An equivalence between high dimensional Bayes optimal inference and M-estimation
Authors: Madhu Advani, Surya Ganguli
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We numerically demonstrate superior performance of our optimal M-estimators relative to MAP. Overall, at the heart of our work is the revelation of a remarkable equivalence between two seemingly very different computational problems: namely that of high dimensional Bayesian integration underlying MMSE inference, and high dimensional convex optimization underlying M-estimation. In essence we show that the former difficult integral may be computed by solving the latter, simpler optimization problem. In Section 4, we also demonstrate, through numerical simulations, a substantial performance improvement in inference accuracy achieved by the optimal M-estimator over MAP under nonlinear measurements with non-additive noise. |
| Researcher Affiliation | Academia | Madhu Advani Surya Ganguli Department of Applied Physics, Stanford University msadvani@stanford.edu and sganguli@stanford.edu |
| Pseudocode | No | The paper describes algorithms (m AMP, b AMP, g AMP) using mathematical equations and textual descriptions, but it does not present any structured pseudocode or an algorithm block explicitly labeled as such. |
| Open Source Code | No | The paper does not provide any explicit statements or links about open-sourcing the code for the described methodology. |
| Open Datasets | No | The paper uses "simulated data generated as in (1), with dense i.i.d Gaussian measurements" and does not refer to any publicly available datasets. |
| Dataset Splits | No | The paper uses simulated data but does not specify any training, validation, or test dataset splits, percentages, or absolute counts. It mentions varying "measurement density α = N/P". |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies (e.g., library names with version numbers) needed to replicate the experiments. |
| Experiment Setup | Yes | The paper specifies the data generation: "simulated data generated as in (1), with dense i.i.d Gaussian measurements." It also states: "For these finite simulated data sets, we varied α = N/P , while holding NP 250." |