Alexander F. Lapanowski

Publications

Papers

Lapanowski, A. F., and Gaynanova, I. "Compressing large sample data for discriminant analysis", arXiv <https://arxiv.org/abs/2005.03858>
Lapanowski, A. F., and Gaynanova, I. "Sparse feature selection in kernel discriminant analysis via optimal scoring", Accepted to AISTAT 2019 Conference Proceedings. [arXiv] [R package] [AISTAT]
Ai, A., Lapanowski, A., Plan, Y., and Vershynin, R. "One-bit compressed sensing with non-gaussian measurements", Linear Algebra and Applications 441 (2014), 222--239. [arXiv]

Sparse Feature Selection in Kernel Discriminant Analysis via Optimal ScoringWe consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernels. We propose fully-automated methods for selection of all tuning parameters, and in particular adapt kernel shrinkage ideas for ridge parameter selection. Numerical studies demonstrate the superior classification performance of the proposed approach compared to existing nonparametric classifiers.

One-bit compressed sensing with non-Gaussian measurementsIn one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples. We show that approximately sparse signals that are not extremely sparse can be accurately reconstructed from single-bit measurements sampled according to a sub-gaussian distribution, and the reconstruction comes as the solution to a convex program.

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