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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
A statistical model for tensor PCA
Authors: Emile Richard, Andrea Montanari
NeurIPS 2014 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate these insights through simulations. 6 Numerical experiments Our empirical results are reported in the appendix. Figure 1: Simultaneous PCA at β = 3. Absolute correlation of the estimated principal component with the truth | bv, v0 |, simultaneous PCA (black) compared with matrix (green) and tensor PCA (blue). We performed the experiments on 100 randomly generated instances with n = 50, 200, 500 and report in Figure 1 the mean values of | v0, bv(X) | with confidence intervals. |
| Researcher Affiliation | Academia | Andrea Montanari Statistics & Electrical Engineering Stanford University Emile Richard Electrical Engineering Stanford University |
| Pseudocode | Yes | v0 = y y 2 , and vt+1 = X{vt} X{vt} 2 . Power Iteration vt+1 = X{f(vt)} bt f(vt 1) , bt = (k 1) f(vt), f(vt 1) k 2 . AMP |
| Open Source Code | No | The paper does not provide any statement or link indicating the availability of open-source code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data based on the 'Spiked Tensor Model' and 'randomly generated instances' for its experiments, rather than using a pre-existing public dataset for which access information would be provided. |
| Dataset Splits | No | The paper uses synthetically generated instances for its experiments but does not describe training, validation, or test splits of a larger dataset. It mentions generating '100 randomly generated instances' for evaluation without specifying data partitioning for model training. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies. |
| Experiment Setup | Yes | We performed the experiments on 100 randomly generated instances with n = 50, 200, 500 and report in Figure 1 the mean values of | v0, bv(X) | with confidence intervals. The analysis in previous sections suggests to use the leading eigenvector of M as the initial point of AMP algorithm for tensor PCA on X. we are given a tensor X 3Rn of Spiked Tensor Model with k = 3 and the signal to noise ratio β = 3 is fixed. In addition, we observe M = λv0v0T + N where N Rn n is a symmetric noise matrix with upper diagonal elements i < j iid Ni,j N(0, 1/n) and the value of λ [0, 2] varies. |