{"id":479495,"date":"2023-08-09T10:40:54","date_gmt":"2023-08-09T10:40:54","guid":{"rendered":""},"modified":"2023-09-05T11:18:56","modified_gmt":"2023-09-05T11:18:56","slug":"vapnik-chervonenkis-vc-dimension","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/vapnik-chervonenkis-vc-dimension\/","title":{"rendered":"K\u00edch th\u01b0\u1edbc Vapnik-Chervonenkis (VC)"},"content":{"rendered":"

Chi\u1ec1u Vapnik-Chervonenkis (VC) l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n trong l\u00fd thuy\u1ebft v\u00e0 th\u1ed1ng k\u00ea h\u1ecdc m\u00e1y t\u00ednh, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch n\u0103ng l\u1ef1c c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft ho\u1eb7c thu\u1eadt to\u00e1n h\u1ecdc. N\u00f3 \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c t\u00ecm hi\u1ec3u kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh h\u1ecdc m\u00e1y v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00e1c l\u0129nh v\u1ef1c nh\u01b0 tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o, nh\u1eadn d\u1ea1ng m\u1eabu v\u00e0 khai th\u00e1c d\u1eef li\u1ec7u. Trong b\u00e0i vi\u1ebft n\u00e0y, ch\u00fang ta s\u1ebd \u0111i s\u00e2u v\u00e0o l\u1ecbch s\u1eed, chi ti\u1ebft, \u1ee9ng d\u1ee5ng v\u00e0 tri\u1ec3n v\u1ecdng trong t\u01b0\u01a1ng lai c\u1ee7a chi\u1ec1u Vapnik-Chervonenkis.<\/p>\n

L\u1ecbch s\u1eed v\u1ec1 ngu\u1ed3n g\u1ed1c c\u1ee7a chi\u1ec1u kh\u00f4ng gian Vapnik-Chervonenkis (VC) v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3<\/h2>\n

Kh\u00e1i ni\u1ec7m v\u1ec1 chi\u1ec1u VC l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u01b0\u1ee3c gi\u1edbi thi\u1ec7u b\u1edfi Vladimir Vapnik v\u00e0 Alexey Chervonenkis v\u00e0o \u0111\u1ea7u nh\u1eefng n\u0103m 1970. C\u1ea3 hai nh\u00e0 nghi\u00ean c\u1ee9u \u0111\u1ec1u l\u00e0 th\u00e0nh vi\u00ean c\u1ee7a Vi\u1ec7n Khoa h\u1ecdc \u0110i\u1ec1u khi\u1ec3n Li\u00ean X\u00f4 v\u00e0 c\u00f4ng tr\u00ecnh c\u1ee7a h\u1ecd \u0111\u00e3 \u0111\u1eb7t n\u1ec1n m\u00f3ng cho l\u00fd thuy\u1ebft h\u1ecdc th\u1ed1ng k\u00ea. Kh\u00e1i ni\u1ec7m n\u00e0y ban \u0111\u1ea7u \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n trong b\u1ed1i c\u1ea3nh c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u00e2n lo\u1ea1i nh\u1ecb ph\u00e2n, trong \u0111\u00f3 c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i th\u00e0nh m\u1ed9t trong hai l\u1edbp.<\/p>\n

L\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn chi\u1ec1u VC xu\u1ea5t hi\u1ec7n trong m\u1ed9t b\u00e0i b\u00e1o chuy\u00ean \u0111\u1ec1 c\u1ee7a Vapnik v\u00e0 Chervonenkis v\u00e0o n\u0103m 1971, c\u00f3 t\u1ef1a \u0111\u1ec1 \u201cV\u1ec1 s\u1ef1 h\u1ed9i t\u1ee5 th\u1ed1ng nh\u1ea5t c\u1ee7a t\u1ea7n su\u1ea5t t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a c\u00e1c s\u1ef1 ki\u1ec7n v\u1edbi x\u00e1c su\u1ea5t c\u1ee7a ch\u00fang\u201d. Trong b\u00e0i b\u00e1o n\u00e0y, h\u1ecd \u0111\u00e3 gi\u1edbi thi\u1ec7u th\u1ee9 nguy\u00ean VC nh\u01b0 m\u1ed9t th\u01b0\u1edbc \u0111o \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft, l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c m\u00f4 h\u00ecnh kh\u1ea3 thi m\u00e0 thu\u1eadt to\u00e1n h\u1ecdc c\u00f3 th\u1ec3 ch\u1ecdn.<\/p>\n

Th\u00f4ng tin chi ti\u1ebft v\u1ec1 chi\u1ec1u Vapnik-Chervonenkis (VC): M\u1edf r\u1ed9ng ch\u1ee7 \u0111\u1ec1<\/h2>\n

