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].
Lower Bounds on the Bayesian Risk via Information Measures
Authors: Amedeo Roberto Esposito, Adrien Vandenbroucque, Michael Gastpar
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The results are then applied to settings of interest involving both discrete and continuous parameters, including the Hide-and-Seek problem, and compared to the state-of-the-art techniques. An important observation is that the behaviour of the lower bound in the number of samples is influenced by the choice of the information measure. We leverage this by introducing a new divergence inspired by the Hockey-Stick divergence, which is demonstrated empirically to provide the largest lower bound across all considered settings. Section 5: Examples, in which we apply the bounds proposed in Section 4 to a variety of classical and less classical settings: estimation of the bias of a Bernoulli random variable (see Section 5.1); estimation of the bias of a Bernoulli random variable after injection of additional noise (e.g., observing privatised samples, see Section 5.2); estimation of the mean of a Gaussian random variable (with Gaussian prior, see Section 5.3); lower bound on the minimax risk for the Hide-and-Seek problem (Shamir, 2014) (see Section 5.4). For each of the problems we derive bounds involving a variety of information measures and we compare said bounds among themselves and with respect to relevant bounds in the literature as well. |
| Researcher Affiliation | Academia | Amedeo Roberto Esposito EMAIL Okinawa Institute of Science and Technology, Okinawa Adrien Vandenbroucque EMAIL Ecole Polytechnique F ed erale de Lausanne, Switzerland Michael Gastpar EMAIL Ecole Polytechnique F ed erale de Lausanne, Switzerland |
| Pseudocode | No | The paper describes theoretical framework, mathematical derivations, and proofs. It does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about providing source code or a link to a repository for the methodology described. |
| Open Datasets | No | The paper applies its theoretical bounds to various estimation settings, such as Bernoulli bias, Gaussian mean, and the Hide-and-Seek problem, which are problem formulations rather than specific publicly available datasets with access information. There is no mention of using or providing access to external datasets. |
| Dataset Splits | No | The paper focuses on theoretical bounds applied to illustrative examples and simulated scenarios. It does not describe experiments using external datasets that would require explicit training/test/validation splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to perform the numerical evaluations or other computations. |
| Software Dependencies | No | The paper presents theoretical work with numerical evaluations. It does not mention any specific software names or version numbers of libraries or tools used. |
| Experiment Setup | No | The paper describes mathematical bounds and applies them to theoretical examples with defined parameters (e.g., W ~ U([0,1]), Xi ~ Ber(W) for Bernoulli bias; W ~ N(0, Ο2W), Xi = W + Zi, Zi ~ N(0, Ο2) for Gaussian mean). It also discusses the parameters of its own bounds (Ξ±, p, Ξ³, ΞΆ) and numerically optimizes over them. However, it does not describe an experimental setup for training a machine learning model, such as hyperparameters for optimizers, learning rates, batch sizes, or model architectures. |