Sample Complexity Bounds for Estimating Probability Divergences under Invariances
Authors: Behrooz Tahmasebi, Stefanie Jegelka
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5. Experiments To observe the gain of invariances, we conduct a simple experiment on the following synthetic dataset. |
| Researcher Affiliation | Academia | 1MIT CSAIL 2TU Munich and MIT CSAIL. Correspondence to: Behrooz Tahmasebi <bzt@mit.edu>. |
| Pseudocode | No | The paper does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating the availability of open-source code for the described methodology. |
| Open Datasets | No | To observe the gain of invariances, we conduct a simple experiment on the following synthetic dataset. The input space is the six-dimensional flat torus T6 = [0, 1]6, and the group of invariances acts as the circular shifts on the last two coordinates; see Example 3 for more details about this action. We consider a non-invariant distribution µnon and an invariant distribution µinv in this setting as follows. Samples from the non-invariant distribution are generated based on the sum of three i.i.d. random variables X = X1+X2+X3, each chosen uniformly from [0, 1/3]6. Moreover, samples from the invariant distribution such as (X, X5, X6) are generated based on the sum of four i.i.d. random variables, denoted by X = X1 + X2 + X3 + X4, each chosen uniformly from [0, 0.25]4, and for the last two coordinates, X5, X6 are chosen uniformly from [0, 1]. |
| Dataset Splits | No | The paper describes a synthetic dataset and experiments but does not provide specific details on training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies or versions used for the experiments. |
| Experiment Setup | No | Indeed, we didn t optimize the parameter T, and just used a fixed regularization parameter, which leads to having parallel plots in the logarithmic scale. |