Th\u1ee9 nguy\u00ean Vapnik-Chervonenkis (VC) l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u1ecbnh l\u01b0\u1ee3ng kh\u1ea3 n\u0103ng c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft trong vi\u1ec7c ph\u00e1 v\u1ee1 c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u. M\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft \u0111\u01b0\u1ee3c cho l\u00e0 ph\u00e1 v\u1ee1 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u n\u1ebfu n\u00f3 c\u00f3 th\u1ec3 ph\u00e2n lo\u1ea1i c\u00e1c \u0111i\u1ec3m \u0111\u00f3 theo b\u1ea5t k\u1ef3 c\u00e1ch n\u00e0o c\u00f3 th\u1ec3, t\u1ee9c l\u00e0 \u0111\u1ed1i v\u1edbi b\u1ea5t k\u1ef3 nh\u00e3n nh\u1ecb ph\u00e2n n\u00e0o c\u1ee7a c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u, t\u1ed3n t\u1ea1i m\u1ed9t m\u00f4 h\u00ecnh trong l\u1edbp gi\u1ea3 thuy\u1ebft ph\u00e2n lo\u1ea1i ch\u00ednh x\u00e1c t\u1eebng \u0111i\u1ec3m t\u01b0\u01a1ng \u1ee9ng.<\/p>\n

K\u00edch th\u01b0\u1edbc VC c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft l\u00e0 s\u1ed1 l\u01b0\u1ee3ng \u0111i\u1ec3m d\u1eef li\u1ec7u l\u1edbn nh\u1ea5t m\u00e0 l\u1edbp \u0111\u00f3 c\u00f3 th\u1ec3 ph\u00e1 v\u1ee1. N\u00f3i c\u00e1ch kh\u00e1c, n\u00f3 \u0111\u1ea1i di\u1ec7n cho s\u1ed1 l\u01b0\u1ee3ng \u0111i\u1ec3m t\u1ed1i \u0111a c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo b\u1ea5t k\u1ef3 c\u00e1ch n\u00e0o c\u00f3 th\u1ec3, sao cho l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 th\u1ec3 t\u00e1ch ch\u00fang m\u1ed9t c\u00e1ch ho\u00e0n h\u1ea3o.<\/p>\n

Chi\u1ec1u VC c\u00f3 \u00fd ngh\u0129a quan tr\u1ecdng \u0111\u1ed1i v\u1edbi kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a c\u1ee7a thu\u1eadt to\u00e1n h\u1ecdc. N\u1ebfu k\u00edch th\u01b0\u1edbc VC c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft nh\u1ecf th\u00ec l\u1edbp \u0111\u00f3 c\u00f3 nhi\u1ec1u kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a t\u1ed1t h\u01a1n t\u1eeb d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n \u0111\u1ebfn d\u1eef li\u1ec7u kh\u00f4ng nh\u00ecn th\u1ea5y \u0111\u01b0\u1ee3c, gi\u1ea3m nguy c\u01a1 kh\u1edbp qu\u00e1 m\u1ee9c. M\u1eb7t kh\u00e1c, n\u1ebfu k\u00edch th\u01b0\u1edbc VC l\u1edbn th\u00ec nguy c\u01a1 trang b\u1ecb qu\u00e1 m\u1ee9c s\u1ebd cao h\u01a1n v\u00ec m\u00f4 h\u00ecnh c\u00f3 th\u1ec3 ghi nh\u1edb nhi\u1ec5u trong d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n.<\/p>\n

C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a chi\u1ec1u Vapnik-Chervonenkis (VC): C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng<\/h2>\n

\u0110\u1ec3 hi\u1ec3u c\u00e1ch ho\u1ea1t \u0111\u1ed9ng c\u1ee7a th\u1ee9 nguy\u00ean VC, h\u00e3y xem x\u00e9t b\u00e0i to\u00e1n ph\u00e2n lo\u1ea1i nh\u1ecb ph\u00e2n v\u1edbi m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u. M\u1ee5c ti\u00eau l\u00e0 t\u00ecm ra m\u1ed9t gi\u1ea3 thuy\u1ebft (m\u00f4 h\u00ecnh) c\u00f3 th\u1ec3 t\u00e1ch c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u th\u00e0nh hai l\u1edbp m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c. M\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n l\u00e0 ph\u00e2n lo\u1ea1i email l\u00e0 th\u01b0 r\u00e1c ho\u1eb7c kh\u00f4ng ph\u1ea3i th\u01b0 r\u00e1c d\u1ef1a tr\u00ean m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng nh\u1ea5t \u0111\u1ecbnh.<\/p>\n

