๋ณธ๋ฌธ ๋ฐ”๋กœ๊ฐ€๊ธฐ

AI ๊ณต๋ถ€ ํ•ญ์ƒํ•˜์ž/๊ด€๋ จ ์ด๋ก 
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[Math] Gradient Descent (์ฐฉํ•œ๋ฏธ๋ถ„๋ง›) ๋”๋ณด๊ธฐ๊ธฐ์กด ๋ถ€์บ  ๋•Œ ๋…ธ์…˜์— ๊ฐœ์ธ์ ์œผ๋กœ ์ •๋ฆฌํ•œ ๊ฒƒ์„ ๊ณต๋ถ€ํ•  ๊ฒธ ์ž‘์„ฑํ•œ ๊ธ€์ž…๋‹ˆ๋‹ค.๊ฐœ์ธ์ ์œผ๋กœ ํ•ด์„ํ•ด์„œ ์ž‘์„ฑํ•ฉ๋‹ˆ๋‹ค. (ํ‹€๋ฆด ์ˆ˜ ์žˆ์Œ. ์ •์ •์š”์ฒญ ์š”๋งใ…‹)** ๊ฐ•์˜์ž๋ฃŒ๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š์Šต๋‹ˆ๋‹ค **** ์ƒ์—…์  ์ด์šฉ์„ ๊ธˆ์ง€ํ•ฉ๋‹ˆ๋‹ค **  Today's Keyword๋ฏธ๋ถ„, ๊ธฐ์šธ๊ธฐ, ๊ฒฝ์‚ฌํ•˜๊ฐ•๋ฒ•, ํŽธ๋ฏธ๋ถ„, gradient vector  ๋ฏธ๋ถ„ (Differentiation)๋ณ€์ˆ˜์˜ ์›€์ง์ž„์— ๋”ฐ๋ฅธ ํ•จ์ˆ˜๊ฐ’์˜ ๋ณ€ํ™” ์ธก์ •์ตœ์ ํ™”์—์„œ ๋งŽ์ด ์‚ฌ์šฉ ๋ฏธ๋ถ„ == ์ ‘์„ ์˜ ๊ธฐ์šธ๊ธฐํ•จ์ˆ˜์˜ ๋ชจ์–‘์ด ๋งค๋„๋Ÿฌ์›Œ์•ผ ํ•œ๋‹ค (์—ฐ์†)ํ•œ ์ ์—์„œ ์ ‘์„ ์˜ ๊ธฐ์šธ๊ธฐ๋ฅผ ์•Œ๋ฉด ์ฆ๊ฐ€ : ๋ฏธ๋ถ„ ๊ฐ’ ๋”ํ•˜๊ธฐ๊ฐ์†Œ : ๋ฏธ๋ถ„ ๊ฐ’ ๋นผ๊ธฐ ๋ฏธ๋ถ„๊ฐ’์ด ์Œ์ˆ˜(์ขŒ๋กœ ์ƒ์Šนํ•˜๋Š” ํ˜•ํƒœ) = x+f'(x) ๋ฏธ๋ถ„๊ฐ’์ด ์•™์ˆ˜(์šฐ๋กœ ์ƒ์Šนํ•˜๋Š” ํ˜•ํƒœ) = x+f'(x) > x ๋Š” ์˜ค๋ฅธ์ชฝ์œผ๋กœ ์ด๋™ํ•˜์—ฌ ํ•จ์ˆ˜๊ฐ’์ด ๊ฐ์†Œsympy.s.. 2024. 12. 16.
