Scale Invariant Power Iteration
Authors: Cheolmin Kim, Youngseok Kim, Diego Klabjan
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In numerical experiments, we introduce applications to independent component analysis, Gaussian mixtures, and non-negative matrix factorization with the KL-divergence. Experimental results demonstrate that SCI-PI is competitive to application specific stateof-the-art algorithms and often yield better solutions. Keywords: scale invariance, power iteration, optimization, convergence analysis, machine learning applications |
| Researcher Affiliation | Academia | Cheolmin Kim* EMAIL Department of Industrial Engineering and Management Sciences Northwestern University Evanston, IL, 60208, USA Youngseok Kim* EMAIL Department of Statistics University of Chicago Chicago, IL, 60637, USA Diego Klabjan EMAIL Department of Industrial Engineering and Management Sciences Northwestern University Evanston, IL, 60208, USA |
| Pseudocode | Yes | Algorithm 1 SCI-PI Output: initial point x0 Bd k 0 while f(xk) = 0 do xk+1 f(xk) f(xk) 2 k k + 1 end while Output: xk |
| Open Source Code | Yes | A description of the data sets is provided below and source codes are available at: https://github.com/youngseok-kim/SCIPI-JMLR. |
| Open Datasets | Yes | For KL-NMF (Section 5.2), we use four public real data sets available online and summarized in Table 1. ... These four data sets are retrieved from https://www.microsoft.com/en-us/research/project, https: //archive.ics.uci.edu/ml/datasets/bag+of+words, and https://snap.stanford.edu/data/wiki-Vote. html For GMM (Section 5.3), we use ten public real data sets, corresponding to all small and moderate data sets provided by the mlbench package in R. ... For ICA, discussed also in Section 5.3, we use nine public data sets (see Table 3) from the UCI Machine Learning repository . |
| Dataset Splits | No | The paper describes the datasets and their characteristics but does not explicitly provide details about training/test/validation splits with percentages, sample counts, or references to predefined splits for reproduction. For GMM, it mentions running EM and SCI-PI for the given number of classes without class labels, implying a lack of explicit train/test splits for supervised evaluation. |
| Hardware Specification | Yes | All experiments are implemented on a standard laptop (2.6 GHz Intel Core i7 processor and 16GM memory) using the Julia programming language. |
| Software Dependencies | No | The paper states using "the Julia programming language" but does not specify its version or the versions of any other software libraries or dependencies used for implementation. |
| Experiment Setup | Yes | We estimate r = 20 factors. ... For PGD, the learning rate is optimized by grid search. ... Our method (SCI-PI): It iterates hnew h (σ +W T z) 2 followed by rescaling, where σ is a shift parameter. We simply use σ = 1 for preconditioning. The stopping criterion is fk f 2 10 6f where fk is the objective value at iteration k and f is the solution obtained by MIXSQP after extensive computation time. ... The EM and SCI-PI updates for π can be written respectively as ... where α is a shift parameter set to 1. |