K\u00edch th\u01b0\u1edbc VC \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi s\u1ed1 l\u01b0\u1ee3ng \u0111i\u1ec3m d\u1eef li\u1ec7u t\u1ed1i \u0111a c\u00f3 th\u1ec3 b\u1ecb ph\u00e1 v\u1ee1 b\u1edfi m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft. N\u1ebfu m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 th\u1ee9 nguy\u00ean VC th\u1ea5p, \u0111i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 n\u00f3 c\u00f3 th\u1ec3 x\u1eed l\u00fd hi\u1ec7u qu\u1ea3 nhi\u1ec1u lo\u1ea1i m\u1eabu \u0111\u1ea7u v\u00e0o m\u00e0 kh\u00f4ng c\u1ea7n trang b\u1ecb qu\u00e1 m\u1ee9c. Ng\u01b0\u1ee3c l\u1ea1i, th\u1ee9 nguy\u00ean VC cao cho th\u1ea5y l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 th\u1ec3 qu\u00e1 ph\u1ee9c t\u1ea1p v\u00e0 c\u00f3 xu h\u01b0\u1edbng trang b\u1ecb qu\u00e1 m\u1ee9c.<\/p>\n

Ph\u00e2n t\u00edch c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh c\u1ee7a chi\u1ec1u Vapnik-Chervonenkis (VC)<\/h2>\n

Th\u1ee9 nguy\u00ean VC cung c\u1ea5p m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng v\u00e0 th\u00f4ng tin chi ti\u1ebft quan tr\u1ecdng:<\/p>\n

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    \u0110o c\u00f4ng su\u1ea5t<\/strong>: N\u00f3 \u0111\u00f3ng vai tr\u00f2 nh\u01b0 th\u01b0\u1edbc \u0111o n\u0103ng l\u1ef1c c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft, cho bi\u1ebft m\u1ee9c \u0111\u1ed9 ph\u00f9 h\u1ee3p c\u1ee7a l\u1edbp \u0111\u00f3 trong vi\u1ec7c ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u.<\/p>\n<\/li>\n

  2. \n

    Gi\u1edbi h\u1ea1n kh\u00e1i qu\u00e1t h\u00f3a<\/strong>: Th\u1ee9 nguy\u00ean VC \u0111\u01b0\u1ee3c li\u00ean k\u1ebft v\u1edbi l\u1ed7i t\u1ed5ng qu\u00e1t h\u00f3a c\u1ee7a thu\u1eadt to\u00e1n h\u1ecdc. K\u00edch th\u01b0\u1edbc VC nh\u1ecf h\u01a1n th\u01b0\u1eddng d\u1eabn \u0111\u1ebfn hi\u1ec7u su\u1ea5t kh\u00e1i qu\u00e1t h\u00f3a t\u1ed1t h\u01a1n.<\/p>\n<\/li>\n

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    L\u1ef1a ch\u1ecdn m\u00f4 h\u00ecnh<\/strong>: Hi\u1ec3u \u0111\u01b0\u1ee3c k\u00edch th\u01b0\u1edbc VC gi\u00fap l\u1ef1a ch\u1ecdn ki\u1ebfn tr\u00fac m\u00f4 h\u00ecnh ph\u00f9 h\u1ee3p cho c\u00e1c nhi\u1ec7m v\u1ee5 kh\u00e1c nhau.<\/p>\n<\/li>\n

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    Dao c\u1ea1o Occam<\/strong>: Th\u1ee9 nguy\u00ean VC h\u1ed7 tr\u1ee3 nguy\u00ean t\u1eafc dao c\u1ea1o c\u1ee7a Occam, g\u1ee3i \u00fd ch\u1ecdn m\u00f4 h\u00ecnh \u0111\u01a1n gi\u1ea3n nh\u1ea5t ph\u00f9 h\u1ee3p nh\u1ea5t v\u1edbi d\u1eef li\u1ec7u.<\/p>\n<\/li>\n<\/ol>\n

    C\u00e1c lo\u1ea1i k\u00edch th\u01b0\u1edbc Vapnik-Chervonenkis (VC)<\/h2>\n

    K\u00edch th\u01b0\u1edbc VC c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i th\u00e0nh c\u00e1c lo\u1ea1i sau:<\/p>\n

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      B\u1ed9 v\u1ee1<\/strong>: M\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c cho l\u00e0 c\u00f3 th\u1ec3 ph\u00e2n h\u1ee7y \u0111\u01b0\u1ee3c n\u1ebfu t\u1ea5t c\u1ea3 c\u00e1c nh\u00e3n nh\u1ecb ph\u00e2n c\u00f3 th\u1ec3 c\u00f3 c\u1ee7a c\u00e1c \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c l\u1edbp gi\u1ea3 thuy\u1ebft nh\u1eadn ra.<\/p>\n<\/li>\n

