C\u00e1c thu\u1eadt to\u00e1n bi\u1ec3u di\u1ec5n v\u00e0 h\u1ecdc t\u1eadp \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ea1o ra m\u1ed9t m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh.<\/em><\/strong><\/p>\n\n\n\n C\u00e1ch chu\u1ea9n b\u1ecb d\u1eef li\u1ec7u t\u1ed1t nh\u1ea5t tr\u01b0\u1edbc khi l\u1eadp m\u00f4 h\u00ecnh b\u1eb1ng h\u1ed3i quy tuy\u1ebfn t\u00ednh.<\/em><\/strong><\/p>\n\n\n\n T\u00f4i s\u1ebd kh\u00f4ng tr\u00ecnh b\u00e0y c\u00e1c kh\u00e1i ni\u1ec7m ph\u1ee9c t\u1ea1p v\u1ec1 th\u1ed1ng k\u00ea ho\u1eb7c \u0111\u1ea1i s\u1ed1 tuy\u1ebfn t\u00ednh. Trong b\u00e0i vi\u1ebft n\u00e0y, t\u00f4i s\u1ebd c\u1ed1 g\u1eafng tr\u00ecnh b\u00e0y m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n nh\u1eb1m cung c\u1ea5p cho b\u1ea1n \u0111\u1ee7 ki\u1ebfn \u200b\u200bth\u1ee9c n\u1ec1n t\u1ea3ng \u0111\u1ec3 c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng n\u00f3 m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 v\u00e0o c\u00e1c v\u1ea5n \u0111\u1ec1 th\u1ef1c ti\u1ec5n.<\/p>\n\n\n\n H\u1ed3i quy tuy\u1ebfn t\u00ednh (linear regression) l\u00e0 g\u00ec, \u0111\u00f3 c\u00f3 ph\u1ea3i l\u00e0 kh\u00e1i ni\u1ec7m c\u1ee7a th\u1ed1ng k\u00ea hay kh\u00f4ng?<\/strong><\/p>\n\n\n\n Tr\u01b0\u1edbc khi ch\u00fang ta t\u00ecm hi\u1ec3u chi ti\u1ebft v\u1ec1 h\u1ed3i quy tuy\u1ebfn t\u00ednh, b\u1ea1n c\u00f3 th\u1ec3 t\u1ef1 h\u1ecfi m\u00ecnh t\u1ea1i sao ch\u00fang ta l\u1ea1i ph\u1ea3i xem x\u00e9t thu\u1eadt to\u00e1n n\u00e0y.<\/p>\n\n\n\n \u0110\u00f3 ch\u1eb3ng ph\u1ea3i l\u00e0 m\u1ed9t k\u1ef9 thu\u1eadt c\u1ee7a m\u00f4n th\u1ed1ng k\u00ea hay sao?<\/p>\n\n\n\n Trong h\u1ecdc m\u00e1y, l\u0129nh v\u1ef1c m\u00f4 h\u00ecnh d\u1ef1 \u0111o\u00e1n (predictive modelling) ch\u1ee7 y\u1ebfu li\u00ean quan \u0111\u01b0a ra d\u1ef1 \u0111o\u00e1n ch\u00ednh x\u00e1c nh\u1ea5t c\u00f3 th\u1ec3 v\u00e0 gi\u1ea3m thi\u1ec3u sai s\u1ed1 c\u1ee7a m\u00f4 h\u00ecnh. Trong h\u1ecdc m\u00e1y \u1ee9ng d\u1ee5ng, ch\u00fang ta s\u1ebd m\u01b0\u1ee3n v\u00e0 s\u1eed d\u1ee5ng l\u1ea1i c\u00e1c thu\u1eadt to\u00e1n t\u1eeb nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m c\u1ea3 th\u1ed1ng k\u00ea v\u00e0 s\u1eed d\u1ee5ng ch\u00fang cho nh\u1eefng m\u1ee5c \u0111\u00edch d\u1ef1 \u0111o\u00e1n hay gi\u1ea3m thi\u1ec3u sai s\u1ed1 n\u00f3i tr\u00ean.<\/p>\n\n\n\n Do \u0111\u00f3, h\u1ed3i quy tuy\u1ebfn t\u00ednh (linear regression) v\u1ed1n \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n trong l\u0129nh v\u1ef1c th\u1ed1ng k\u00ea v\u00e0 \u0111\u01b0\u1ee3c nghi\u00ean c\u1ee9u nh\u01b0 m\u1ed9t m\u00f4 h\u00ecnh \u0111\u1ec3 hi\u1ec3u m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn s\u1ed1 \u0111\u1ea7u v\u00e0o v\u00e0 \u0111\u1ea7u ra, \u0111\u00e3 \u0111\u01b0\u1ee3c l\u0129nh v\u1ef1c h\u1ecdc m\u00e1y m\u01b0\u1ee3n \u0111\u1ec3 s\u1eed d\u1ee5ng. C\u00f3 th\u1ec3 n\u00f3i h\u1ed3i quy tuy\u1ebfn t\u00ednh v\u1eeba l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n th\u1ed1ng k\u00ea v\u1eeba l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n h\u1ecdc m\u00e1y.