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].
Asymptotic Consistency of $\alpha$-{R}\'enyi-Approximate Posteriors
Authors: Prateek Jaiswal, Vinayak Rao, Harsha Honnappa
JMLR 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our primary result identifies sufficient conditions under which consistency holds, centering around the existence of a good sequence of distributions in the approximating family that possesses, among other properties, the right rate of convergence to a limit distribution. We further characterize the good sequence by demonstrating that a sequence of distributions that converges too quickly cannot be a good sequence. We also extend our analysis to the setting where α equals one, corresponding to the minimizer of the reverse KL divergence, and to models with local latent variables. We also illustrate the existence of good sequence with a number of examples. Our results complement a growing body of work focused on the frequentist properties of variational Bayesian methods. |
| Researcher Affiliation | Academia | Prateek Jaiswal EMAIL School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA Vinayak Rao EMAIL Department of Statistics, Purdue University, West Lafayette, IN 47907, USA Harsha Honnappa EMAIL School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA |
| Pseudocode | No | The paper describes theoretical concepts, mathematical derivations, and proofs (e.g., Lemma 6, Theorem 9), but does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code, links to code repositories, or mention of code in supplementary materials. |
| Open Datasets | No | The paper discusses theoretical models and provides examples (e.g., Example 1: multivariate Gaussian likelihood, Example 2: univariate normal distribution, Example 3: univariate exponential likelihood, Example 4: Bayesian mixture model) to illustrate concepts, but it does not utilize or provide access to any specific publicly available datasets for empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments with datasets, therefore, no information regarding training/test/validation dataset splits is provided. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical proofs and analysis; therefore, it does not describe any specific hardware used for experiments. |
| Software Dependencies | No | The paper is theoretical and presents mathematical proofs and concepts, thus it does not specify any software dependencies or versions for replicating experiments. |
| Experiment Setup | No | The paper is entirely theoretical, presenting proofs and analyses of α-Rényi approximate posteriors. It does not include any experimental setup, hyperparameters, or training configurations. |