    2. \n

      H\u00e0m t\u0103ng tr\u01b0\u1edfng<\/strong>: H\u00e0m t\u0103ng tr\u01b0\u1edfng m\u00f4 t\u1ea3 s\u1ed1 l\u01b0\u1ee3ng ph\u00e2n \u0111\u00f4i ri\u00eang bi\u1ec7t t\u1ed1i \u0111a (nh\u00e3n nh\u1ecb ph\u00e2n) m\u00e0 m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u0111\u1ed1i v\u1edbi m\u1ed9t s\u1ed1 \u0111i\u1ec3m d\u1eef li\u1ec7u nh\u1ea5t \u0111\u1ecbnh.<\/p>\n<\/li>\n

    3. \n

      \u0110i\u1ec3m d\u1eebng<\/strong>: \u0110i\u1ec3m d\u1eebng l\u00e0 s\u1ed1 \u0111i\u1ec3m l\u1edbn nh\u1ea5t m\u00e0 t\u1ea5t c\u1ea3 c\u00e1c ph\u00e2n \u0111\u00f4i c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n, nh\u01b0ng ch\u1ec9 th\u00eam m\u1ed9t \u0111i\u1ec3m n\u1eefa s\u1ebd khi\u1ebfn \u00edt nh\u1ea5t m\u1ed9t ph\u00e2n \u0111\u00f4i kh\u00f4ng th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c.<\/p>\n<\/li>\n<\/ol>\n

      \u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c lo\u1ea1i kh\u00e1c nhau, h\u00e3y xem x\u00e9t v\u00ed d\u1ee5 sau:<\/p>\n

      V\u00ed d\u1ee5<\/strong>: H\u00e3y xem x\u00e9t m\u1ed9t b\u1ed9 ph\u00e2n lo\u1ea1i tuy\u1ebfn t\u00ednh trong kh\u00f4ng gian 2D ph\u00e2n t\u00e1ch c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u b\u1eb1ng c\u00e1ch v\u1ebd m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng. N\u1ebfu c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo c\u00e1ch m\u00e0 d\u00f9 ch\u00fang ta g\u1eafn nh\u00e3n nh\u01b0 th\u1ebf n\u00e0o th\u00ec lu\u00f4n c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 ng\u0103n c\u00e1ch ch\u00fang, l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 \u0111i\u1ec3m d\u1eebng l\u00e0 0. N\u1ebfu c\u00e1c \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo c\u00e1ch m\u00e0 \u0111\u1ed1i v\u1edbi m\u1ed9t s\u1ed1 c\u00e1ch g\u1eafn nh\u00e3n, kh\u00f4ng c\u00f3 ranh gi\u1edbi ng\u0103n c\u00e1ch ch\u00fang, l\u1edbp gi\u1ea3 thuy\u1ebft \u0111\u01b0\u1ee3c cho l\u00e0 ph\u00e1 v\u1ee1 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<\/p>\n

      C\u00e1c c\u00e1ch s\u1eed d\u1ee5ng k\u00edch th\u01b0\u1edbc Vapnik-Chervonenkis (VC), c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n

      Th\u1ee9 nguy\u00ean VC t\u00ecm th\u1ea5y c\u00e1c \u1ee9ng d\u1ee5ng trong c\u00e1c l\u0129nh v\u1ef1c h\u1ecdc m\u00e1y v\u00e0 nh\u1eadn d\u1ea1ng m\u1eabu kh\u00e1c nhau. M\u1ed9t s\u1ed1 c\u00f4ng d\u1ee5ng c\u1ee7a n\u00f3 bao g\u1ed3m:<\/p>\n

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      1. \n

        L\u1ef1a ch\u1ecdn m\u00f4 h\u00ecnh<\/strong>: Th\u1ee9 nguy\u00ean VC gi\u00fap l\u1ef1a ch\u1ecdn \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u00f4 h\u00ecnh ph\u00f9 h\u1ee3p cho m\u1ed9t nhi\u1ec7m v\u1ee5 h\u1ecdc t\u1eadp nh\u1ea5t \u0111\u1ecbnh. B\u1eb1ng c\u00e1ch ch\u1ecdn m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft c\u00f3 th\u1ee9 nguy\u00ean VC th\u00edch h\u1ee3p, ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 tr\u00e1nh \u0111\u01b0\u1ee3c vi\u1ec7c trang b\u1ecb qu\u00e1 m\u1ee9c v\u00e0 c\u1ea3i thi\u1ec7n kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a.<\/p>\n<\/li>\n

      2. \n

        L\u1ed7i t\u1ed5ng qu\u00e1t h\u00f3a gi\u1edbi h\u1ea1n<\/strong>: Th\u1ee9 nguy\u00ean VC cho ph\u00e9p ch\u00fang ta r\u00fat ra c\u00e1c gi\u1edbi h\u1ea1n v\u1ec1 l\u1ed7i t\u1ed5ng qu\u00e1t h\u00f3a c\u1ee7a thu\u1eadt to\u00e1n h\u1ecdc d\u1ef1a tr\u00ean s\u1ed1 l\u01b0\u1ee3ng m\u1eabu \u0111\u00e0o t\u1ea1o.<\/p>\n<\/li>\n

