Weilin Li
CUNY City College, NY·Mathematics & Statistics
Many areas of science need to recover hidden quantities from measurements that are incomplete or noisy, such as the positions of objects in an image or the few simple components that make up a signal. A common strategy is to write down an optimization problem and let a computer search for the parameters that best explain the data.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
parameter estimation
nonconvex optimization
optimization landscape
- Grants
- 1 known grant, through Aug 2029
What they work on
- Construct objective functions for continuous parameter estimation whose informative minima lie close to the true parameters and have large basins of attraction, so standard local optimization methods can locate them efficiently.
- Establish that spurious minima in these objective functions remain shallow, and develop a rejection strategy that detects and discards such wrong answers during the search.
- Prove that these geometric properties are governed by an underlying correlation kernel, yielding a single theoretical framework covering a broad class of parameter estimation problems.
- Derive recovery guarantees and structure-exploiting algorithms for three representative applications: wave-based imaging, sparse decompositions of signals, and reconstruction from noisy random rotations.
More about the research
These searches can fail in two ways: they can get stuck at a wrong answer, called a spurious minimum, or the best answer they find can itself be inaccurate because of noise. This project asks when such searches can be trusted and how to design them so they reliably land near the truth.
Why it matters
Reliable parameter estimation underlies imaging and signal analysis across many fields. Knowing when an optimization method can be trusted, and having algorithms with proven accuracy guarantees, could let researchers in wave-based imaging and related areas extract finer detail from noisy or incomplete measurements with more confidence. Freely available software may also make such results easier to reproduce and reuse.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Somayeh Sojoudi
University of California-Berkeley, CA·Engineering·Early-career
Analyze when key non-convex machine-learning problems have spurious solutions (points that look locally best but are not globally best), and how the amount of data and problem structure remove them.
Patrick Combettes
North Carolina State University, NC·Mathematics & Statistics
Develop a geometric framework unifying stochastic algorithms for convex feasibility, best approximation, convex optimization, fixed-point, variational inequality and monotone inclusion problems, and use it to design new methods.
Frank Curtis
Lehigh University, PA·Mathematics & Statistics
Revisit the basic properties that gradient sampling methods rely on to guarantee convergence, and strengthen them for nonconvex, nonsmooth, locally Lipschitz problems whose function values are corrupted by computational noise.
The school
CUNY City College: 9 labs on PI Pages, $72M a year on research, 31 research doctorates a year.
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