Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Asymptotic Risk of Bézier Simplex Fitting
Authors: Akinori Tanaka, Akiyoshi Sannai, Ken Kobayashi, Naoki Hamada2416-2424
AAAI 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Those results are verified numerically under small to moderate sample sizes. In this paper, we study the asymptotic risk of the two fitting methods of the B ezier simplex: the all-at-once fitting and the inductive skeleton fitting, and compare their performance with respect to the degree. We examine the empirical performances of the all-at-once fitting and the inductive skeleton fitting and verify the asymptotic risks derived in Section 3.1 over synthetic instances and multi-objective optimization instances. |
| Researcher Affiliation | Collaboration | Akinori Tanaka RIKEN AIP, Keio University EMAIL Akiyoshi Sannai RIKEN AIP, Keio University EMAIL Ken Kobayashi Fujitsu Laboratories LTD., RIKEN AIP, Tokyo Tech EMAIL Naoki Hamada Fujitsu Laboratories LTD., RIKEN AIP EMAIL |
| Pseudocode | No | The paper does not contain any clearly labeled 'Pseudocode' or 'Algorithm' blocks or figures. |
| Open Source Code | Yes | The source code and library dependencies are provided in https://github.com/rafcc/aaai-20.1534. |
| Open Datasets | Yes | To investigate the relationship between the generalization performance and our theoretical risk, we provide two complementary instances of multi-objective optimization problems: a generalized location problem called MED (Harada, Sakuma, and Kobayashi 2006; Hamada et al. 2010) and a multi-objective hyper-parameter tuning of the group lasso (Yuan and Lin 2006) on the Birthwt dataset (Hosmer and Lemeshow 1989; Venables and Ripley 2002). |
| Dataset Splits | No | The paper mentions 'training points' and a 'test set', but it does not explicitly describe a 'validation set' or provide specific percentages/counts for a train/validation/test split. |
| Hardware Specification | Yes | Experiment programs were implemented in Python 3.7.1 and run on a Windows 7 PC with an Intel Core i7-4790CPU (3.60 GHz) and 16 GB RAM. |
| Software Dependencies | No | Experiment programs were implemented in Python 3.7.1 and run on a Windows 7 PC with an Intel Core i7-4790CPU (3.60 GHz) and 16 GB RAM. The source code and library dependencies are provided in https://github.com/rafcc/aaai-20.1534. While Python version is specified, the paper does not list other ancillary software dependencies with specific version numbers directly in the main text. |
| Experiment Setup | Yes | In this experiment, we estimated the B ezier simplex with degree D = 2 or 3, and compared the following three fitting methods: all-at-once the all-at-once fitting (Section 3.1); inductive skeleton (non-optimal) the inductive skeleton fitting (Section 3.2) with N (0) = = N (M 1) = N/M, which does not provide the optimal value of the risk shown in Table 1; inductive skeleton (optimal) the inductive skeleton fitting (Section 3.2) where N (0), . . . , N (M 1) are determined by minimizing the risk shown in Table 1 under the constraints M 1 m=0 N (m) = N and N (m) 0 (m = 0, . . . , M 1). We make them strongly convex by the following perturbation: f1 = f1 + ε x 2 , f2 = f2 + ε x 2 , f3 = f3 + ε x 2 where ε is an arbitrarily small positive number (we set ε = 10 4). We changed the size of the training set from N { 250, 500, 1000, 2000 }. |