      3. \n

        Gi\u1ea3m thi\u1ec3u r\u1ee7i ro c\u01a1 c\u1ea5u<\/strong>: K\u00edch th\u01b0\u1edbc VC l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong vi\u1ec7c gi\u1ea3m thi\u1ec3u r\u1ee7i ro c\u1ea5u tr\u00fac, m\u1ed9t nguy\u00ean t\u1eafc \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 c\u00e2n b\u1eb1ng s\u1ef1 \u0111\u00e1nh \u0111\u1ed5i gi\u1eefa sai s\u1ed1 th\u1ef1c nghi\u1ec7m v\u00e0 \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u00f4 h\u00ecnh.<\/p>\n<\/li>\n

      4. \n

        M\u00e1y vect\u01a1 h\u1ed7 tr\u1ee3 (SVM)<\/strong>: SVM, m\u1ed9t thu\u1eadt to\u00e1n h\u1ecdc m\u00e1y ph\u1ed5 bi\u1ebfn, s\u1eed d\u1ee5ng chi\u1ec1u VC \u0111\u1ec3 t\u00ecm si\u00eau ph\u1eb3ng ph\u00e2n t\u00e1ch t\u1ed1i \u01b0u trong kh\u00f4ng gian \u0111\u1eb7c tr\u01b0ng nhi\u1ec1u chi\u1ec1u.<\/p>\n<\/li>\n<\/ol>\n

        Tuy nhi\u00ean, m\u1eb7c d\u00f9 chi\u1ec1u VC l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 c\u00f3 gi\u00e1 tr\u1ecb nh\u01b0ng n\u00f3 c\u0169ng \u0111\u1eb7t ra m\u1ed9t s\u1ed1 th\u00e1ch th\u1ee9c:<\/p>\n

          \n
        1. \n

          \u0110\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/strong>: Vi\u1ec7c t\u00ednh to\u00e1n k\u00edch th\u01b0\u1edbc VC cho c\u00e1c l\u1edbp gi\u1ea3 thuy\u1ebft ph\u1ee9c t\u1ea1p c\u00f3 th\u1ec3 t\u1ed1n k\u00e9m v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n.<\/p>\n<\/li>\n

        2. \n

          Ph\u00e2n lo\u1ea1i kh\u00f4ng nh\u1ecb ph\u00e2n<\/strong>: Th\u1ee9 nguy\u00ean VC ban \u0111\u1ea7u \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n cho c\u00e1c b\u00e0i to\u00e1n ph\u00e2n lo\u1ea1i nh\u1ecb ph\u00e2n v\u00e0 vi\u1ec7c m\u1edf r\u1ed9ng n\u00f3 sang c\u00e1c b\u00e0i to\u00e1n nhi\u1ec1u l\u1edbp c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t th\u00e1ch th\u1ee9c.<\/p>\n<\/li>\n

        3. \n

          Ph\u1ee5 thu\u1ed9c d\u1eef li\u1ec7u<\/strong>: Th\u1ee9 nguy\u00ean VC ph\u1ee5 thu\u1ed9c v\u00e0o ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u v\u00e0 nh\u1eefng thay \u0111\u1ed5i trong ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u c\u00f3 th\u1ec3 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn hi\u1ec7u su\u1ea5t c\u1ee7a thu\u1eadt to\u00e1n h\u1ecdc.<\/p>\n<\/li>\n<\/ol>\n

          \u0110\u1ec3 gi\u1ea3i quy\u1ebft nh\u1eefng th\u00e1ch th\u1ee9c n\u00e0y, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u \u0111\u00e3 ph\u00e1t tri\u1ec3n nhi\u1ec1u thu\u1eadt to\u00e1n v\u00e0 k\u1ef9 thu\u1eadt g\u1ea7n \u0111\u00fang kh\u00e1c nhau \u0111\u1ec3 \u01b0\u1edbc t\u00ednh k\u00edch th\u01b0\u1edbc VC v\u00e0 \u00e1p d\u1ee5ng n\u00f3 cho c\u00e1c t\u00ecnh hu\u1ed1ng ph\u1ee9c t\u1ea1p h\u01a1n.<\/p>\n

          C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n

          Th\u1ee9 nguy\u00ean VC c\u00f3 chung m\u1ed9t s\u1ed1 \u0111\u1eb7c \u0111i\u1ec3m v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m kh\u00e1c \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong h\u1ecdc m\u00e1y v\u00e0 th\u1ed1ng k\u00ea:<\/p>\n

