Convex Parameter Recovery for Interacting Marked Processes - Multidisciplinary Institute in Artificial intelligence - Grenoble Alpes
Journal Articles IEEE Journal on Selected Areas in Information Theory Year : 2020

Convex Parameter Recovery for Interacting Marked Processes

Abstract

We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset.
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Dates and versions

hal-03185491 , version 1 (07-01-2025)

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Anatoli B. Juditsky, Arkadi Nemirovski, Liyan Xie, Yao Xie. Convex Parameter Recovery for Interacting Marked Processes. IEEE Journal on Selected Areas in Information Theory, 2020, 1 (3), pp.799-813. ⟨10.1109/JSAIT.2020.3040999⟩. ⟨hal-03185491⟩
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