addresses the problem of estimating self-excitation parameters and inferring the underlying functional network structure from self-exciting point process data. Past work in this area was limited by strong assumptions which are addressed by the novel approach here. Specifically, in this paper we (1) incorporate saturation in a point process model which both ensures stability and models non-linear thresholding effects;(2) impose general low-dimensional structural assumptions that include sparsity, group sparsity and low-rankness that allows bounds to be developed in the high-dimensional setting; and (3) incorporate long-range memory effects through moving average and higher-order auto-regressive components. Using our general framework, we provide a number of novel theoretical guarantees for high-dimensional self-exciting point processes that reflect the role played by the underlying network structure and long-term memory. We also provide simulations and real data examples to support our methodology and main results.

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Section: Numerical Experimentssupporting

confidence: 82%

Network Estimation From Point Process Data

Mark

Raskutti

Willett

2019

IEEE Trans. Inform. Theory

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“…Whilst we opted to use crime data to demonstrate its utility, the framework can be used to assess predictions in fields such as ecology (Tuia et al 2008), geophysics (Marzocchi et al 2012) and civil engineering (Ertekin et al 2015). Predictive accuracy measures such as hit rate or PAI have a similar meaning and interpretation irrespective of domain and can therefore be applied directly.…”

Section: Discussionmentioning

confidence: 99%

“…Introduction 1.1. Spatio-temporal point processes and hotspot prediction Many physical and sociological processes of interest take the form of events that occur at discrete points in space and time, including crime (Mohler et al 2011), earthquakes (Zhuang et al 2002) and infrastructure failures (Ertekin et al 2015). These are referred to as spatio-temporal point processes (henceforth denoted STPPs).…”

mentioning

confidence: 99%

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

Adepeju

Rosser

Cheng

2016

International Journal of Geographical Information Science

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Many physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point processbased prediction. ARTICLE HISTORY

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“…Wang et al (2016) presented a recurrent marked temporal point process (RMT-PP) and demonstrated its effectiveness in predicting the timing of taxi pick-ups. Log Gaussian Cox process (LGCP) has been used to effectively model temporal events, such as wildfires [30] and infrastructure failures [9], in which the logarithm of the intensity is assumed to be drawn from a Gaussian process. The spatio-temporal point process is a more general framework, and considers both spatial and temporal domains.…”

Section: Related Workmentioning

confidence: 99%

Deep Mixture Point Processes

Okawa¹,

Iwata²,

Kurashima³

et al. 2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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ZUSAMMENFASSUNGPredicting when and where events will occur in cities, like taxi pickups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and location-based marketing. Though many point processes have been proposed to model events in a continuous spatio-temporal space, none of them allow for the consideration of the rich contextual factors that affect event occurrence, such as weather, social activities, geographical characteristics, and traffic. In this paper, we propose DMPP (Deep Mixture Point Processes), a point process model for predicting spatio-temporal events with the use of rich contextual information; a key advance is its incorporation of the heterogeneous and high-dimensional context available in image and text data. Specifically, we design the intensity of our point process model as a mixture of kernels, where the mixture weights are modeled by a deep neural network. This formulation allows us to automatically learn the complex nonlinear effects of the contextual factors on event occurrence. At the same time, this formulation makes analytical integration over the intensity, which is required for point process estimation, tractable. We use real-world data sets from different domains to demonstrate that DMPP has better predictive performance than existing methods.

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Reactive point processes: A new approach to predicting power failures in underground electrical systems

Cited by 57 publications

References 35 publications

Network Estimation From Point Process Data

Network Estimation From Point Process Data

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

Deep Mixture Point Processes

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