<\/p>\n\n\n\n H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t m\u00f4 h\u00ecnh tuy\u1ebfn t\u00ednh, v\u00ed d\u1ee5: m\u1ed9t m\u00f4 h\u00ecnh trong \u0111\u00f3 gi\u1ea3 \u0111\u1ecbnh m\u1ed1i quan h\u1ec7 tuy\u1ebfn t\u00ednh gi\u1eefa c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o (x) v\u00e0 bi\u1ebfn \u0111\u1ea7u ra duy nh\u1ea5t (y). N\u00f3i c\u00e1ch kh\u00e1c, y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n t\u1eeb s\u1ef1 k\u1ebft h\u1ee3p tuy\u1ebfn t\u00ednh c\u1ee7a c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o (x).<\/p>\n\n\n\n Khi c\u00f3 m\u1ed9t bi\u1ebfn \u0111\u1ea7u v\u00e0o duy nh\u1ea5t (x), ph\u01b0\u01a1ng ph\u00e1p n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n gi\u1ea3n (simple linear regression). Khi c\u00f3 nhi\u1ec1u bi\u1ebfn \u0111\u1ea7u v\u00e0o, ta c\u00f3 ph\u01b0\u01a1ng ph\u00e1p l\u00e0 h\u1ed3i quy tuy\u1ebfn t\u00ednh nhi\u1ec1u bi\u1ebfn (multiple linear regression).<\/p>\n\n\n\n C\u00e1c k\u1ef9 thu\u1eadt kh\u00e1c nhau c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 chu\u1ea9n b\u1ecb ho\u1eb7c hu\u1ea5n luy\u1ec7n ph\u01b0\u01a1ng tr\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh t\u1eeb d\u1eef li\u1ec7u, trong \u0111\u00f3 ph\u01b0\u01a1ng ph\u00e1p ph\u1ed5 bi\u1ebfn nh\u1ea5t \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 B\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t th\u00f4ng th\u01b0\u1eddng (Ordinary least squares). M\u00f4 h\u00ecnh h\u1ed3i quy n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 Ordinary least squares linear regression, hay ng\u1eafn g\u1ecdn h\u01a1n l\u00e0 Least squares regression<\/p>\n\n\n\n C\u00e1ch bi\u1ec3u di\u1ec5n m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong><\/p>\n\n\n\n Bi\u1ec3u di\u1ec5n l\u00e0 c\u1ee7a m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh k\u1ebft h\u1ee3p m\u1ed9t t\u1eadp gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o c\u1ee5 th\u1ec3 (x), nghi\u1ec7m l\u00e0 \u0111\u1ea7u ra d\u1ef1 \u0111o\u00e1n cho t\u1eadp gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o \u0111\u00f3 (y). C\u1ea3 gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o (x) v\u00e0 gi\u00e1 tr\u1ecb \u0111\u1ea7u ra (y) \u0111\u1ec1u l\u00e0 d\u1ea1ng s\u1ed1 (numeric).<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh \u0111\u01b0a ra m\u1ed9t h\u1ec7 s\u1ed1 t\u1ef7 l\u1ec7 cho m\u1ed7i gi\u00e1 tr\u1ecb ho\u1eb7c c\u1ed9t \u0111\u1ea7u v\u00e0o, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u1ec7 s\u1ed1 (coefficient) v\u00e0 \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1eb1ng ch\u1eef c\u00e1i Hy L\u1ea1p vi\u1ebft hoa Beta (B). Ngo\u00e0i h\u1ec7 s\u1ed1 c\u1ee7a bi\u1ebfn \u0111\u1ea7u v\u00e0o, trong ph\u01b0\u01a1ng tr\u00ecnh c\u00f2n c\u00f3 th\u00eam 1 h\u1ec7 s\u1ed1 t\u1ef1 do (intercept\/ bias coefficient), h\u1ec7 s\u1ed1 n\u00e0y t\u0103ng hay gi\u1ea3m s\u1ebd l\u00e0m \u0111\u01b0\u1eddng th\u1eb3ng t\u1ecbnh ti\u1ebfn l\u00ean tr\u00ean ho\u1eb7c xu\u1ed1ng d\u01b0\u1edbi trong \u0111\u1ed3 th\u1ecb hai chi\u1ec1u.