Zachary Chase

Approximate trace reconstruction of random strings from a constant number of traces

2021 · arXiv (Cornell University)

In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace …

Dual VC Dimension Obstructs Sample Compression by Embeddings

2024 · arXiv (Cornell University)

This work studies embedding of arbitrary VC classes in well-behaved VC classes, focusing particularly on extremal classes. Our main result expresses an impossibility: such embeddings necessarily require a significant increase in dimension. In particular, we …