This repository illustrates some aspects of the dimensionality reduction addressed in [1], [2], [3] when applied to practical supervised learning problems, and as compared to the simplest case of adaptive dimensionality reduction, i.e., principal component analysis (PCA).
[1]: Valerio Cambareri, Chunlei Xu, and Laurent Jacques. "The Rare Eclipse Problem on Tiles: Quantised Embeddings of Disjoint Convex Sets." arXiv preprint arXiv:1702.04664 (2017). Submitted to 12th International Conference on Sampling Theory and Applications (SampTA 2017), July 3 – 7, 2017, Tallinn, Estonia. An earlier version of this work was presented at SPARS'17, Lisbon, June 5th-8th 2017.
[2]: Laurent Jacques and Valerio Cambareri. "Time for dithering: fast and quantized random embeddings via the restricted isometry property." arXiv preprint arXiv:1607.00816 (2016). In Information and Inference: A Journal of the IMA, accepted and in press, Mar. 2017.
[3]: Laurent Jacques. "Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets." arXiv preprint arXiv:1504.06170 (2015). IEEE Trans. Inf. Theory, in peer review, Mar. 2017.