Riemannian Metric Learning via Optimal Transport
Authors: Christopher Scarvelis, Justin Solomon
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we first use synthetic data to demonstrate that our algorithm successfully recovers the correct eigenspaces of a known metric A(x) from cross-sectional samples satisfying our model. We then use our method to learn a metric from cross-sectional sc RNA data and show that this metric improves the accuracy of trajectory inference for sc RNA data that is sampled sparsely in time. We finally show that by learning a metric from time-stamped bird sightings, we can infer curved migratory trajectories for individual birds given the initial and final points of their trajectories. Details for all experiments are provided in Appendix D. |
| Researcher Affiliation | Academia | Christopher Scarvelis MIT CSAIL scarv@mit.edu Justin Solomon MIT CSAIL jsolomon@mit.edu |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. Procedures are described in text. |
| Open Source Code | No | The paper does not contain any explicit statement about providing open-source code for the described methodology or a direct link to a code repository. |
| Open Datasets | Yes | sc RNA data. We perform trajectory inference experiments with the sc RNA data drawn from Schiebinger et al. (2019). This data consists of force-directed layout embedding coordinates of gene expression data collected over 18 days of reprogramming (39 time points total). We construct populations Xti for i = 1, . . . , 39 by drawing 500 samples per time point in the original data; this sampling uses 8.25% of the available data on average. Snow goose data. The training data for this experiment consists of time-stamped sightings of untagged snow geese (Anser caerulescens) across the U.S. and Canada during their spring migration. This data is drawn from the e Bird basic dataset (Sullivan et al., 2009), current as of February 2022. |
| Dataset Splits | No | The paper discusses training and testing procedures but does not explicitly provide details about specific training/validation/test dataset splits (e.g., percentages or counts for each split). |
| Hardware Specification | Yes | Learning the tensor takes 16 minutes on a single V100 GPU. |
| Software Dependencies | Yes | We implement (8) in Pytorch using a time-invariant vector field vθ parametrized by a fully connected two-layer neural network with ELU nonlinearities and 64 hidden dimensions. We set λ = 1 and solve the initial value problem x(t) = vθ(x(t)); x(0) = x0 using the explicit Adams solver in torchdiffeq s odeint with default hyperparameters (Chen et al., 2018a). |
| Experiment Setup | Yes | We optimize the objective using Adam W with learning rate 10 3 and weight decay 10 3 and train for 100 epochs per pair of samples. |