Team: F. Baudier, S. Foucart (lead), K. Narayanan, R. Tuo

Synopsizing points

• Exploit some a priori structure to learn/recover from few data - this incorporates Compressive Sensing, where the specific structure is vector sparsity

• Handle other structures such as low rank for matrices and tensors, variable reduction for multivariate functions, etc.

• Active/directed learning to address the choice of the few datasites

• In particular, uncover near-optimal choices via deterministic (not random) means - this constitutes a major mathematical challenge

Related grants

• TAMU T3 Triads: Learning More Efficiently with Less Labels, 2020-22 (PI: Foucart, coPI: Tuo)

Recent relevant papers

• S. Foucart. The sparsity of LASSO-type minimizers. (arXiv)

• S. Foucart, E. Tadmor, M. Zhong. On the sparsity of LASSO minimizers in sparse data recovery. Constructive Approximation, to appear. (arXiv)

• V. K. Amalladinne, J. R. Ebert, J. F. Chamberland, K. Narayanan. An enhanced decoding algorithm for coded compressed sensing with applications to unsourced random access. Sensors, 22/2, 676, 2022. (doi)

• S. Foucart, D. Needell, R. Pathak, Y. Plan, M. Wootters. Weighted matrix completion from non-random, non-uniform sampling patterns. IEEE Transactions on Information Theory, 67/2, 1264-1290, 2021. (doi)

• S. Foucart. Facilitating OWL norm minimizations. Optimization Letters, 15/1, 263-269, 2021. (doi)