A statistical model for tensor PCA
Authors: Emile Richard, Andrea Montanari
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | 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. |