Related papers: Convex Parameter Recovery for Interacting Marked Processes

Convex Parameter Recovery for Interacting Marked Processes

URL: http://arxiv.org/abs/2003.12935v3
Date: Thu, 12 Nov 2020 17:53:00 GMT
Title: Convex Parameter Recovery for Interacting Marked Processes
Authors: Anatoli Juditsky, Arkadi Nemirovski, Liyan Xie, Yao Xie
Abstract summary: The probability of an event 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. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters.
Score: 9.578874709168561
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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