Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Estimating Differential Equations from Temporal Point Processes
Authors: Shuichi Miyazawa, Daichi Mochihashi
TMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In the experiments with different types of ODEs regarding infectious disease, predator-prey interaction, and competition among participants, our method outperformed existing baseline methods assuming regularly observed continuous data with respect to the accuracy of recovering the latent parameters of ODEs. Through both synthetic and actual examples, we also showed the ability of our method to extrapolate, model latent events that cannot be observed, and offer interpretability of phenomena from the viewpoint of the estimated parameters of ODE. |
| Researcher Affiliation | Academia | Shuichi Miyazawa EMAIL Department of Statistical Science, The Graduate University for Advanced Studies Daichi Mochihashi EMAIL The Institute of Statistical Mathematics |
| Pseudocode | No | The paper describes the proposed model and inference method in detail, including mathematical derivations and graphical representations (Figure 2), but it does not present any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an explicit statement about the release of source code for the described methodology, nor does it provide a link to a code repository. It only refers to data sources for real-world applications. |
| Open Datasets | Yes | To show an application example of the proposed method to real data, we estimate the competitive relationships among companies related to a specific technological theme using actual patent application data published by the United States Patent and Trademark Office.4 Data source: USPTO patent application data (https://doi.org/10.7910/DVN/TKURPB) We retrieved data from Google Trends, a tool that evaluates search volume over time, for worldwide web searches in the Internet and telecommunications category from January 1, 2005, to December 31, 2021. To understand the trend spreading on Twitter, many attempts have been made to analyze tweet data using epidemiological mathematical models (Abdullah & Wu, 2011; Jin et al., 2013). In these studies, a user who tweeted about a topic was considered as an infectious agent in the mathematical model of infectious diseases with respect to the given topic. Then, using SIR model with S and R as components that cannot be observed, we attempted to analyze movie trends from Movie Tweetings (Dooms et al., 2013), a dataset of movie review tweets.5 Data source: Movie Tweetings (https://github.com/sidooms/Movie Tweetings) |
| Dataset Splits | No | For the simulated study, the authors synthesize data by drawing event counts from Poisson distributions after numerically solving the ODE. For real-world applications, they use full datasets (patent data, Google Trends, Movie Tweetings) without explicit training/test/validation splits in the typical machine learning sense. Instead, they define an "interpolation time" (0 to 1) and "extrapolation time" (1 < t <= 1.5) for evaluation, but this is about time ranges rather than standard dataset partitioning. |
| Hardware Specification | No | The paper does not specify any particular hardware (e.g., CPU, GPU models, memory) used for running the experiments. It describes the computational methods (HMC, MCMC) but not the machines they ran on. |
| Software Dependencies | No | The paper mentions Hamiltonian Monte Carlo (HMC) and Markov Chain Monte Carlo (MCMC) methods, as well as Gaussian processes (GPs) and specific kernel functions. However, it does not provide specific version numbers for any software, libraries, or programming languages used for implementation. |
| Experiment Setup | Yes | Times were normalized to values between 0 and 1. For observation points, T = 100 and τ = [0.005, 0.015, . . . , 0.995]. For inducing points, U = 21 and υ = [0.00, 0.05, . . . , 1.00]. We used the squared exponential kernel function with an additive noise term, k(t, t ) = ϕ2 1 exp |t t |2 / ϕ2 2 + ϕ2 3δ(t t ), where ϕ1, ϕ2, and ϕ3 denote the amplitude, length, and white noise scales, respectively. As mentioned in Section 3.2.3, through preliminary experiments using grid search, we empirically set ϕ1 = 5.0, ϕ2 = 0.15 for SIR and competition equations and ϕ2 = 0.1 for predator-prey equations, ϕ3 = 0.1, and γ = 0.1, as hyperparameters. For the HMC setup, the number of leapfrog steps was fixed at 10, and the step size was adjusted within the burn-in MCMC simulations. After 10, 000 burn-in iterations, 1, 000 posterior samples were collected from the subsequent 20, 000 simulations thinned to every 20 samples. |