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.