            \n
          1. \n

            \u0110\u1ed9 ph\u1ee9c t\u1ea1p Rademacher<\/strong>: \u0110\u1ed9 ph\u1ee9c t\u1ea1p Rademacher \u0111o l\u01b0\u1eddng kh\u1ea3 n\u0103ng c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft v\u1ec1 kh\u1ea3 n\u0103ng ph\u00f9 h\u1ee3p v\u1edbi nhi\u1ec5u ng\u1eabu nhi\u00ean. N\u00f3 li\u00ean quan ch\u1eb7t ch\u1ebd \u0111\u1ebfn k\u00edch th\u01b0\u1edbc VC v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1edbi h\u1ea1n l\u1ed7i t\u1ed5ng qu\u00e1t h\u00f3a.<\/p>\n<\/li>\n

          2. \n

            H\u1ec7 s\u1ed1 v\u1ee1<\/strong>: H\u1ec7 s\u1ed1 ph\u00e1 v\u1ee1 c\u1ee7a m\u1ed9t l\u1edbp gi\u1ea3 thuy\u1ebft \u0111o s\u1ed1 \u0111i\u1ec3m t\u1ed1i \u0111a c\u00f3 th\u1ec3 b\u1ecb ph\u00e1 v\u1ee1, t\u01b0\u01a1ng t\u1ef1 nh\u01b0 k\u00edch th\u01b0\u1edbc VC.<\/p>\n<\/li>\n

          3. \n

            H\u1ecdc t\u1eadp PAC<\/strong>: H\u1ecdc c\u00f3 l\u1ebd \u0111\u00fang (PAC) l\u00e0 m\u1ed9t khu\u00f4n kh\u1ed5 d\u00e0nh cho h\u1ecdc m\u00e1y t\u1eadp trung v\u00e0o \u0111\u1ed9 ph\u1ee9c t\u1ea1p m\u1eabu hi\u1ec7u qu\u1ea3 c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n h\u1ecdc. Th\u1ee9 nguy\u00ean VC \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c ph\u00e2n t\u00edch \u0111\u1ed9 ph\u1ee9c t\u1ea1p m\u1eabu c\u1ee7a qu\u00e1 tr\u00ecnh h\u1ecdc PAC.<\/p>\n<\/li>\n<\/ol>\n

            C\u00e1c quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn chi\u1ec1u Vapnik-Chervonenkis (VC)<\/h2>\n

            Chi\u1ec1u Vapnik-Chervonenkis (VC) s\u1ebd ti\u1ebfp t\u1ee5c l\u00e0 kh\u00e1i ni\u1ec7m trung t\u00e2m trong vi\u1ec7c ph\u00e1t tri\u1ec3n c\u00e1c thu\u1eadt to\u00e1n h\u1ecdc m\u00e1y v\u00e0 l\u00fd thuy\u1ebft h\u1ecdc th\u1ed1ng k\u00ea. Khi c\u00e1c t\u1eadp d\u1eef li\u1ec7u tr\u1edf n\u00ean l\u1edbn h\u01a1n v\u00e0 ph\u1ee9c t\u1ea1p h\u01a1n, vi\u1ec7c hi\u1ec3u v\u00e0 t\u1eadn d\u1ee5ng chi\u1ec1u VC s\u1ebd ng\u00e0y c\u00e0ng tr\u1edf n\u00ean quan tr\u1ecdng trong vi\u1ec7c x\u00e2y d\u1ef1ng c\u00e1c m\u00f4 h\u00ecnh c\u00f3 kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a t\u1ed1t.<\/p>\n

            Nh\u1eefng ti\u1ebfn b\u1ed9 trong vi\u1ec7c \u01b0\u1edbc t\u00ednh k\u00edch th\u01b0\u1edbc VC v\u00e0 s\u1ef1 t\u00edch h\u1ee3p c\u1ee7a n\u00f3 v\u00e0o c\u00e1c khung h\u1ecdc t\u1eadp kh\u00e1c nhau c\u00f3 th\u1ec3 s\u1ebd d\u1eabn \u0111\u1ebfn c\u00e1c thu\u1eadt to\u00e1n h\u1ecdc t\u1eadp hi\u1ec7u qu\u1ea3 v\u00e0 ch\u00ednh x\u00e1c h\u01a1n. H\u01a1n n\u1eefa, s\u1ef1 k\u1ebft h\u1ee3p gi\u1eefa chi\u1ec1u VC v\u1edbi ki\u1ebfn tr\u00fac m\u1ea1ng l\u01b0\u1edbi th\u1ea7n kinh v\u00e0 h\u1ecdc s\u00e2u c\u00f3 th\u1ec3 t\u1ea1o ra c\u00e1c m\u00f4 h\u00ecnh h\u1ecdc s\u00e2u m\u1ea1nh m\u1ebd v\u00e0 d\u1ec5 hi\u1ec3u h\u01a1n.<\/p>\n

            C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi th\u1ee9 nguy\u00ean Vapnik-Chervonenkis (VC)<\/h2>\n

