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 also want clever tools with practical applications to realistic signal processing tasks. 

Presently, I'm a Staff Research Scientist at Deep Render where I develop mathematical, statistical and deep learning tools to advance the world's first real-time fully AI video codec. Until July 2023 I was 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., Plan, Y., Scott, M., Sheng, S., Yılmaz, Ö. (2023)
   Model-adapted Fourier sampling for generative compressed sensing.
   NeurIPS 2023 Workshop on Deep Learning and Inverse Problems. arXiv:2310.04984. (url).

2. 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 

3. AB, Ma, Y., Boufounos, P., Wang, P., & Mansour, H. (2022).
   Deep proximal gradient method for learned convex regularizers.
   ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). doi:10.1109/ICASSP49357.2023.10094632.

4. 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).

5. AB, Ozturan, G., Delavari, P., Maberley, D., Yilmaz, Ö., & Oruc, I. (2022).
   Learning from few examples: Classifying sex from retinal images via deep learning.
   PLOS One. doi:10.1371/journal.pone.0289211. arXiv:2207.09624. (url).

6. Hoheisel, T., Brugiapaglia, S., & AB. (2022).
   LASSO reloaded: a variational analysis perspective with applications to compressed sensing.
   SIAM Journal on Mathematics of Data Science. doi:10.1137/22M1498991. arXiv:2205.06872. (url).

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

8. 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.

9. 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.

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

11. 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

12. 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

13. 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.