Research

I research at the interface of the mathematics of machine learning and signal processing, using high-dimensional probability, optimization and machine learning to understand novel aspects of high-dimensional structured signal recovery, the mathematics of information and deep learning. 

I want provable guarantees with practical relevance for the design and analysis of methods for structured underdetermined linear inverse problems, like LASSO for compressed sensing or deep learning methods for computational sensing.

I am a CRM Applied Math Lab- and IVADO-funded postdoctoral researcher in the Department of Mathematics & Statistics at McGill University in Montréal, Canada with Drs. Tim Hoheisel (McGill) and Simone Brugiapaglia (Concordia). 

1. AB, Brugiapaglia, S., Hoheisel, T. (2023).
   Square Root LASSO: well-posedness, Lipschitz stability and the tuning trade off.
   Submitted to SIAM Journal on Optimization (SIOPT). arXiv:2303.15588 

2. AB, Ma, Y., Boufounos, P., Wang, P., & Mansour, H. (2022).
   Deep proximal gradient method for learned convex regularizers.
   Submitted to ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

3. AB, Brugiapaglia, S., Joshi, B., Plan, Y., Scott, M., & Yilmaz, Ö. (2022).
   A coherence parameter characterizing generative compressed sensing with Fourier measurements.
   IEEE Journal on Selected Areas in Information Theory (JSAIT). doi:10.1109/JSAIT.2022.3220196. arXiv:2207.09340. (url).

4. AB, Ozturan, G., Delavari, P., Maberley, D., Yilmaz, Ö., & Oruc, I. (2022).
   Learning from few examples: Classifying sex from retinal images via deep learning.
   Submitted to PLOS One. arXiv:2207.09624. (url).

5. Hoheisel, T., Brugiapaglia, S., & AB. (2022).
   LASSO reloaded: a variational analysis perspective with applications to compressed sensing.
   Submitted to SIAM Journal on Mathematics of Data Science. arXiv:2205.06872. (url).

6. AB. (2021).
   On LASSO parameter sensitivity (Doctoral dissertation).
   University of British Columbia. (url).

7. AB. (2021).
   Deep generative demixing: error bounds for demixing subgaussian mixtures of lipschitz signals.
   In ICASSP 2021 — 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 4010–4014). doi:10.1109/ICASSP39728.2021.9413573.

8. AB., Plan, Y., & Yilmaz, Ö. (2021).
   On the best choice of LASSO program given data parameters.
   IEEE Transactions on Information Theory. doi:10.1109/TIT.2021.3138772.

9. AB. (2020).
   Deep generative demixing: recovering Lipschitz signals from noisy subgaussian mixtures.
   arXiv:2010.06652

10. AB, Plan, Y., & Yilmaz, Ö. (2020).
    Sensitivity of ℓ1 minimization to parameter choice.
    Information and Inference: A Journal of the IMA. doi:10.1093/imaiai/iaaa014

11. AB, Plan, Y., & Yilmaz, Ö. (2019).
    Parameter instability regimes in sparse proximal denoising programs.
    In 2019 13th International conference on Sampling Theory and Applications (SampTA) (pp. 1–5). doi:10.1109/SampTA45681.2019.9030982

12. Karagiannis, G. S., AB, Dimitromanolakis, A., & Diamandis, E. P. (2013).
    Enrichment map profiling of the cancer invasion front suggests regulation of colorectal cancer progression by the bone morphogenetic protein antagonist, gremlin-1.
    Molecular oncology, 7(4), 826–839. doi:10.1016/j.molonc.2013.04.002

For a non-exhaustive list of talks I have given, see my CV.