A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods
Authors: Piotr Tempczyk, Łukasz Garncarek, Dominik Filipiak, Adam Kurpisz
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experiments with ID-NF (described below) and FLIPD show, that the latter is more scalable than ID-NF (and ID-DM) due to the high memory and computational complexity of SVD (which has to be calculated for each data point). ... Another interesting example occurs when the data on both parallel manifolds follow uniform density functions. Although the derivation in Eq. (19) requires the density functions to be probability distributions, this scenario can be simulated by considering two Gaussian distributions with relatively large standard deviations. This yields the following formula for βt(x), presented in Fig. 2b for v = 1, λ = 1. ... Finally, our brief experiments show that using density models to estimate Laplacian can be beneficial in the process of improving LIDL estimate for higher values of t and non-uniform densities, leading to a promising future direction of research. |
| Researcher Affiliation | Collaboration | Piotr Tempczyk*1,2,3, Łukasz Garncarek3,4, Dominik Filipiak5,6,7, Adam Kurpisz*3,8,9 1Institute of Informatics, University of Warsaw, Poland 2NASK National Research Institute, Warsaw, Poland 3PL4AI, Poland 4Snowflake, USA 5Adam Mickiewicz University, Pozna n, Poland 6Perelyn, Warsaw, Poland 7University of Innsbruck, Austria 8BFH Bern Business School, Switzerland 9ETH Zurich, Switzerland |
| Pseudocode | No | The paper describes mathematical derivations and concepts in prose. It does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide explicit statements about releasing code for the described methodology, nor does it include links to a code repository. It refers to 'numerical calculations' and 'simulations' but does not offer the code for these. |
| Open Datasets | No | The paper discusses theoretical distributions (e.g., normal distribution, uniform distribution) and states that scenarios 'can be simulated' from these. It does not mention using or providing access to any specific named public datasets for its analysis or experiments. |
| Dataset Splits | No | The paper primarily deals with theoretical analysis and simulations from known distributions, rather than empirical evaluation on specific datasets. Therefore, it does not provide any dataset split information like percentages or sample counts. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory specifications) used for running its described 'experiments' or 'numerical calculations'. |
| Software Dependencies | No | The paper does not list specific software dependencies, libraries, or solvers with version numbers that would be required to reproduce the work. |
| Experiment Setup | No | The paper focuses on mathematical derivations and theoretical behavior of methods. While it references 'LIDL estimates' and 'numerical calculations', it does not provide specific experimental setup details such as hyperparameters, learning rates, batch sizes, or training configurations for any 'experiments' mentioned. |