Deterministic Coreset for Lp Subspace
Rachit Chhaya, Anirban Dasgupta, Dan Feldman, Supratim Shit

TL;DR
This paper presents a deterministic iterative algorithm for constructing small, optimal coresets that guarantee $ ext{l}_p$ subspace embeddings for any $p$ in $[1, olinebreak \infty)$, removing long-standing $ ext{log}$ factors.
Contribution
The authors develop the first deterministic algorithm for $ ext{l}_p$ subspace coresets with optimal size, removing $ ext{log}$ factors and providing tight bounds.
Findings
Algorithm constructs $ ext{l}_p$ coresets in polynomial time.
Coreset size matches the theoretical lower bound, proving optimality.
Enables deterministic approximation for $ ext{l}_p$ regression.
Abstract
We introduce the first iterative algorithm for constructing a -coreset that guarantees deterministic subspace embedding for any and any . For a given full rank matrix where , is an -subspace embedding of , if for every , . Specifically, in this paper, is a weighted subset of rows of which is commonly known in the literature as a coreset. In every iteration, the algorithm ensures that the loss on the maintained set is upper and lower bounded by the loss on the original dataset with appropriate scalings. So, unlike typical coreset…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Stochastic Gradient Optimization Techniques · Advanced Optimization Algorithms Research
