Nonparametric Regression for 3D Point Cloud Learning
Authors: Xinyi Li, Shan Yu, Yueying Wang, Guannan Wang, Li Wang, Ming-Jun Lai
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction. In this section, we conduct various simulation studies to assess the performance of the proposed TPST method. |
| Researcher Affiliation | Collaboration | Xinyi Li EMAIL School of Mathematical and Statistical Sciences, Clemson University Clemson, SC 29634, USA; Yueying Wang1 EMAIL Amazon.com, Inc. Seattle, WA 98121, USA |
| Pseudocode | Yes | Algorithm A.1 Algorithm for the derivatives of ϕ(p) Input: Polynomial with B-form ϕ(p) = P i+j+k+l=d γijkl Bd ijkl(p), directions u1, . . . , um with associated directional coordinates a(ı) = (a(ı) 1 , a(ı) 2 , a(ı) 3 , a(ı) 4 ), ı = 1, . . . , m. Initialization: ı := 0, γ(0) ijkl := γijkl. for ı = 1, . . . , m do for i + j + k + l = d ı do Compute γ(ı) ijkl(a(1), . . . , a(m)) =a(ı) 1 γ(ı 1) i+1,j,k,l(a(1), . . . , a(ı 1)) + a(ı) 2 γ(ı 1) i,j+1,k,l(a(1), . . . , a(ı 1)) + a(ı) 3 γ(ı 1) i,j,k+1,l(a(1), . . . , a(ı 1)) + a(ı) 4 γ(ı 1) i,j,k,l+1(a(1), . . . , a(ı 1)). end for end for Output: Dum Du1ϕ(p) = d! (d m)! P i+j+k+l=d m γ(m) ijkl(a(1), . . . , a(m))Bd m ijkl (p). |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described in this paper. |
| Open Datasets | Yes | Data used in preparation of this article were obtained from the Alzheimer s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | Yes | In this simulation example, the TPST method takes less than twenty seconds to fit the model for most of the simulation samples on a single Intel E5-2640 v3 core. |
| Software Dependencies | No | The paper mentions several software tools (MATLAB, CGAL, TetGen, iso2mesh, R package mgcv) but does not provide specific version numbers for any of them. |
| Experiment Setup | Yes | In this study, we set PSNR = 5 and 10, representing scenarios of high and moderate noise levels, respectively. To effectively capture high-frequency oscillations present in human brain scans, we set the polynomial degree d to at least 4. Additionally, we investigate the impact of different levels of global smoothness by considering r = 0 and r = 1. |