Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression
Authors: Youngsoo Baek, Samuel Berchuck, Sayan Mukherjee
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, which is of independent theoretical interest. |
| Researcher Affiliation | Academia | Youngsoo Baek Department of Statistical Science Duke University Durham, NC 27705 youngsoo.baek@duke.edu Samuel I. Berchuck Department of Biostatistics & Bioinformatics Duke University Durham, NC 27705 sib2@duke.edu Sayan Mukherjee Center for Scalable Data Analysis and Artificial Intelligence Universität Leipzig Leipzig 04105 sayan.mukherjee@mis.mpg.de |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. |
| Open Source Code | Yes | MATLAB codes used to produce simulation results are included in the Supplementary Materials. |
| Open Datasets | No | The paper describes generating synthetic data for simulations using a "noiseless linear model y = x, β (||β|| = 1, ρ = )" and does not refer to any external public datasets or provide access information for specific training data. |
| Dataset Splits | No | The paper describes simulation setups and discusses training, but does not provide specific train/validation/test dataset splits as it generates synthetic data for its experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions "MATLAB codes" are included in supplementary materials, but does not specify any version numbers for MATLAB or other software dependencies. |
| Experiment Setup | Yes | Figure 1: Comparison of asymptotic formula and 20 instances of S2 RF (12). Data are generated via noiseless linear model y = x, β (||β|| = 1, ρ = ). Activation is Re LU: σ(x) = max{0, x}. d and n are fixed to 100 and 300, respectively. The asymptotic formula for RRF (8) is plotted for comparison (red, dashed). Figure 2: Ratio of R(λopt) to S2(λopt) τ 2 as a function of ψ1 (2a) and of ψ2 (2b). In each plot, ψ2 and ψ1 are respectively fixed to 3, while F1 = 1, F = 0, and ρ = 1/τ 2 for noise variance τ 2 {.2, 5}. Figure 3: Histograms of 1e+4 draws of RRF and S2 RF τ 2 under low-noise linear model y = x, β + τ 2 with τ 2 = 1/5. |