Hi! I am a fifth year Applied and Interdisciplinary Mathematics Ph.D. student at University of Michigan. My advisors are Anna C. Gilbert and Raj Rao Nadakuditi. I did my undergrad at Carnegie Mellon University where I obtained a B.S. in Discrete Math and Computer Science. I am interested in using Math to develop and analyze tools and algorithms for data science and machine learning.

I am also involved in running MCAIM gradute student colloquium. More information about the upcoming talks can be found here.

Current Projects

More details about each project can be found in my research statement.

1. Denoising Autoencoder - Denosing autoencoders work by learning a map from nosiy data to denoised data. Hence we need to have denoised training data to train the neurla network. Currently, this noise is either added in an ad hoc manner or added so that the training data SNR is the same as the test data SNR. I currently working on theoretically deteriming for the training data SNR should be.

2. Cryo-EM imaging - In 2017, the Nobel prize in Chemistry was awarded to Jacques Dubochet, Joachim Frank, and Richard Henderson for the cryogenic electron microscope (cryo-em). The cryo-em works by cryogenically freezing a crystal, passing radiation through it, and capturing various pictures from different angles. These are extremely noisy 2-dimensional pictures of 3-dimensional crystals. Hence we need to apply computational techniques to reconstruct the 3-dimensional representation. More recently, researchers in this area have been looking at imagining heterogenous molecules. That is, there is not one crystal structure, but that the structure of the crystal could lie on some low dimensional manifold. I am working on recovering this manifold structure.

3. Trajectory detection of single cell data - Many different biological phenomena can be modeled as hierarchies. Phylogenetic trees that represent evolutionary trajectories is one such example. Another example is cell development trajectories. That is, as cells develop and specialize into different types of cells, this process can be represented as a tree. Recently there has been great success in learning such trees using hyperbolic representations. Here the crucial innovation is due to the development of methods that learn hyperbolic metrics and representations. Hence I am exploring how use TreeRep for such problems.

4. Robustness of cMDS - cMDS is an approximation to the true MDS problem. I am analyzing the robustness of this approximation comapred to the solving the true problem.

Past Projects

1. Highly Contrained Convex Optimization

2. Hyperbolic embedding via learning Trees.

3. Sparse Metric Repair

4. Manifold Learning with missing data

5. Reconstruction of Ancient Greek Texts

6. Dual regualrized optimal transport

If you have any questions, ideas you want to discuss, or just want to talk about math and computer science, ways to contact me can be found under the contact me tab.