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.