Trajectory Inference with Smooth Schrödinger Bridges
Authors: Wanli Hong, Yuliang Shi, Jonathan Niles-Weed
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. ... We test our algorithm on two kinds of low-dimensional smooth trajectory inference tasks. |
| Researcher Affiliation | Academia | 1Center for Data Science, New York University, New York, United States 2Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning New York University Shanghai Shanghai, China 3Department of Mathematics, The University of British Columbia, Vancouver, Canada 4Courant Institute of Mathematical Science, New York University, New York, United States. Correspondence to: Jonathan Niles-Weed <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Vanilla Sinkhorn Algorithm ... Algorithm 2 Belief Propagation with Continuous Massages ... Algorithm 3 Approximate Belief Propagation Algorithm ... Algorithm 4 Trajectory Inference Through Sampling ... Algorithm 5 Trajectory Inference Through Arg Max |
| Open Source Code | Yes | Our code for reproducing these experiments is available on Github.1 1https://github.com/Wanli Hong C/Smooth_SB |
| Open Datasets | Yes | We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. ... We test our algorithm on three data sets, two 2-dimensional data sets (Fig 7 in Appendix F) and a 3-dimensional data set consisting of the simulated orbits of an N-body physical system (Fig. 4). ... We also test our algorithm on five challenging baselines in the trajectory inference literature. ... Petal dataset was introduced in (Huguet et al., 2022b) ... Embryoid Body ... (Tong et al., 2020). ... Dyngen Tree (Dyg Tree): This is another sc-RNAseq dataset crafted by (Huguet et al., 2022b) using Dyngen (Cannoodt et al., 2021). ... Dyngen Cycle (Dyg Cycle): Another 10-D sc-RNAseq dataset inherited from (Banerjee et al.). |
| Dataset Splits | Yes | Secondly, we will leave out observations at a certain timestep and instead infer the position of particles at this timestep and evaluate the distance between the inferred and real observations, which we call Leave-One-Timestep-Out (LOT) tasks. |
| Hardware Specification | Yes | We ran our experiments on an x86-64 setup. Smooth SB (ours) and F&S do not require GPU support; for DMSB and MIOFlow experiments, we utilized an NVIDIA A100-SXM4-80GB. |
| Software Dependencies | No | In tracking individual particles, standard SB with Brownian motion prior and W2 matching is implemented by Python s OT library (Flamary et al., 2021). ... We assume all observations occur equally over the time period t = 2, hence the observation duration is dt = 2/K, which is utilized to compute covariance between timesteps. For datasets with dimensions greater than one, the kernel is assumed to be identical and independent for each dimension, simplifying the tensor Γ by factoring it across dimensions, thereby reducing the computational load in the matrix-vector multiplication during the message-passing phase. |
| Experiment Setup | Yes | For all experiments, we consider datasets with the number of points being constant at each step and each particle has uniform weight. For the kernel, we use either Matern kernel with ν = 1.5 or ν = 2.5, as specified in (5), utilizing the wavelet basis. We conduct 200 iterations of message-passing algorithms (T = 200). The initial covariance, Σ0,0, is derived from the stationary distribution s covariance of the lifted Gaussian process corresponding to the kernel, ensuring Σk,k remains steady over time (refer to Equation (2.39) in (Saatc i, 2012) for stationary distribution calculation). We assume all observations occur equally over the time period t = 2, hence the observation duration is dt = 2/K, which is utilized to compute covariance between timesteps. ... Detailed parameter settings for each task can be found in 5 and 6. |