<\/p>\n\n\n\n V\u00ed d\u1ee5, trong m\u1ed9t b\u00e0i to\u00e1n h\u1ed3i quy \u0111\u01a1n gi\u1ea3n (m\u1ed9t x v\u00e0 m\u1ed9t y duy nh\u1ea5t), d\u1ea1ng c\u1ee7a m\u00f4 h\u00ecnh s\u1ebd l\u00e0:<\/p>\n\n\n\n y = B0 + B1 * x<\/p>\n\n\n\n Trong tr\u01b0\u1eddng h\u1ee3p ch\u00fang ta c\u00f3 nhi\u1ec1u h\u01a1n m\u1ed9t \u0111\u1ea7u v\u00e0o (x), bi\u1ec3u di\u1ec5n c\u1ee7a y thay v\u00ec \u0111\u01b0\u1eddng th\u1eb3ng s\u1ebd l\u00e0 m\u1eb7t ph\u1eb3ng ho\u1eb7c si\u00eau m\u1eb7t ph\u1eb3ng.<\/p>\n\n\n\n Khi m\u1ed9t h\u1ec7 s\u1ed1 b\u1eb1ng 0, n\u00f3 s\u1ebd lo\u1ea1i b\u1ecf hi\u1ec7u qu\u1ea3 \u1ea3nh h\u01b0\u1edfng c\u1ee7a bi\u1ebfn \u0111\u1ea7u v\u00e0o l\u00ean m\u00f4 h\u00ecnh (0 * x = 0). Nh\u01b0 v\u1eady, m\u1ed9t c\u00e1ch \u0111\u1ec3 gi\u1ea3m \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy l\u00e0 gi\u1ea3m b\u1edbt s\u1ed1 bi\u1ebfn, b\u1eb1ng c\u00e1ch \u0111\u01b0a m\u1ed9t s\u1ed1 h\u1ec7 s\u1ed1 v\u1ec1 0.<\/p>\n\n\n\n Th\u1ef1c hi\u1ec7n m\u00f4 h\u00ecnh H\u1ed3i quy tuy\u1ebfn t\u00ednh<\/p>\n\n\n\n Trong m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh, ta c\u1ea7n \u01b0\u1edbc t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong bi\u1ec3u di\u1ec5n v\u1edbi d\u1eef li\u1ec7u m\u00e0 ch\u00fang ta c\u00f3 s\u1eb5n.<\/p>\n\n\n\n Trong ph\u1ea7n n\u00e0y, t\u00f4i s\u1ebd tr\u00ecnh b\u00e0y kh\u00e1i qu\u00e1t b\u1ed1n k\u1ef9 thu\u1eadt \u0111\u1ec3 chu\u1ea9n b\u1ecb m\u1ed9t m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh. Ph\u1ea7n tr\u00ecnh b\u00e0y d\u01b0\u1edbi \u0111\u00e2y s\u1ebd kh\u00f4ng \u0111i s\u00e2u v\u00e0o h\u01b0\u1edbng d\u1eabn t\u1eebng b\u01b0\u1edbc th\u1ef1c hi\u1ec7n m\u00f4 h\u00ecnh, m\u00e0 ch\u1ee7 y\u1ebfu n\u00eau nh\u1eefng \u0111i\u1ec3m ch\u00ednh c\u01a1 b\u1ea3n.<\/p>\n\n\n\n Ngo\u00e0i c\u00e1c ph\u01b0\u01a1ng ph\u00e1p \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y \u1edf \u0111\u00e2y, c\u00f2n nhi\u1ec1u k\u1ef9 thu\u1eadt kh\u00e1c c\u1ee7a m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 \u0111i s\u00e2u t\u00ecm hi\u1ec3u th\u00eam. Tuy nhi\u00ean, ph\u01b0\u01a1ng ph\u00e1p \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng nhi\u1ec1u nh\u1ea5t v\u00e0 c\u0169ng c\u1ea7n \u0111\u01b0\u1ee3c ch\u00fa \u00fd nh\u1ea5t l\u00e0 ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t (Ordinary least squares). Ngo\u00e0i ra, ph\u01b0\u01a1ng ph\u00e1p Gradient Descent c\u0169ng \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng r\u1ea5t ph\u1ed5 bi\u1ebfn trong h\u1ecdc m\u00e1y.<\/p>\n\n\n\n 1. H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n gi\u1ea3n (simple linear regression)<\/em><\/strong><\/p>\n\n\n\n V\u1edbi h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n gi\u1ea3n khi ch\u1ec9 c\u00f3 m\u1ed9t bi\u1ebfn \u0111\u1ea7u v\u00e0o duy nh\u1ea5t, ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c ph\u00e9p to\u00e1n th\u1ed1ng k\u00ea \u0111\u1ec3 \u01b0\u1edbc t\u00ednh c\u00e1c h\u1ec7 s\u1ed1.