            C\u00e1c m\u00e1y ch\u1ee7 proxy, gi\u1ed1ng nh\u01b0 c\u00e1c m\u00e1y ch\u1ee7 do OneProxy (oneproxy.pro) cung c\u1ea5p, \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c duy tr\u00ec quy\u1ec1n ri\u00eang t\u01b0 v\u00e0 b\u1ea3o m\u1eadt khi truy c\u1eadp internet. Ch\u00fang \u0111\u00f3ng vai tr\u00f2 trung gian gi\u1eefa ng\u01b0\u1eddi d\u00f9ng v\u00e0 m\u00e1y ch\u1ee7 web, cho ph\u00e9p ng\u01b0\u1eddi d\u00f9ng \u1ea9n \u0111\u1ecba ch\u1ec9 IP c\u1ee7a h\u1ecd v\u00e0 truy c\u1eadp n\u1ed9i dung t\u1eeb c\u00e1c v\u1ecb tr\u00ed \u0111\u1ecba l\u00fd kh\u00e1c nhau.<\/p>\n

            Trong b\u1ed1i c\u1ea3nh k\u00edch th\u01b0\u1edbc Vapnik-Chervonenkis (VC), m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng theo nh\u1eefng c\u00e1ch sau:<\/p>\n

              \n
            1. \n

              B\u1ea3o m\u1eadt d\u1eef li\u1ec7u n\u00e2ng cao<\/strong>: Khi ti\u1ebfn h\u00e0nh th\u00ed nghi\u1ec7m ho\u1eb7c thu th\u1eadp d\u1eef li\u1ec7u cho c\u00e1c t\u00e1c v\u1ee5 h\u1ecdc m\u00e1y, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u00e1y ch\u1ee7 proxy \u0111\u1ec3 duy tr\u00ec t\u00ednh \u1ea9n danh v\u00e0 b\u1ea3o v\u1ec7 danh t\u00ednh c\u1ee7a h\u1ecd.<\/p>\n<\/li>\n

            2. \n

              Tr\u00e1nh trang b\u1ecb qu\u00e1 m\u1ee9c<\/strong>: M\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 truy c\u1eadp c\u00e1c b\u1ed9 d\u1eef li\u1ec7u kh\u00e1c nhau t\u1eeb nhi\u1ec1u v\u1ecb tr\u00ed kh\u00e1c nhau, g\u00f3p ph\u1ea7n t\u1ea1o ra t\u1eadp hu\u1ea5n luy\u1ec7n \u0111a d\u1ea1ng h\u01a1n, gi\u00fap gi\u1ea3m t\u00ecnh tr\u1ea1ng trang b\u1ecb qu\u00e1 m\u1ee9c.<\/p>\n<\/li>\n

            3. \n

              Truy c\u1eadp n\u1ed9i dung b\u1ecb gi\u1edbi h\u1ea1n v\u1ec1 m\u1eb7t \u0111\u1ecba l\u00fd<\/strong>: M\u00e1y ch\u1ee7 proxy cho ph\u00e9p ng\u01b0\u1eddi d\u00f9ng truy c\u1eadp n\u1ed9i dung t\u1eeb c\u00e1c khu v\u1ef1c kh\u00e1c nhau, cho ph\u00e9p th\u1eed nghi\u1ec7m c\u00e1c m\u00f4 h\u00ecnh h\u1ecdc m\u00e1y tr\u00ean c\u00e1c ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u \u0111a d\u1ea1ng.<\/p>\n<\/li>\n<\/ol>\n

              B\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng m\u00e1y ch\u1ee7 proxy m\u1ed9t c\u00e1ch chi\u1ebfn l\u01b0\u1ee3c, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u v\u00e0 nh\u00e0 ph\u00e1t tri\u1ec3n c\u00f3 th\u1ec3 qu\u1ea3n l\u00fd vi\u1ec7c thu th\u1eadp d\u1eef li\u1ec7u m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3, c\u1ea3i thi\u1ec7n kh\u1ea3 n\u0103ng kh\u00e1i qu\u00e1t h\u00f3a m\u00f4 h\u00ecnh v\u00e0 n\u00e2ng cao hi\u1ec7u su\u1ea5t t\u1ed5ng th\u1ec3 c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n h\u1ecdc m\u00e1y c\u1ee7a h\u1ecd.<\/p>\n

              Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n

              \u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 th\u1ee9 nguy\u00ean Vapnik-Chervonenkis (VC) v\u00e0 c\u00e1c ch\u1ee7 \u0111\u1ec1 li\u00ean quan, vui l\u00f2ng tham kh\u1ea3o c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n

                \n
              1. \n

                Vapnik, V., & Chervonenkis, A. (1971). V\u1ec1 s\u1ef1 h\u1ed9i t\u1ee5 th\u1ed1ng nh\u1ea5t c\u1ee7a t\u1ea7n su\u1ea5t t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a c\u00e1c s\u1ef1 ki\u1ec7n v\u1edbi x\u00e1c su\u1ea5t c\u1ee7a ch\u00fang<\/a><\/p>\n<\/li>\n

