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UID:20250918T114255EDT-0357WOMt8U@132.216.98.100
DTSTAMP:20250918T154255Z
DESCRIPTION:Title: High-dimensional limit of streaming SGD for generalized 
 linear models\n\nAbstract: We provide a characterization of the high dimen
 sional limit of one-pass\, single batch stochastic gradient descent (SGD) 
 in the case where the number of samples scales proportionally with the pro
 blem dimension. We characterize the limiting process in terms of its conve
 rgence to a high-dimensional stochastic differential equation\, referred t
 o as the homogenized SGD. Our proofs assume Gaussian data but allow for a 
 very general covariance structure. Our set-up covers a range of optimizati
 on problems including linear regression\, logistic regression\, and some s
 imple neural nets. For each of these models\, the convergence of SGD to ho
 mogenized SGD enables us to derive a close approximation of the statistica
 l risk (with explicit and vanishing error bounds) as the solution to a Vol
 terra integral equation. I will also discuss the implications of our theor
 em in terms of SGD step-size and optimality conditions for descent. (Based
  on joint work with C. Paquette\, E. Paquette\, I. Seroussi).\n\nReference
 s: The talk is mostly based on this preprint: https://arxiv.org/abs/2308.0
 8977. The special case of linear regression (without Gaussian assumption) 
 is studied in this preprint: https://arxiv.org/abs/2304.06847.\n
DTSTART:20230920T170000Z
DTEND:20230920T180000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Elizabeth Collins-Woodfin (9IÖÆ×÷³§Ãâ·Ñ)
URL:/mathstat/channels/event/elizabeth-collins-woodfin
 -mcgill-university-351011
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