<\/p>\n\n\n\n B\u1ea1n s\u1ebd ph\u1ea3i t\u00ednh to\u00e1n c\u00e1c thu\u1ed9c t\u00ednh th\u1ed1ng k\u00ea t\u1eeb d\u1eef li\u1ec7u nh\u01b0 trung b\u00ecnh (means), \u0111\u1ed9 l\u1ec7ch chu\u1ea9n (standard deviations), t\u01b0\u01a1ng quan (correlations) v\u00e0 hi\u1ec7p ph\u01b0\u01a1ng sai (covariance). B\u1ea1n ph\u1ea3i th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p to\u00e1n n\u00e0y tr\u00ean to\u00e0n b\u1ed9 d\u1eef li\u1ec7u.<\/p>\n\n\n\n B\u1ea1n ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n k\u1ef9 thu\u1eadt n\u00e0y b\u1eb1ng excel. Tuy nhi\u00ean, trong th\u1ef1c t\u1ebf, k\u1ef9 th\u1eadt n\u00e0y kh\u00f4ng th\u1ef1c s\u1ef1 c\u00f3 nhi\u1ec1u t\u00ednh \u1ee9ng d\u1ee5ng.<\/p>\n\n\n\n 2. B\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t (ordinary least square)<\/em><\/strong><\/p>\n\n\n\n Khi c\u00f3 nhi\u1ec1u h\u01a1n m\u1ed9t bi\u1ebfn \u0111\u1ea7u v\u00e0o (x), ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p B\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t (ordinary least square) \u0111\u1ec3 \u01b0\u1edbc t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1.<\/p>\n\n\n\n Nguy\u00ean t\u1eafc c\u1ee7a ph\u01b0\u01a1ng ph\u00e1p n\u00e0y l\u00e0 t\u00ecm c\u00e1c gia tr\u1ecb h\u1ec7 s\u1ed1 sao cho t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ph\u1ea7n d\u01b0 (residuals) l\u00e0 nh\u1ecf nh\u1ea5t. V\u1edbi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng h\u1ed3i quy, ta t\u00ednh to\u00e1n kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ed7i \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111\u1ebfn \u0111\u01b0\u1eddng h\u1ed3i quy \u0111\u00f3, b\u00ecnh ph\u01b0\u01a1ng gi\u00e1 tr\u1ecb n\u00e0y v\u00e0 t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c l\u1ed7i b\u00ecnh ph\u01b0\u01a1ng l\u1ea1i v\u1edbi nhau. M\u1ee5c \u0111\u00edch c\u1ee7a ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t (ordinary least square) l\u00e0 t\u1ed1i thi\u1ec3u gi\u00e1 tr\u1ecb t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng n\u00e0y.<\/p>\n\n\n\n C\u00e1ch ti\u1ebfp c\u1eadn n\u00e0y coi d\u1eef li\u1ec7u nh\u01b0 m\u1ed9t ma tr\u1eadn v\u00e0 s\u1eed d\u1ee5ng c\u00e1c ph\u00e9p to\u00e1n \u0111\u1ea1i s\u1ed1 tuy\u1ebfn t\u00ednh \u0111\u1ec3 \u01b0\u1edbc t\u00ednh c\u00e1c gi\u00e1 tr\u1ecb t\u1ed1i \u01b0u cho c\u00e1c h\u1ec7 s\u1ed1. B\u1ea1n ph\u1ea3i th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p to\u00e1n n\u00e0y tr\u00ean to\u00e0n b\u1ed9 d\u1eef li\u1ec7u, \u0111i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 b\u1ea1n ph\u1ea3i c\u00f3 \u0111\u1ee7 b\u1ed9 nh\u1edb \u0111\u1ec3 ch\u1ee9a d\u1eef li\u1ec7u v\u00e0 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p to\u00e1n ma tr\u1eadn.<\/p>\n\n\n\n Trong th\u1ef1c t\u1ebf, tr\u1eeb khi l\u00e0m m\u1ed9t b\u00e0i t\u1eadp trong m\u00f4n \u0111\u1ea1i s\u1ed1 tuy\u1ebfn t\u00ednh, b\u1ea1n kh\u00f4ng c\u1ea7n ph\u1ea3i t\u1ef1 m\u00ecnh t\u00ednh to\u00e1n khi s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t. Ph\u00e9p to\u00e1n n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng s\u1eb5n trong c\u00e1c ph\u1ea7n m\u1ec1m th\u1ed1ng k\u00ea v\u00e0 b\u1ea1n c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n ch\u1ec9 b\u1eb1ng m\u1ed9t v\u00e0i thao t\u00e1c \u0111\u01a1n gi\u1ea3n.