Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Continuous-Time View of Early Stopping for Least Squares   We study the statistical properties of the iterates generated by gradient
descent, applied to the fundamental problem of least squares regression. We
take a continuous-time view, i.e., consider infinitesimal step sizes in
gradient descent, in which case the iterates form a trajectory called gradient
flow. Our primary focus is to compare the risk of gradient flow to that of
ridge regression. Under the calibration $t=1/\lambda$---where $t$ is the time
parameter in gradient flow, and $\lambda$ the tuning parameter in ridge
regression---we prove that the risk of gradient flow is no less than 1.69 times
that of ridge, along the entire path (for all $t \geq 0$). This holds in finite
samples with very weak assumptions on the data model (in particular, with no
assumptions on the features $X$). We prove that the same relative risk bound
holds for prediction risk, in an average sense over the underlying signal
$\beta_0$. Finally, we examine limiting risk expressions (under standard
Marchenko-Pastur asymptotics), and give supporting numerical experiments.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: math