Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Density estimation on low-dimensional manifolds: an inflation-deflation approach
Authors: Christian Horvat, Jean-Pascal Pfister
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We have three goals in this section: first, we numerically confirm the scaling factor in equation (4) for different manifolds. Second, we verify that Gaussian noise can be used to approximate a Gaussian noise restricted to the normal space. Third, we numerically test the bounds for σ2 derived in section3.3. For training details, we refer to appendix B.2. The code for our experiments can be found at https://github.com/chrvt/Inflation-Deflation. |
| Researcher Affiliation | Academia | Christian Horvat EMAIL Jean-Pascal Pfister EMAIL Department of Physiology University of Bern Bern, Switzerland |
| Pseudocode | No | The paper describes the proposed method, including the inflation and deflation steps, and provides theoretical proofs and examples. However, it does not contain any structured pseudocode or algorithm blocks explicitly labeled as such. |
| Open Source Code | Yes | The code for our experiments can be found at https://github.com/chrvt/Inflation-Deflation. |
| Open Datasets | Yes | Finally, we end this section with an application on the handwritten digit dataset MNIST, Lecun et al. (1998). |
| Dataset Splits | Yes | We test the utility of learned digit 1 likelihoods for out-of-distribution detection (OOD) using IID (isotropic inflation-deflation) and the M flow. In figure 7, we show the log-likelihood densities (estimated using kernel density estimation) on the MNIST test set after training on digit 1 images from the training set only. [...] We train on 100 epochs with a batch size of 100, and take the model yielding the best result on the validation set (10% of the training set). |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments, such as GPU or CPU models. It only generally refers to the training process. |
| Software Dependencies | No | The paper mentions using a block neural autoregressive flow (BNAF), Adam optimizer, and Adam W optimizer, but it does not specify the version numbers for these software components or the underlying machine learning frameworks (e.g., PyTorch, TensorFlow). |
| Experiment Setup | Yes | We use Adam optimizer with an initial learning rate 0.1, a learning rate decay of 0.5 after 2000 optimization steps without improvement (learning rate patience). We use a batch size of 200. [...] We train on 100 epochs with a batch size of 100, and take the model yielding the best result on the validation set (10% of the training set). We use Adam W optimizer (Loshchilov and Hutter (2017)) and anneal the learning rate to 0 after 100 epochs using a cosine schedule (Loshchilov and Hutter (2016)). We apply weight decay with a prefactor of 10-6 without dropout. Furthermore, a L2 regularization on the latent variable with a prefactor of 0.01 was used to stabilize the training. |