<\/p>\n\n\n\n 3. Gradient Descent<\/em><\/strong><\/p>\n\n\n\n Gradient Descent l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p ph\u1ed5 bi\u1ebfn trong h\u1ecdc m\u00e1y (machine learning). Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng v\u1edbi b\u00e0i to\u00e1n h\u1ed3i quy tuy\u1ebfn t\u00ednh khi c\u00f3 m\u1ed9t ho\u1eb7c nhi\u1ec1u bi\u1ebfn \u0111\u1ea7u v\u00e0o (x). \u00dd t\u01b0\u1edfng l\u00e0 t\u1ed1i \u01b0u h\u00f3a gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1 Beta b\u1eb1ng c\u00e1ch th\u1eed r\u1ea5t nhi\u1ec1u c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a h\u1ec7 s\u1ed1 tr\u00ean d\u1eef li\u1ec7u \u0111\u00e0o t\u1ea1o (training data) v\u00e0 ch\u1ecdn ra c\u00e1c gi\u00e1 tr\u1ecb sao cho sai s\u1ed1 c\u1ee7a m\u00f4 h\u00ecnh l\u00e0 nh\u1ecf nh\u1ea5t.<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y b\u1eaft \u0111\u1ea7u v\u1edbi vi\u1ec7c ch\u1ecdn c\u00e1c gi\u00e1 tr\u1ecb ng\u1eabu nhi\u00ean cho m\u1ed7i h\u1ec7 s\u1ed1. T\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u00e1c sai s\u1ed1 (residual) \u0111\u01b0\u1ee3c t\u00ednh cho t\u1eebng c\u1eb7p gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o v\u00e0 \u0111\u1ea7u ra. C\u00e1c h\u1ec7 s\u1ed1 Beta \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt theo h\u01b0\u1edbng gi\u1ea3m thi\u1ec3u t\u1ed1i \u0111a t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng sai s\u1ed1. Qu\u00e1 tr\u00ecnh \u0111\u01b0\u1ee3c l\u1eb7p l\u1ea1i cho \u0111\u1ebfn khi \u0111\u1ea1t \u0111\u01b0\u1ee3c t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng sai s\u1ed1 nh\u1ecf nh\u1ea5t ho\u1eb7c kh\u00f4ng th\u1ec3 c\u1ea3i thi\u1ec7n th\u00eam \u0111\u01b0\u1ee3c n\u1eefa.<\/p>\n\n\n\n Khi s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y, b\u1ea1n ph\u1ea3i ch\u1ecdn learning rate (alpha) x\u00e1c \u0111\u1ecbnh k\u00edch th\u01b0\u1edbc c\u1ee7a b\u01b0\u1edbc c\u1ea3i ti\u1ebfn c\u1ea7n th\u1ef1c hi\u1ec7n tr\u00ean m\u1ed7i l\u1ea7n l\u1eb7p l\u1ea1i quy tr\u00ecnh.<\/p>\n\n\n\n Gradient descent th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng v\u00e0o ph\u00e9p to\u00e1n h\u1ed3i quy tuy\u1ebfn t\u00ednh v\u00ec n\u00f3 t\u01b0\u01a1ng \u0111\u1ed1i d\u1ec5 hi\u1ec3u. Trong th\u1ef1c t\u1ebf, ph\u01b0\u01a1ng ph\u00e1p n\u00e0y r\u1ea5t h\u1eefu \u00edch khi b\u1ea1n c\u00f3 m\u1ed9t t\u1eadp d\u1eef li\u1ec7u r\u1ea5t l\u1edbn v\u1edbi s\u1ed1 l\u01b0\u1ee3ng h\u00e0ng ho\u1eb7c s\u1ed1 c\u1ed9t l\u1edbn h\u01a1n b\u1ed9 nh\u1edb.