Cumulants of Hawkes Processes are Robust to Observation Noise
Authors: William Trouleau, Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To illustrate the result of Theorem 1 and to characterize the effect of random translations on the estimation of MHPs, we carry out two sets of experiments. First, we simulate a synthetic dataset from an MHP and quantify the ability of two maximum likelihood-based and two cumulant-based approaches for learning the ground-truth excitation matrix under varying levels of noise power. Second, we evaluate the stability of each approach to random translations on a real dataset pertaining to Bund Future traded at Eurex. |
| Researcher Affiliation | Academia | 1School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland 2College of Management of Technology, EPFL, Lausanne, Switzerland. |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | In addition, the open-source code is publicly available on Git Hub5. 5https://github.com/trouleau/noisy-hawkes-cumulants |
| Open Datasets | Yes | We also evaluated the effect of random translations on a publicly available real-world dataset of Bund Futures traded at Eurex7. 7The dataset is publicly available at: https://github. com/X-Data Initiative/tick-datasets/ |
| Dataset Splits | No | The paper mentions simulating datasets and using a real-world dataset for evaluation but does not provide specific details on train/validation/test splits, such as percentages or sample counts, or refer to predefined splits. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9) required to replicate the experiment. |
| Experiment Setup | Yes | We considered a non-symmetric block-matrix G depicted in Figure 4(a), with exponential excitation functions G i,j(t) = αi,jβ exp( βt), i, j, with β = 1, and baseline intensity µi = 0.01, i. We simulated 20 datasets, each comprised of 5 realizations of 105 events. We then randomly translated each dataset with distributions Fi N(0, σ2), 1 i d, for varying noise powers σ2, and we estimated the excitation matrix for the aforementioned approaches. All reported values are averaged over the 20 simulated datasets ( standard error). |