Detecting Structural Shifts in Multivariate Hawkes Processes with Fréchet Statistics

• URL: http://arxiv.org/abs/2308.06769v3
• Date: Wed, 22 Jan 2025 08:24:15 GMT
• Title: Detecting Structural Shifts in Multivariate Hawkes Processes with Fréchet Statistics
• Authors: Rui Luo, Vikram Krishnamurthy,
• Abstract summary: We propose a new approach for change point detection in multivariate Hawkes processes using Fr'echet statistic of a network. The proposed method is an extension of previous work on Fr'echet statistics in point process settings.
• Score: 15.004064264384546
• License:
• Abstract: This paper proposes a new approach for change point detection in multivariate Hawkes processes using Fr\'echet statistic of a network. The method splits the point process into overlapping windows, estimates kernel matrices in each window, and reconstructs the signed Laplacians by treating the kernel matrices as the adjacency matrices of the causal network. We demonstrate the effectiveness of our method through experiments on both simulated and cryptocurrency datasets. Our results show that our method is capable of accurately detecting and characterizing changes in the causal structure of multivariate Hawkes processes, and may have potential applications in fields such as finance and neuroscience. The proposed method is an extension of previous work on Fr\'echet statistics in point process settings and represents an important contribution to the field of change point detection in multivariate point processes.

Related papers

• The Kernel Density Integral Transformation [0.0]
  We propose the use of the kernel density integral transformation as a feature preprocessing step. Our approach subsumes the two leading feature preprocessing methods as limiting cases. We show that the kernel density transformation can be profitably applied to statistical data analysis.
  arXiv  Detail & Related papers  (2023-09-18T22:54:05Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Scalable and adaptive variational Bayes methods for Hawkes processes [4.580983642743026]
  We propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting.
  arXiv  Detail & Related papers  (2022-12-01T05:35:32Z)
• MARS: Meta-Learning as Score Matching in the Function Space [79.73213540203389]
  We present a novel approach to extracting inductive biases from a set of related datasets. We use functional Bayesian neural network inference, which views the prior as a process and performs inference in the function space. Our approach can seamlessly acquire and represent complex prior knowledge by metalearning the score function of the data-generating process.
  arXiv  Detail & Related papers  (2022-10-24T15:14:26Z)
• Invariant Causal Mechanisms through Distribution Matching [86.07327840293894]
  In this work we provide a causal perspective and a new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization.
  arXiv  Detail & Related papers  (2022-06-23T12:06:54Z)
• Expert-Guided Symmetry Detection in Markov Decision Processes [0.0]
  We propose a paradigm that aims to detect the presence of some transformations of the state-action space for which the MDP dynamics is invariant. The results show that the model distributional shift is reduced when the dataset is augmented with the data obtained by using the detected symmetries.
  arXiv  Detail & Related papers  (2021-11-19T16:12:30Z)
• Row-clustering of a Point Process-valued Matrix [2.0391237204597363]
  We study a matrix whose entries are marked log-Gaussian Cox processes and cluster rows of such a matrix. An efficient semi-parametric Expectation-Solution (ES) algorithm combined with functional principal component analysis (FPCA) of point processes is proposed for model estimation. The effectiveness of the proposed framework is demonstrated through simulation studies and a real data analysis.
  arXiv  Detail & Related papers  (2021-10-04T06:27:26Z)
• On Contrastive Representations of Stochastic Processes [53.21653429290478]
  Learning representations of processes is an emerging problem in machine learning. We show that our methods are effective for learning representations of periodic functions, 3D objects and dynamical processes.
  arXiv  Detail & Related papers  (2021-06-18T11:00:24Z)
• A Kernel-Based Approach to Non-Stationary Reinforcement Learning in Metric Spaces [53.47210316424326]
  KeRNS is an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes. We prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time.
  arXiv  Detail & Related papers  (2020-07-09T21:37:13Z)
• Multi-Decoder RNN Autoencoder Based on Variational Bayes Method [0.3007949058551534]
  We propose a new clustering algorithm focusing on the generative process of the signal with a recurrent neural network and the variational Bayes method. Our experiments show that the proposed algorithm not only has a robustness against for phase shift, amplitude and signal length variations but also provide a flexible clustering based on the property of the variational Bayes method.
  arXiv  Detail & Related papers  (2020-04-29T08:25:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.