<\/p>\n\n\n\n 4. Ch\u00ednh quy h\u00f3a (Regularization)<\/em><\/strong><\/p>\n\n\n\n C\u00f3 nh\u1eefng ph\u1ea7n m\u1edf r\u1ed9ng c\u1ee7a vi\u1ec7c \u0111\u00e0o t\u1ea1o m\u00f4 h\u00ecnh tuy\u1ebfn t\u00ednh \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p ch\u00ednh quy h\u00f3a (regularization). M\u1ee5c \u0111\u00edch l\u00e0 gi\u1ea3m thi\u1ec3u t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng sai s\u1ed1 c\u1ee7a m\u00f4 h\u00ecnh tr\u00ean d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n (s\u1eed d\u1ee5ng b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t) v\u00e0 c\u00f9ng v\u1edbi \u0111\u00f3 l\u00e0 gi\u1ea3m c\u1ea3 \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u00f4 h\u00ecnh (nh\u01b0 s\u1ed1 l\u01b0\u1ee3ng ho\u1eb7c k\u00edch th\u01b0\u1edbc tuy\u1ec7t \u0111\u1ed1i c\u1ee7a t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c h\u1ec7 s\u1ed1 trong m\u00f4 h\u00ecnh) .<\/p>\n\n\n\n Hai thu\u1eadt to\u00e1n ch\u00ednh quy h\u00f3a ph\u1ed5 bi\u1ebfn s\u1eed d\u1ee5ng trong h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0:<\/p>\n\n\n\n \u2022 Lasso Regression: trong \u0111\u00f3 ph\u01b0\u01a1ng ph\u00e1p B\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t \u0111\u01b0\u1ee3c s\u1eeda \u0111\u1ed5i \u0111\u1ec3 c\u0169ng gi\u1ea3m thi\u1ec3u t\u1ed5ng tuy\u1ec7t \u0111\u1ed1i c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1 (\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ch\u00ednh quy L1).<\/p>\n\n\n\n \u2022 Ridge Regression: trong \u0111\u00f3 ph\u01b0\u01a1ng ph\u00e1p B\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t \u0111\u01b0\u1ee3c s\u1eeda \u0111\u1ed5i \u0111\u1ec3 c\u0169ng gi\u1ea3m thi\u1ec3u t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng tuy\u1ec7t \u0111\u1ed1i c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1 (\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ch\u00ednh quy L2).<\/p>\n\n\n\n C\u00e1c ph\u01b0\u01a1ng ph\u00e1p n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o c\u00f3 s\u1ef1 t\u01b0\u01a1ng quan (collinearity) v\u1edbi nhau, khi \u0111\u00f3 n\u1ebfu ch\u1ec9 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t tr\u00ean d\u1eef li\u1ec7u \u0111\u00e0o t\u1ea1o s\u1ebd kh\u00f4ng cho k\u1ebft qu\u1ea3 t\u1ed1t.<\/p>\n\n\n\n \u0110\u01b0a ra d\u1ef1 \u0111o\u00e1n v\u1edbi h\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong><\/p>\n\n\n\n V\u1edbi bi\u1ec3u di\u1ec5n l\u00e0 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh, vi\u1ec7c \u0111\u01b0a ra d\u1ef1 \u0111o\u00e1n c\u0169ng \u0111\u01a1n gi\u1ea3n nh\u01b0 vi\u1ec7c gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh cho m\u1ed9t t\u1eadp h\u1ee3p bi\u1ec5n (x) \u0111\u1ea7u v\u00e0o c\u1ee5 th\u1ec3.<\/p>\n\n\n\n T\u00f4i s\u1ebd l\u1ea5y m\u1ed9t v\u00ed d\u1ee5 c\u1ee5 th\u1ec3. H\u00e3y t\u01b0\u1edfng t\u01b0\u1ee3ng ch\u00fang ta \u0111ang d\u1ef1 \u0111o\u00e1n c\u00e2n n\u1eb7ng (y) t\u1eeb chi\u1ec1u cao (x). Bi\u1ec3u di\u1ec5n m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh c\u1ee7a ch\u00fang t\u00f4i cho v\u1ea5n \u0111\u1ec1 n\u00e0y s\u1ebd l\u00e0:<\/p>\n\n\n\n y = B0 + B1 * x1<\/p>\n\n\n\n ho\u1eb7c l\u00e0<\/p>\n\n\n\n c\u00e2n n\u1eb7ng = B0 + B1 * chi\u1ec1u cao<\/p>\n\n\n\n Trong \u0111\u00f3 B0 l\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do v\u00e0 B1 l\u00e0 h\u1ec7 s\u1ed1 cho bi\u1ebfn