Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows
Authors: Brendan Ross, Jesse Cresswell
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We apply them in experiments with synthetic and realworld data to demonstrate that flows can model manifold-supported distributions without sacrificing tractable likelihoods. Lastly, we demonstrate their efficacy on synthetic and real-world data. We now evaluate manifold flows on image data. Our aim is to show that, although they represent a strict architectural subset of mainstream injective flows, CEFs remain competitive in generative performance [6, 39]. In doing so, this work is the first to include end-to-end maximum likelihood training with an injective flow on image data. Three approaches were evaluated on each dataset: a jointly trained CEF, a sequentially trained CEF, and for a baseline a sequentially trained injective flow, as in Brehmer and Cranmer [6], labelled manifold flow (MF). Injective models cannot be compared on the basis of log-likelihood, since each model may have a different manifold support. Instead, we evaluate generative performance in terms of fidelity and diversity [61]. The FID score [28] is a single metric which combines these factors, whereas density and coverage [49] measure them separately. For FID, lower is better, while for density and coverage, higher is better. We use the Py Torch-FID package [62] and the implementation of density and coverage from Naeem et al. [49]. (Tables 3 and 4 display performance metrics). |
| Researcher Affiliation | Industry | Brendan Leigh Ross Layer 6 AI brendan@layer6.ai Jesse C. Cresswell Layer 6 AI jesse@layer6.ai |
| Pseudocode | No | The paper describes algorithms and building blocks but does not contain structured pseudocode or algorithm blocks that are clearly labeled or formatted like code. |
| Open Source Code | Yes | To implement CEFs, we worked off of the nflows github repo [20], which is derived from the code of Durkan et al. [19]. Our code is available at https://github.com/layer6ai-labs/CEF. |
| Open Datasets | Yes | We generate data using a GAN pretrained on CIFAR-10 [40] by sampling from a selected number of latent space dimensions (64 and 512) with others held fixed. We scale CEFs to natural data by training on the MNIST [42] and Celeb A [46] datasets, for which a low-dimensional manifold structure is postulated but unknown. |
| Dataset Splits | No | The paper mentions training on datasets (CIFAR-10, MNIST, Celeb A) but does not provide specific training, validation, or test split percentages, sample counts, or explicit references to predefined splits for reproducibility. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., GPU models, CPU models, memory specifications) used for running its experiments. |
| Software Dependencies | No | The paper mentions using 'nflows github repo [20]' and 'Py Torch-FID package [62]' but does not provide specific version numbers for these or other software dependencies, which are necessary for full reproducibility. |
| Experiment Setup | No | Full model and training details are provided in App. C, while additional reconstructions and generated images are presented in App. D. This indicates that the specific experimental setup details, such as hyperparameters, are not included in the main text of the paper. |