Active Manifolds: A non-linear analogue to Active Subspaces
Authors: Robert Bridges, Anthony Gruber, Christopher Felder, Miki Verma, Chelsey Hoff
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Using accessible, low-dimensional functions as initial examples, we show AM reduces approximation error by an order of magnitude compared to AS, at the expense of more computation. Following this, we revisit the sensitivity analysis by Glaws et al. (2017), who apply AS to analyze a magnetohydrodynamic power generator model, and compare the performance of AM on the same data. Our analysis provides detailed information not captured by AS, exhibiting the influence of each parameter individually along an active manifold. |
| Researcher Affiliation | Collaboration | 1Cyber & Applied Data Analytics Division, Oak Ridge National Laboratory 2Department of Mathematics, Texas Tech University 3Department of Mathematics and Statistics, Washington University in St. Louis. |
| Pseudocode | Yes | 3.2. Active Manifolds Pseudo-Algorithm: The AM algorithm has three broad components: (1) Build the active manifold M = Im(γ(t)); (2) Approximate the function of interest f on M with ˆf; (3) For p U traverse the level set to M to estimate f(p). |
| Open Source Code | Yes | Results code on https://github.com/bridgesra/ active-manifold-icml2019-code. |
| Open Datasets | No | The paper states using data provided by Glaws et al. (2017) and refers to Constantine's AS data sets repository, but does not provide direct public access links (DOI, URL) to the *specific* datasets used for their experiments. |
| Dataset Splits | No | A uniform grid P = {pi} of 10K points was built on [ 1, 1]2, with a random 80/20% partition for training/testing. The paper mentions training and testing splits, but does not explicitly describe a separate validation split. |
| Hardware Specification | No | The paper discusses computational expense and performance, but does not specify any particular hardware components (e.g., CPU, GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions using 'Constantine s software package (Constantine, 2016a)' but does not provide a specific version number for this or any other software dependency. |
| Experiment Setup | Yes | We require two parameters: δ, a step size for the numerical approximation of paths, and ϵ, a tolerance for when to terminate walking. The AM algorithm was run on this data from random seed 46 with δ = ϵ = 0.02. We constructed a uniform grid of 100K points on [ 1, 1]m, and ran AM using stepsize 0.15 over three random 98K / 2K test/train splits, each with three initial AM start points. |