Bayesian Learning via Q-Exponential Process
Authors: Shuyi Li, Michael O'Connor, Shiwei Lan
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We compare GP, Besov and Q-EP in modeling functional data, reconstructing images and solving inverse problems and demonstrate the advantage of our proposed methodology. In this section, we compare GP, Besov and Q-EP by modeling time series (temporal), reconstructing images (spatial) from computed tomography and solving a (spatiotemporal) inverse problem (Appendix C.4). These numerical experiments demonstrate that our proposed Q-EP enables faster convergence in obtaining a better maximum a posterior (MAP) estimate. |
| Researcher Affiliation | Academia | Shuyi Li Michael O Connor Shiwei Lan School of Mathematical & Statistical Sciences Arizona State University, Tempe, AZ 85287 slan@asu.edu |
| Pseudocode | Yes | Algorithm 1 White-noise Preconditioed Crank-Nicolson (wn-p CN) for Q-EP Prior Models |
| Open Source Code | Yes | All the computer codes are publicly available at https://github.com/lanzithinking/Q-EXP. |
| Open Datasets | Yes | In addition, we also consider two real data sets of Tesla and Google stock prices in 2022. We first consider the Shepp Logan phantom, a standard test image created by Shepp and Logan in [42] to model a human head and to test image reconstruction algorithms. Finally, we apply these methods to CT scans of a human cadaver and torso from the Visible Human Project [1]. |
| Dataset Splits | No | The paper specifies training and testing splits for its datasets, but does not explicitly mention a distinct validation set or its proportion. |
| Hardware Specification | No | The paper does not provide specific details on the hardware used for running experiments, such as GPU/CPU models or cloud instance types. |
| Software Dependencies | No | The paper mentions algorithms used (e.g., BFGS, MCMC) but does not provide specific version numbers for software dependencies or libraries. |
| Experiment Setup | Yes | For both GP and Q-EP, we adopt the Matérn kernel with ν = 1 2, σ2 = 1, ρ = 0.5 and s = 1: C(t,t ) = σ2 21 ν Γ(ν) wνKν(w), w = 2ν( t t /ρ)s. In both Besov and Q-EP, we set q = 1. The generated sinogram is then added by noise with signal noise ratio SNR = Au / ε = 100. We set γ = 1 and δ = 8 in this example. For Besov, we adopt 2d Fourier basis... and truncate the series (1) for the first L = 1000 terms. |