Learning Hawkes Processes Under Synchronization Noise
Authors: William Trouleau, Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods. We performed two sets of experiments. First, we used synthetic data to show that, despite the non-smoothness and non-convexity of (5), our approach can accurately recover the excitation matrix of the MHP and significantly outperform the classic ML estimator. We further investigated the effects of dimensionality d and the scale of the noise on the performance of our estimator. Second, we validated our approach using a dataset of neuronal spike trains obtained from measurements of the motor cortex of a monkey. |
| Researcher Affiliation | Collaboration | 1School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland 2Bosch Center for Artificial Intelligence 3Dept. of Electrical and Computer Eng. (ECE), Georgia Institute of Technology 4Dept. of Industrial and Systems Eng. (ISy E), Georgia Institute of Technology. |
| Pseudocode | Yes | Algorithm 1 summarizes the steps of our approach. |
| Open Source Code | Yes | Source code of the algorithm is available publicly. |
| Open Datasets | Yes | In addition to simulations on synthetic data, we also evaluated our approach on an experimental dataset of neuronal spike trains from Wu & Hatsopoulos (2006); Quinn et al. (2011). |
| Dataset Splits | No | The paper states 'We used the first 70% of the dataset for training and kept the last 30% for testing.' but does not mention a separate validation split or explicit details for its use. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper mentions 'We used the Python library tick to generate synthetic samples of the processes (Bacry et al., 2017).' but does not provide specific version numbers for Python or the 'tick' library. |
| Experiment Setup | Yes | We set the exponential decay to β = 1. For smoothing, we used β = 50 and γ = 500, which were found to work well in practice. For each experiment, we chose small positive background intensities {µi} and generated a random4 excitation matrices with entries {αij} {0, 1} by sampling edges randomly with probability 2/d. The average in-degree and out-degree of each nodes was hence close to two. We then rescaled the entries to obtain a spectral radius of 0.95 to ensure that the simulated processes are stable5. We generated C = 5 realizations of 50, 000 samples from the MHP using Ogata s thinning algorithm6 (Ogata, 2006). We set the hyper-parameters (β, β , γ) to (0.0047, 0.16, 1.6) using grid-search. |