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Machine Learning Research
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Published in IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019
In this project, I helped develop the state of the art algorithm for deblurring QR codes. Our method is able to handle much more severe blurs than have previously been considered in the literature. As a bonus, it’s easy to implement using well-documented Python packages.
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Published in Unpublished technical report, 2019
In this project, we developed an asymptotic polynomial-time approximation scheme (APTAS) for a special case of the minimum makespan job scheduling problem with job cost constraints motivated by applications to fair chore division problems.
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Published in Inverse Problems, 2020
This paper extends our earlier work on QR code deblurring to the case of general images. We develop a deblurring algorithm that achieves strong results on images that include calibration patterns and in cases where the blur kernel is known in advance.
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Published in ICLR, 2023
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model’s objective using a simple alternating scheme. Using this learned metric, we can nonlinearly interpolate between probability measures and compute geodesics on the manifold. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sectional data.
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Published in Under review, 2023
Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves sampling times competitive with neural SGMs while running on consumer-grade CPUs.
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