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X-WR-CALNAME:Discrete Mathematics Group
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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260908T163000
DTEND;TZID=Asia/Seoul:20260908T173000
DTSTAMP:20260825T051917Z
CREATED:20260812T064149Z
LAST-MODIFIED:20260825T051917Z
UID:13089-1788885000-1788888600@dimag.ibs.re.kr
SUMMARY:Olga Medrano Martín del Campo\, Epsilon-saturation for Littlestone classes and stable graphs
DESCRIPTION:We introduce the concept of the saturation of a (bi)graph: the union closure after inductively adding its virtual elements\, which are weighted ε-good (respectively ε-excellent sets) as in the Stable Regularity Lemma. In the Littlestone class and stable graph case\, we show that if the saturation has bounded Littlestone dimension\, then it is the smallest ε-saturated object containing the initial one. We show that for certain values of ε\, the saturations of Littlestone classes are Littlestone\, although not necessarily of the same dimension. For ε large enough\, we find examples to show that VC and Littlestone dimensions may grow arbitrarily. For certain ε\, we bound Littlestone dimension of the saturation by a finite value depending on VC dimension\, by using techniques including the Fundamental Theorem of Statistical Learning and the Littlestone Minimax Theorem. We will focus on the class (or bigraph) case and time permitting\, we will discuss the stable graph case. Joint work with Maryanthe Malliaris and Shay Moran.
URL:https://dimag.ibs.re.kr/event/2026-09-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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