chi\u1ec1u cao. Gi\u1ea3 s\u1eed sau khi s\u1eed d\u1ee5ng c\u00e1c k\u1ef9 thu\u1eadt h\u1ecdc m\u00e1y nh\u01b0 \u0111\u00e3 n\u00eau \u1edf tr\u00ean, ch\u00fang ta s\u1ebd t\u00ecm \u0111\u01b0\u1ee3c c\u00e1c gi\u00e1 tr\u1ecb B ph\u00f9 h\u1ee3p. Sau khi c\u00f3 c\u00e1c gi\u00e1 tr\u1ecb n\u00e0y, ch\u00fang ta c\u00f3 th\u1ec3 \u0111\u01b0a v\u00e0o c\u00e1c th\u00f4ng s\u1ed1 chi\u1ec1u cao kh\u00e1c nhau \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n tr\u1ecdng l\u01b0\u1ee3ng.<\/p>\n\n\n\n Ch\u1eb3ng h\u1ea1n ch\u00fang ta thu \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0 B0 = 0,1 v\u00e0 B1 = 0,5. V\u1edbi m\u1ed9t ng\u01b0\u1eddi c\u00f3 chi\u1ec1u cao 182 cm:<\/p>\n\n\n\n tr\u1ecdng l\u01b0\u1ee3ng = 0,1 + 0,5 * 182<\/p>\n\n\n\n tr\u1ecdng l\u01b0\u1ee3ng = 91,1<\/p>\n\n\n\n B\u1ea1n c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng trong m\u1eb7t ph\u1eb3ng hai chi\u1ec1u, v\u1edbi B0 l\u00e0 \u0111i\u1ec3m xu\u1ea5t ph\u00e1t, nh\u01b0 trong h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n\n\n\n Chu\u1ea9n b\u1ecb d\u1eef li\u1ec7u cho h\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong><\/p>\n\n\n\n B\u1ea1n c\u1ea7n l\u01b0u \u00fd m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh d\u1ef1a tr\u00ean m\u1ed9t s\u1ed1 gi\u1ea3 \u0111\u1ecbnh (assumption) v\u1ec1 d\u1eef li\u1ec7u. B\u1ea1n c\u1ea7n \u0111\u1ea3m b\u1ea3o th\u1ecfa m\u00e3n c\u00e1c gi\u1ea3 \u0111\u1ecbnh n\u00e0y \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o m\u00f4 h\u00ecnh h\u1ed3i quy c\u00f3 \u00fd ngh\u0129a. Sau \u0111\u00e2y s\u1ebd l\u00e0 m\u1ed9t s\u1ed1 l\u01b0u \u00fd cho m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh ph\u1ed5 bi\u1ebfn nh\u1ea5t \u2013 m\u00f4 h\u00ecnh b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t (Ordinary least squares):<\/p>\n\n\n\n \u2022 Gi\u1ea3 \u0111\u1ecbnh tuy\u1ebfn t\u00ednh (Linear Assumption)<\/em><\/strong>. H\u1ed3i quy tuy\u1ebfn t\u00ednh gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng m\u1ed1i quan h\u1ec7 gi\u1eefa bi\u1ebfn \u0111\u1ed9c l\u1eadp v\u00e0 bi\u1ebfn ph\u1ee5 thu\u1ed9c l\u00e0 tuy\u1ebfn t\u00ednh, ch\u1ee9 kh\u00f4ng h\u1ed7 tr\u1ee3 c\u00e1c quan h\u1ec7 kh\u00e1c. B\u1ea1n c\u00f3 th\u1ec3 c\u1ea7n ph\u1ea3i chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u \u0111\u1ec3 l\u00e0m cho m\u1ed1i quan h\u1ec7 tr\u1edf n\u00ean tuy\u1ebfn t\u00ednh (v\u00ed d\u1ee5: l\u1ea5y logarit trong tr\u01b0\u1eddng h\u1ee3p quan h\u1ec7 l\u00e0 h\u00e0m m\u0169).<\/p>\n\n\n\n \u2022 Lo\u1ea1i b\u1ecf nhi\u1ec5u (noise)<\/em><\/strong>. H\u1ed3i quy tuy\u1ebfn t\u00ednh gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o v\u00e0 \u0111\u1ea7u ra c\u1ee7a b\u1ea1n kh\u00f4ng b\u1ecb nhi\u1ec5u. B\u1ea1n c\u00f3 th\u1ec3 c\u1ea7n s\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p l\u00e0m s\u1ea1ch d\u1eef li\u1ec7u cho ph\u00e9p b\u1ea1n l\u00e0m r\u00f5 h\u01a1n t\u00edn hi\u1ec7u trong d\u1eef li\u1ec7u c\u1ee7a m\u00ecnh t\u1ed1. \u0110i\u1ec1u n\u00e0y quan tr\u1ecdng nh\u1ea5t \u0111\u1ed1i v\u1edbi bi\u1ebfn \u0111\u1ea7u ra v\u00e0 b\u1ea1n c\u1ea7n lo\u1ea1i b\u1ecf c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 trong bi\u1ebfn \u0111\u1ea7u ra (y) n\u1ebfu c\u00f3 th\u1ec3.