Bootstrapping the Error of Oja's Algorithm
Authors: Robert Lunde, Purnamrita Sarkar, Rachel Ward
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Experimental validation of the online multiplier bootstrap |
| Researcher Affiliation | Academia | Robert Lunde University of Michigan rlunde@umich.edu Purnamrita Sarkar University of Texas at Austin purna.sarkar@austin.utexas.edu Rachel Ward University of Texas at Austin rward@math.utexas.edu |
| Pseudocode | Yes | Algorithm 1: Bootstrap for Oja s algorithm |
| Open Source Code | No | The paper does not provide an explicit statement or link for open-source code for the described methodology. |
| Open Datasets | No | We draw Zij IID Uniform(-√3, √3), for i = 1, . . . , n and j = 1, . . . d. Consider a PSD matrix Kij = exp(-|i - j|c) with c = 0.01. We create a covariance matrix such that Σij = K(i, j)σiσj. We consider σi = 5i-β for β = 0.2 and β = 1. Now we transform the data to introduce dependence by letting Xi = Σ1/2Zi. By construction, we have that E[Xi Xi^T] = Σ for all 1 <= i <= n. |
| Dataset Splits | No | The paper describes generating synthetic datasets but does not specify any explicit training, validation, or test data splits. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers. |
| Experiment Setup | Yes | We use ηn = log n. In Figure 1, we see that for β = 0.2 (see (A) and (B)), where the variance decay is slow and therefore the error bounds of the residual terms are expected to be large, the quality of approximation is poorer compared to (C) and (D), where β = 1. We draw g N(0, Id) Create unit vector u0 g/ g Initialize ˆv1, v (1) 1 , . . . , v (m) 1 u0 for t=2,..., n do Update ˆv1 ˆv1 + η(XT t ˆv1)ˆv1 Normalize ˆv1 to have unit norm; for i=1:m do Draw Wi N(0, 1/2); and We draw Zij IID Uniform(-√3, √3), for i = 1, . . . , n and j = 1, . . . d. and for n = 1000, d = 500 in (A) and (C) and for n = 10, 000, d = 500 in (B) and (D). |