Bayesian Computation Meets Topology
Authors: Julius von Rohrscheidt, Bastian Rieck, Sebastian M Schmon
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically validate the utility of our proposed method in the form of three main experiments that compare topological losses and respective geometrical losses, by using the results from Section 3. In the first two experiments, we focus on parameter inference for chaotic simulation models, which can be seen as (approximately) solving an inverse problem. ... For the inference of η, we use 250 simulations for each sampling method, aiming to infer η after 5, 10, and 50 iterations (time steps) of the model, respectively, repeating the inference 5 times. |
| Researcher Affiliation | Collaboration | Julius von Rohrscheidt EMAIL Technical University of Munich, Helmholtz Munich Bastian Rieck EMAIL University of Fribourg, Technical University of Munich, Helmholtz Munich Sebastian M. Schmon EMAIL Altos Labs, Cambridge, UK |
| Pseudocode | Yes | Algorithm 1 Importance sampling estimation of the mean 1: Input: Observed data y, test function h 2: for i = 1 : n do 3: Sample θi p(θ) 4: Sample xi p(x | θi) 5: end for 6: Output: ˆh(θ) = Pn i=1 h(θi)e wℓ(y,xi) Pn i=1 e wℓ(y,xi) Algorithm 2 MCMC approximation of the target 1: Input: Observed data y, start value θ0, proposal distribution q(ϑ | θ) 2: Sample X0 p(x | θ0) 3: for i = 1 : K do 4: Sample U Unif[0, 1] 5: Sample θ q( | θi 1) 6: Sample X p(x | θ ) 7: Compute a(θi 1, θ ) = e ℓ(y,X )p(θ ) e ℓ(y,Xi 1)p(θi 1) q(θi 1 | θ ) q(θ | θi 1) 8: if U a(θi 1, θ ) then 9: Set θi = θ , Xi = X 10: else 11: Set θi = θi 1, Xi = Xi 1 12: end if 13: end for 14: Output: θ = (θ1:K). |
| Open Source Code | Yes | Reproducibility We provide code for the given method and of the experiments shown in this paper under https://github.com/aidos-lab/TABAC. |
| Open Datasets | No | The Vicsek model is an agent-based model that is particularly useful to study collective motion like swarming and flocking. ... The lattice Boltzmann methods (LBM) are a collection of algorithms that are used for fluid simulation. ... In our setting, the percolation model is probabilistic in the sense that links are added randomly, with some probability p, and the goal is to infer p. We realise such a network as a square 2D greyscale image of pixel size n2... (The paper describes simulation models for data generation but does not provide specific links, DOIs, or citations to pre-existing, publicly available datasets for download.) |
| Dataset Splits | No | For the inference of η, we use 250 simulations for each sampling method, aiming to infer η after 5, 10, and 50 iterations (time steps) of the model, respectively, repeating the inference 5 times. ... we use 100 observation points for inference, and normal distributions for both the prior and the proposal distribution in the MCMC procedure. (The paper mentions the number of simulations and observation points for inference, but not explicit training/validation/test splits of a dataset.) |
| Hardware Specification | No | No specific hardware details (e.g., GPU models, CPU models, or cloud computing specifications) are mentioned in the paper regarding the experimental setup. |
| Software Dependencies | No | Moreover, we note that the implementation of giotto-tda (Tauzin et al., 2020), which we use in our experiments, uses a faster approximate algorithm rather than the actual loss. (The paper mentions 'giotto-tda' but does not provide a specific version number for it or any other software dependency.) |
| Experiment Setup | Yes | For the inference of η, we use 250 simulations for each sampling method, aiming to infer η after 5, 10, and 50 iterations (time steps) of the model, respectively, repeating the inference 5 times. ... we use 100 observation points for inference, and normal distributions for both the prior and the proposal distribution in the MCMC procedure. The weight parameter w in the importance sampling procedure is set to 10. |