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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 11: AAAI-21 Technical Tracks 11

UNIPoint: Universally Approximating Point Processes Intensities

February 1, 2023

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Authors

Alexander Soen

The Australian National University


Alexander Mathews

The Australian National University


Daniel Grixti-Cheng

The Australian National University


Lexing Xie

The Australian National University


DOI:

10.1609/aaai.v35i11.17165


Abstract:

Point processes are a useful mathematical tool for describing events over time, and so there are many recent approaches for representing and learning them. One notable open question is how to precisely describe the flexibility of point process models and whether there exists a general model that can represent all point processes. Our work bridges this gap. Focusing on the widely used event intensity function representation of point processes, we provide a proof that a class of learnable functions can universally approximate any valid intensity function. The proof connects the well known Stone-Weierstrass Theorem for function approximation, the uniform density of non-negative continuous functions using a transfer functions, the formulation of the parameters of a piece-wise continuous functions as a dynamic system, and a recurrent neural network implementation for capturing the dynamics. Using these insights, we design and implement UNIPoint, a novel neural point process model, using recurrent neural networks to parameterise sums of basis function upon each event. Evaluations on synthetic and real world datasets show that this simpler representation performs better than Hawkes process variants and more complex neural network-based approaches. We expect this result will provide a practical basis for selecting and tuning models, as well as furthering theoretical work on representational complexity and learnability.

Topics: AAAI

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HOW TO CITE:

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie UNIPoint: Universally Approximating Point Processes Intensities Proceedings of the AAAI Conference on Artificial Intelligence (2021) 9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie UNIPoint: Universally Approximating Point Processes Intensities AAAI 2021, 9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie (2021). UNIPoint: Universally Approximating Point Processes Intensities. Proceedings of the AAAI Conference on Artificial Intelligence, 9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. UNIPoint: Universally Approximating Point Processes Intensities. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. 2021. UNIPoint: Universally Approximating Point Processes Intensities. "Proceedings of the AAAI Conference on Artificial Intelligence". 9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. (2021) "UNIPoint: Universally Approximating Point Processes Intensities", Proceedings of the AAAI Conference on Artificial Intelligence, p.9685-9694

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie, "UNIPoint: Universally Approximating Point Processes Intensities", AAAI, p.9685-9694, 2021.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. "UNIPoint: Universally Approximating Point Processes Intensities". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. "UNIPoint: Universally Approximating Point Processes Intensities". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 9685-9694.

Alexander Soen||Alexander Mathews||Daniel Grixti-Cheng||Lexing Xie. UNIPoint: Universally Approximating Point Processes Intensities. AAAI[Internet]. 2021[cited 2023]; 9685-9694.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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