Multiscale Dictionary Learning: Non-Asymptotic Bounds and Robustness
Authors: Mauro Maggioni, Stanislav Minsker, Nate Strawn
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We include several numerical experiments confirming these theoretical results, and our theoretical framework provides new tools for assessing the behavior of manifold learning and dictionary learning procedures on a large class of interesting models. (Section 1: Introduction) and Section 6: Numerical Experiments |
| Researcher Affiliation | Academia | Departments of Mathematics, Electrical and Computer Engineering, and Computer Science Duke University Durham, NC 27708, USA; Department of Mathematics University of Southern California Los Angeles, CA 90089, USA; Department of Mathematics and Statistics Georgetown University Washington D.C., 20057, USA |
| Pseudocode | No | The paper describes methods like Geometric Multi-Resolution Analysis (GMRA) and mathematical proofs but does not present them in a structured pseudocode or algorithm block. |
| Open Source Code | Yes | The code provided at www.math.duke.edu/~mauro/code.html can generate all the figures, re-create the data sets, and is easily modified to do more experiments. |
| Open Datasets | Yes | 6.3 The MNIST Dataset of Handwritten Digits We consider the MNIST data set of images of handwritten digits3, each of size 28 28, grayscale. There are total of 60, 000, from ten classes consisting of digits 0, 1, . . . , 9. ... 3. Available at http://yann.lecun.com/exdb/mnist/. |
| Dataset Splits | No | The paper mentions using 'the first n/2 points {X1, . . . , X n/2 } to obtain the partition {Cj,k}N(j) k=1 , while the remaining {X n/2 +1, . . . , Xn} are used to construct the operator ˆPj (see (4))' for its GMRA construction, but does not provide standard train/test/validation dataset splits for external reproduction. |
| Hardware Specification | No | The paper mentions 'The running time on a desktop was few minutes' for MNIST and Sonata Kreutzer experiments, but provides no specific hardware details such as CPU model, GPU model, or memory. |
| Software Dependencies | No | The paper does not provide specific software dependencies or version numbers for any libraries, frameworks, or tools used in the experiments. |
| Experiment Setup | Yes | We consider various settings of the parameters, namely all combinations of: d {1, 2, 4, 6, 8}, n {8000, 16000, 32000, 64000, 128000}, D {100, 1000}, σ {0, 0.05, 0.1}. (Section 6.1: Spheres of Varying Dimension in RD); We run GMRA by setting the cover tree scaling parameter θ equal to 0.9 ... we set GMRA to pick the dimension of the planes Vj,k adaptively, as the smallest dimension needed to capture half of the energy of the data in Cj,k. (Section 6.3: The MNIST Dataset of Handwritten Digits); In our experiment we choose w = 0.1 seconds, δw = 0.05 seconds, and the resulting vectors X i are D = 551-dimensional. (Section 6.4: Sonata Kreutzer) |