[Math] ํ–‰๋ ฌ์„ ์•Œ์•„๋ณด์ž ๋”๋ณด๊ธฐ๊ธฐ์กด ๋ถ€์บ  ๋•Œ ๋…ธ์…˜์— ๊ฐœ์ธ์ ์œผ๋กœ ์ •๋ฆฌํ•œ ๊ฒƒ์„ ๊ณต๋ถ€ํ•  ๊ฒธ ์ž‘์„ฑํ•œ ๊ธ€์ž…๋‹ˆ๋‹ค.๊ฐœ์ธ์ ์œผ๋กœ ํ•ด์„ํ•ด์„œ ์ž‘์„ฑํ•ฉ๋‹ˆ๋‹ค. (ํ‹€๋ฆด ์ˆ˜ ์žˆ์Œ. ์ •์ •์š”์ฒญ ์š”๋งใ…‹)** ๊ฐ•์˜์ž๋ฃŒ๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š์Šต๋‹ˆ๋‹ค **** ์ƒ์—…์  ์ด์šฉ์„ ๊ธˆ์ง€ํ•ฉ๋‹ˆ๋‹ค **Today's Keywordํ–‰๋ ฌ ๊ณฑ์…ˆ, ํ–‰๋ ฌ ๋‚ด์ , ํ–‰x์—ดy, ํ–‰๋ ฌ๋ฒกํ„ฐ๋ฅผ ์›์†Œ๋กœ ๊ฐ€์ง€๋Š” 2์ฐจ์› ๋ฐฐ์—ดํ–‰๋ฒกํ„ฐ(row), ์—ด๋ฒกํ„ฐ(column)๋ฒกํ„ฐ๊ฐ€ ๊ณต๊ฐ„์—์„œ ํ•œ ์ ์„ ์˜๋ฏธํ•œ๋‹ค๋ฉด, ํ–‰๋ ฌ์€ ์—ฌ๋Ÿฌ ์ ๋“ค์„ ๋‚˜ํƒ€๋ƒ„. ๊ฐ™์€ ๋ชจ์–‘์ด๋ฉด๋ง์…ˆ, ๋บ„์…ˆ์„ฑ๋ถ„๊ณฑ (๊ฐ ์ธ๋ฑ์Šค ์œ„์น˜๋ผ๋ฆฌ ๊ณฑํ•˜๊ธฐ) X * Y = (Xij Yij)์Šค์นผ๋ผ๊ณฑ aX = aXijvector ๊ณต๊ฐ„์—์„œ ์‚ฌ์šฉ๋˜๋Š” ์—ฐ์‚ฐ์ž operator๋กœ ์ดํ•ด. ํ–‰๋ ฌ๊ณฑ์œผ๋กœ ๋ฒกํ„ฐ๋ฅผ ๋‹ค๋ฅธ ์ฐจ์› ๋ณด๋‚ด๋ฒ„๋ฆฌ๊ธฐ.ํŒจํ„ด์„ ์ถ”์ถœํ•  ์ˆ˜ ์žˆ๊ณ , ๋ฐ์ดํ„ฐ๋ฅผ ์••์ถ•ํ•  ์ˆ˜๋„ ์žˆ์Œ. ๋ชจ๋“  ์„ ํ˜•๋ณ€ํ™˜ linea.. 2024. 12. 2.
[Math] ๋ฒกํ„ฐ๋ฅผ ์•Œ์•„๋ณด์ž ๋”๋ณด๊ธฐ๊ธฐ์กด ๋ถ€์บ  ๋•Œ ๋…ธ์…˜์— ๊ฐœ์ธ์ ์œผ๋กœ ์ •๋ฆฌํ•œ ๊ฒƒ์„ ๊ณต๋ถ€ํ•  ๊ฒธ ์ž‘์„ฑํ•œ ๊ธ€์ž…๋‹ˆ๋‹ค.๊ฐœ์ธ์ ์œผ๋กœ ํ•ด์„ํ•ด์„œ ์ž‘์„ฑํ•ฉ๋‹ˆ๋‹ค. (ํ‹€๋ฆด ์ˆ˜ ์žˆ์Œ. ์ •์ •์š”์ฒญ ์š”๋งใ…‹)** ๊ฐ•์˜์ž๋ฃŒ๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š์Šต๋‹ˆ๋‹ค **** ์ƒ์—…์  ์ด์šฉ์„ ๊ธˆ์ง€ํ•ฉ๋‹ˆ๋‹ค **Today's Keyword๋ฒกํ„ฐ, Norm, L1-norm, L2-norm, ๋‚ด์ , ์ •์‚ฌ์˜๋ฒกํ„ฐ๊ณต๊ฐ„์—์„œ ํ•œ ์ . ์›์ ์œผ๋กœ๋ถ€ํ„ฐ ์ƒ๋Œ€์  ์œ„์น˜ ํ‘œํ˜„์Šค์นผ๋ผ ๊ณฑ ํ•˜๋ฉด ๊ธธ์ด๋งŒ ๋ณ€ํ•จ.์ˆซ์ž๋ฅผ ์›์†Œ๋กœ ๊ฐ€์ง€๋Š” ๋ฆฌ์ŠคํŠธ, ๋ฐฐ์—ด๊ฐ™์€ ๋ชจ์–‘์ด๋ฉด ์„ฑ๋ถ„๊ณฑ Hadamard product๋ฒกํ„ฐ์˜ ๋ง์…ˆ == ๋‹ค๋ฅธ ๋ฒกํ„ฐ๋กœ๋ถ€ํ„ฐ ์ƒ๋Œ€์  ์ด๋™Norm = ์›์ ์—์„œ ๋ถ€ํ„ฐ์˜ ๊ฑฐ๋ฆฌ๋…ธ๋ฆ„์˜ ์ข…๋ฅ˜๋”ฐ๋ผ ๋‹ค๋ฆ„ -> ๊ธฐํ•˜ํ•™์  ์„ฑ์งˆ๋„ ๋‹ฌ๋ผ์งL1 norm - ๋ณ€ํ™”๋Ÿ‰์˜ ์ ˆ๋Œ€๊ฐ’ ๋ชจ๋‘ ๋”ํ•ด !for Robust ํ•™์Šต, Lasso ํšŒ๊ท€L2 norm - ํ”ผํƒ€๊ณ ๋ผ์Šค ์ •๋ฆฌ.. 2024. 11. 22.
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