Gaussian Processes with Errors in Variables: Theory and Computation
Authors: Shuang Zhou, Debdeep Pati, Tianying Wang, Yun Yang, Raymond J. Carroll
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the empirical performance of our approach and compare it with competitors in a wide range of simulation experiments and a real data example. |
| Researcher Affiliation | Academia | Shuang Zhou EMAIL School of Mathematical and Statistical Sciences Arizona State University Tempe, AZ 85287-1804, USA, Debdeep Pati EMAIL Department of Statistics Texas A&M University College Station, TX 77843-3143, USA, Tianying Wang EMAIL Center for Statistical Science Department of Industrial Engineering Tsinghua University Beijing 100084, China, Yun Yang EMAIL Department of Statistics University of Illinois at Urbana-Champaign Champaign, IL 61820-3633, USA, Raymond J. Carroll EMAIL Department of Statistics Texas A&M University College Station, TX 77843-3143, USA School of Mathematical and Physical Sciences University of Technology Sydney Ultimo NSW 2007, Australia |
| Pseudocode | Yes | Appendix F. Posterior Computation: A Gibbs Sampler... The updating scheme runs as follows: 1. Update [ w | ]... 2. Update [ s | ]... 3. Update [ a | ]... 4. Update the parameters [ S, µ, τ, π | ]... 5. Update [ X | ]... 6. Update [ λ | ]... 7. Update [ σ2 | ]... |
| Open Source Code | No | The paper discusses the source code of a third-party tool or platform (decon) that the authors used for comparison, but does not provide their own implementation code for the methodology described in the paper. No explicit statement or link to the authors' own source code is provided. |
| Open Datasets | Yes | We re-analyzed the real data set studied in Berry et al. (2002) using the proposed gpev method. |
| Dataset Splits | No | The paper mentions 'out-of-sample prediction results' evaluated on an 'evenly spaced test grid' for simulated data, and re-analyzes a real dataset. However, it does not specify explicit training/validation/test splits, their percentages, or how data was partitioned for reproduction of experiments. |
| Hardware Specification | Yes | To gauge the computational efficiency of gpev-based methods, we report that the computation time of gpeva, gpevn, gpevf for a single Markov chain iteration when n = 500 are 0.025, 0.022, 0.197 second separately, on an 8-Core Intel Core i9 computer with 32 GB RAM. |
| Software Dependencies | No | The paper describes the use of a Gibbs sampler and various statistical distributions for posterior computation but does not list specific software packages, libraries, or their version numbers. |
| Experiment Setup | Yes | For Bayesian approaches, we ran the Gibbs sampler with 2,000 iterations and discarded the first 1,500 iterations as a burn-in... In both simulation studies and the real application, we set the hyperparameters µ0 = 0, κ0 = 1, aτ = 1, bτ = 1, and we choose a0 = 5, b0 = 1 for the hyperprior Ga(a0, b0)... with the number of mixture components truncated at 20... In particular, in Metropolis-Hasting algorithm used for updating {wj} in Step 1, we consider a random walk proposal wprop j N(wcur j , 1/4)... the proposal variance is tuned to obtain average pointwise acceptance rate around 0.7. In Metropolis-Hasting algorithm used for updating {si} in Step 2, we consider the independence proposal sprop i Unif [0, 2π]... We note that the averaged pointwise acceptance rate for si is around 0.6. Finally, to update {xi} in Step 5, we use an adaptive proposal xprop i N(Wi/δ2 + µSiτSi, 1/(1/δ2 + τSi))... with the averaged acceptance rate around 0.8. |