<\/p>\n\n\n\n \u2022 Lo\u1ea1i b\u1ecf t\u01b0\u01a1ng quan gi\u1eefa c\u00e1c bi\u1ebfn (Collinearity)<\/em><\/strong>. M\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd kh\u00f4ng ch\u00ednh x\u00e1c khi b\u1ea1n c\u00f3 c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o t\u01b0\u01a1ng quan cao v\u1edbi nhau. B\u1eadn c\u1ea7n t\u00ednh to\u00e1n c\u00e1c h\u1ec7 s\u1ed1 t\u01b0\u01a1ng quan theo c\u1eb7p cho d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o c\u1ee7a b\u1ea1n v\u00e0 lo\u1ea1i b\u1ecf b\u1edbt bi\u1ebfn \u0111\u1ea7u v\u00e0o n\u1ebfu n\u00f3 c\u00f3 t\u01b0\u01a1ng quan qu\u00e1 cao v\u1edbi bi\u1ebfn kh\u00e1c.<\/p>\n\n\n\n \u2022 Ph\u00e2n ph\u1ed1i Gaussian<\/em><\/strong>. H\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd \u0111\u01b0a ra c\u00e1c d\u1ef1 \u0111o\u00e1n \u0111\u00e1ng tin c\u1eady h\u01a1n n\u1ebfu c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o v\u00e0 \u0111\u1ea7u ra c\u1ee7a b\u1ea1n c\u00f3 ph\u00e2n ph\u1ed1i Gaussian (ph\u00e2n ph\u1ed1i chu\u1ea9n). B\u1ea1n c\u00f3 th\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 l\u1ee3i \u00edch b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c ph\u00e9p bi\u1ebfn \u0111\u1ed5i (v\u00ed d\u1ee5: log ho\u1eb7c BoxCox) tr\u00ean c\u00e1c bi\u1ebfn c\u1ee7a b\u1ea1n \u0111\u1ec3 l\u00e0m cho ph\u00e2n ph\u1ed1i c\u1ee7a ch\u00fang g\u1ea7n gi\u1ed1ng ph\u00e2n ph\u1ed1i chu\u1ea9n h\u01a1n.<\/p>\n\n\n\n \u2022 Thay \u0111\u1ed5i thang \u0111o c\u1ee7a bi\u1ebfn \u0111\u1ea7u v\u00e0o<\/em><\/strong>. H\u1ed3i quy tuy\u1ebfn t\u00ednh th\u01b0\u1eddng s\u1ebd \u0111\u01b0a ra c\u00e1c d\u1ef1 \u0111o\u00e1n \u0111\u00e1ng tin c\u1eady h\u01a1n n\u1ebfu thay \u0111\u1ed5i l\u1ea1i thang \u0111o c\u1ee7a c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o b\u1eb1ng c\u00e1ch ti\u00eau chu\u1ea9n h\u00f3a (standardization) ho\u1eb7c chu\u1ea9n h\u00f3a (normalization).<\/p>\n\n\n\n Tham kh\u1ea3o<\/strong><\/p>\n\n\n\n D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 t\u00e0i li\u1ec7u v\u1ec1 h\u1ecdc m\u00e1y \u0111\u1ec1 c\u1eadp \u0111\u1ebfn h\u1ed3i quy tuy\u1ebfn t\u00ednh m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam:<\/p>\n\n\n\n H\u1ed3i quy tuy\u1ebfn t\u00ednh c\u00f3 l\u1ebd l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n n\u1ed5i ti\u1ebfng v\u00e0 \u0111\u01b0\u1ee3c nghi\u00ean c\u1ee9 nhi\u1ec1u nh\u1ea5t […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-116","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=116"}],"version-history":[{"count":2,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/116\/revisions"}],"predecessor-version":[{"id":120,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/116\/revisions\/120"}],"wp:attachment":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/regression.png?resize=480%2C341&ssl=1\")
<\/figure><\/div>\n\n\n\n