Statistics / Machine Learning

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VC dimension of ellipsoids

VC dimension of ellipsoids

: ๋ณธ ๋…ผ๋ฌธ์€ ์—˜๋ฆฝ์†Œ์ด๋“œ์˜ ๋ณต์žก์„ฑ์„ ์ธก์ •ํ•˜๋Š” VC ์ฐจ์›์— ๋Œ€ํ•œ ์‹ฌ์ธต์ ์ธ ์—ฐ๊ตฌ๋ฅผ ์ˆ˜ํ–‰ํ•œ๋‹ค. ์ด๋Š” ํ•™์Šต ์ด๋ก ์—์„œ ์ค‘์š”ํ•œ ๊ฐœ๋…์œผ๋กœ, ๋ฐ์ดํ„ฐ ๋ถ„์„ ๋ฐ ๋ชจ๋ธ ์„ ํƒ์— ํ™œ์šฉ๋œ๋‹ค. 1. VC ์ฐจ์›์˜ ์ •์˜์™€ ์ค‘์š”์„ฑ VC ์ฐจ์›์€ ์ง‘ํ•ฉ์ด ์–ผ๋งˆ๋‚˜ ๋ณต์žกํ•œ ํ˜•ํƒœ๋ฅผ ๊ฐ€์งˆ ์ˆ˜ ์žˆ๋Š”์ง€๋ฅผ ์ธก์ •ํ•˜๋Š” ์ง€ํ‘œ๋กœ, ๊ฒฝํ—˜์  ๊ณผ์ • ์ด๋ก , ํ†ต๊ณ„ ๋ฐ ๊ณ„์‚ฐ ํ•™์Šต ์ด๋ก , ๊ทธ๋ฆฌ๊ณ  ์ด์‚ฐ ๊ธฐํ•˜ํ•™ ๋“ฑ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ํ™œ์šฉ๋œ๋‹ค. ํŠนํžˆ, VC ์ฐจ์›์€ ๋ฐ์ดํ„ฐ์˜ ๋ณต์žก์„ฑ์„ ์ธก์ •ํ•˜๊ณ  ๋ชจ๋ธ ์„ ํƒ์— ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•œ๋‹ค. 2. ์—˜๋ฆฝ์†Œ์ด๋“œ์™€ ๊ฐ€์šฐ์‹œ์•ˆ ํ˜ผํ•ฉ ๋ชจ๋ธ ์—˜๋ฆฝ์†Œ์ด๋“œ๋Š” d์ฐจ์› ๊ณต๊ฐ„์—์„œ ์ •์˜๋˜๋Š” ์ง‘ํ•ฉ์œผ๋กœ,

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