              2. \n

                Vapnik, V., & Chervonenkis, A. (1974). L\u00fd thuy\u1ebft nh\u1eadn d\u1ea1ng m\u1eabu<\/a><\/p>\n<\/li>\n

              3. \n

                Shalev-Shwartz, S., & Ben-David, S. (2014). T\u00ecm hi\u1ec3u v\u1ec1 Machine Learning: T\u1eeb l\u00fd thuy\u1ebft \u0111\u1ebfn thu\u1eadt to\u00e1n<\/a><\/p>\n<\/li>\n

              4. \n

                Vapnik, VN (1998). L\u00fd thuy\u1ebft h\u1ecdc th\u1ed1ng k\u00ea<\/a><\/p>\n<\/li>\n

              5. \n

                Wikipedia - Th\u1ee9 nguy\u00ean VC<\/a><\/p>\n<\/li>\n

              6. \n

                K\u00edch th\u01b0\u1edbc Vapnik-Chervonenkis - \u0110\u1ea1i h\u1ecdc Cornell<\/a><\/p>\n<\/li>\n

              7. \n

                Gi\u1ea3m thi\u1ec3u r\u1ee7i ro c\u1ea5u tr\u00fac - H\u1ec7 th\u1ed1ng x\u1eed l\u00fd th\u00f4ng tin th\u1ea7n kinh (NIPS)<\/a><\/p>\n<\/li>\n<\/ol>\n

                B\u1eb1ng c\u00e1ch kh\u00e1m ph\u00e1 nh\u1eefng t\u00e0i nguy\u00ean n\u00e0y, ng\u01b0\u1eddi \u0111\u1ecdc c\u00f3 th\u1ec3 hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 n\u1ec1n t\u1ea3ng l\u00fd thuy\u1ebft v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a chi\u1ec1u Vapnik-Chervonenkis.<\/p>","protected":false},"featured_media":470805,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-479495","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Vapnik-Chervonenkis (VC) Dimension: A Comprehensive Guide<\/mark>","faq_items":[{"question":"What is the Vapnik-Chervonenkis (VC) dimension?","answer":"

                The Vapnik-Chervonenkis (VC) dimension is a fundamental concept in computational learning theory and statistics. It measures the capacity of a hypothesis class or learning algorithm to shatter data points, enabling a deeper understanding of generalization ability in machine learning models.<\/p>"},{"question":"Who introduced the VC dimension, and when was it first mentioned?","answer":"

                The VC dimension was introduced by Vladimir Vapnik and Alexey Chervonenkis in the early 1970s. They first mentioned it in their 1971 paper titled \"On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities.\"<\/p>"},{"question":"How does the VC dimension work?","answer":"

                The VC dimension quantifies the maximum number of data points that a hypothesis class can shatter, meaning it can correctly classify any possible binary labeling of the data points. It plays a crucial role in determining a model's ability to generalize from training data to unseen data, helping to prevent overfitting.<\/p>"},{"question":"What are the key features of the VC dimension?","answer":"

                The VC dimension offers important insights, including its role as a capacity measure for hypothesis classes, its link to generalization error in learning algorithms, its significance in model selection, and its support for the principle of Occam's razor.<\/p>"},{"question":"What types of VC dimension exist?","answer":"

                The VC dimension can be categorized into shatterable sets, growth functions, and breakpoints. A set of data points is considered shatterable if all possible binary labelings can be realized by the hypothesis class.<\/p>"},{"question":"How can the VC dimension be used, and what problems can arise?","answer":"

                The VC dimension finds applications in model selection, bounding generalization error, structural risk minimization, and support vector machines (SVM). However, challenges include computational complexity, non-binary classification, and data dependency. Researchers have developed approximation algorithms and techniques to address these issues.<\/p>"},{"question":"What are the perspectives and future technologies related to the VC dimension?","answer":"

                The VC dimension will continue to play a central role in machine learning and statistical learning theory. As data sets grow larger and more complex, understanding and leveraging the VC dimension will be crucial in developing models that generalize well and achieve better performance.<\/p>"},{"question":"How can proxy servers be associated with the VC dimension?","answer":"

                Proxy servers, like those provided by OneProxy (oneproxy.pro), can enhance data privacy during experiments or data collection for machine learning tasks. They can also help access diverse datasets from different geographical locations, contributing to more robust and generalized models.<\/p>"},{"question":"Where can I find more information about the VC dimension?","answer":"

                For more information about the VC dimension and related topics, you can explore the provided links to resources, research papers, and books on statistical learning theory and machine learning algorithms.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/479495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/479495\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/470805"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=479495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}