{"id":477408,"date":"2023-08-09T09:14:25","date_gmt":"2023-08-09T09:14:25","guid":{"rendered":""},"modified":"2023-09-05T11:14:40","modified_gmt":"2023-09-05T11:14:40","slug":"hamiltonian-monte-carlo","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/hamiltonian-monte-carlo\/","title":{"rendered":"Hamiltonian Monte Carlo"},"content":{"rendered":"

Hamiltonian Monte Carlo (HMC) l\u00e0 m\u1ed9t k\u1ef9 thu\u1eadt l\u1ea5y m\u1eabu ph\u1ee9c t\u1ea1p \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong th\u1ed1ng k\u00ea Bayes v\u00e0 v\u1eadt l\u00fd t\u00ednh to\u00e1n. N\u00f3 \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 kh\u00e1m ph\u00e1 m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 s\u1ef1 ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t nhi\u1ec1u chi\u1ec1u b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton, m\u1ed9t khu\u00f4n kh\u1ed5 to\u00e1n h\u1ecdc b\u1eaft ngu\u1ed3n t\u1eeb c\u01a1 h\u1ecdc c\u1ed5 \u0111i\u1ec3n. B\u1eb1ng c\u00e1ch m\u00f4 ph\u1ecfng ho\u1ea1t \u0111\u1ed9ng c\u1ee7a m\u1ed9t h\u1ec7 th\u1ed1ng v\u1eadt l\u00fd, HMC t\u1ea1o ra c\u00e1c m\u1eabu c\u00f3 hi\u1ec7u qu\u1ea3 h\u01a1n trong vi\u1ec7c kh\u00e1m ph\u00e1 c\u00e1c kh\u00f4ng gian ph\u1ee9c t\u1ea1p so v\u1edbi c\u00e1c ph\u01b0\u01a1ng ph\u00e1p truy\u1ec1n th\u1ed1ng nh\u01b0 thu\u1eadt to\u00e1n Metropolis-Hastings. \u1ee8ng d\u1ee5ng c\u1ee7a HMC m\u1edf r\u1ed9ng ra ngo\u00e0i mi\u1ec1n ban \u0111\u1ea7u c\u1ee7a n\u00f3, v\u1edbi c\u00e1c tr\u01b0\u1eddng h\u1ee3p s\u1eed d\u1ee5ng \u0111\u1ea7y h\u1ee9a h\u1eb9n trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 v\u1eadn h\u00e0nh m\u00e1y ch\u1ee7 proxy.<\/p>\n

L\u1ecbch s\u1eed v\u1ec1 ngu\u1ed3n g\u1ed1c c\u1ee7a Hamiltonian Monte Carlo v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3.<\/h2>\n

Hamiltonian Monte Carlo l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u01b0\u1ee3c gi\u1edbi thi\u1ec7u b\u1edfi Simon Duane, Adrienne Kennedy, Brian Pendleton v\u00e0 Duncan Roweth trong b\u00e0i b\u00e1o n\u0103m 1987 c\u1ee7a h\u1ecd c\u00f3 t\u1ef1a \u0111\u1ec1 \u201cHybrid Monte Carlo\u201d. Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y ban \u0111\u1ea7u \u0111\u01b0\u1ee3c ngh\u0129 ra \u0111\u1ec3 m\u00f4 ph\u1ecfng c\u00e1c h\u1ec7 l\u01b0\u1ee3ng t\u1eed trong l\u00fd thuy\u1ebft tr\u01b0\u1eddng m\u1ea1ng, m\u1ed9t l\u0129nh v\u1ef1c v\u1eadt l\u00fd l\u00fd thuy\u1ebft. Kh\u00eda c\u1ea1nh lai c\u1ee7a thu\u1eadt to\u00e1n \u0111\u1ec1 c\u1eadp \u0111\u1ebfn s\u1ef1 k\u1ebft h\u1ee3p c\u1ee7a c\u1ea3 hai bi\u1ebfn li\u00ean t\u1ee5c v\u00e0 r\u1eddi r\u1ea1c.<\/p>\n

Theo th\u1eddi gian, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u v\u1ec1 th\u1ed1ng k\u00ea Bayes \u0111\u00e3 nh\u1eadn ra ti\u1ec1m n\u0103ng c\u1ee7a k\u1ef9 thu\u1eadt n\u00e0y trong vi\u1ec7c l\u1ea5y m\u1eabu t\u1eeb c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t ph\u1ee9c t\u1ea1p, v\u00e0 do \u0111\u00f3, thu\u1eadt ng\u1eef \u201cHamiltonian Monte Carlo\u201d \u0111\u00e3 tr\u1edf n\u00ean ph\u1ed5 bi\u1ebfn. Nh\u1eefng \u0111\u00f3ng g\u00f3p c\u1ee7a Radford Neal v\u00e0o \u0111\u1ea7u nh\u1eefng n\u0103m 1990 \u0111\u00e3 c\u1ea3i thi\u1ec7n \u0111\u00e1ng k\u1ec3 hi\u1ec7u qu\u1ea3 c\u1ee7a HMC, khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t c\u00f4ng c\u1ee5 thi\u1ebft th\u1ef1c v\u00e0 m\u1ea1nh m\u1ebd cho suy lu\u1eadn Bayes.<\/p>\n

Th\u00f4ng tin chi ti\u1ebft v\u1ec1 Hamiltonian Monte Carlo. M\u1edf r\u1ed9ng ch\u1ee7 \u0111\u1ec1 Hamiltonian Monte Carlo.<\/h2>\n

Hamiltonian Monte Carlo v\u1eadn h\u00e0nh b\u1eb1ng c\u00e1ch \u0111\u01b0a c\u00e1c bi\u1ebfn \u0111\u1ed9ng l\u01b0\u1ee3ng ph\u1ee5 v\u00e0o thu\u1eadt to\u00e1n Metropolis-Hastings ti\u00eau chu\u1ea9n. C\u00e1c bi\u1ebfn \u0111\u1ed9ng l\u01b0\u1ee3ng n\u00e0y l\u00e0 c\u00e1c bi\u1ebfn nh\u00e2n t\u1ea1o, li\u00ean t\u1ee5c v\u00e0 s\u1ef1 t\u01b0\u01a1ng t\u00e1c c\u1ee7a ch\u00fang v\u1edbi c\u00e1c bi\u1ebfn v\u1ecb tr\u00ed c\u1ee7a ph\u00e2n ph\u1ed1i m\u1ee5c ti\u00eau t\u1ea1o ra m\u1ed9t h\u1ec7 th\u1ed1ng lai. C\u00e1c bi\u1ebfn v\u1ecb tr\u00ed \u0111\u1ea1i di\u1ec7n cho c\u00e1c tham s\u1ed1 quan t\u00e2m trong ph\u00e2n b\u1ed1 m\u1ee5c ti\u00eau, trong khi c\u00e1c bi\u1ebfn \u0111\u1ed9ng l\u01b0\u1ee3ng gi\u00fap h\u01b0\u1edbng d\u1eabn vi\u1ec7c kh\u00e1m ph\u00e1 kh\u00f4ng gian.<\/p>\n

Ho\u1ea1t \u0111\u1ed9ng n\u1ed9i b\u1ed9 c\u1ee7a Hamiltonian Monte Carlo c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00f3m t\u1eaft nh\u01b0 sau:<\/p>\n

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    \u0110\u1ed9ng l\u1ef1c h\u1ecdc Hamilton:<\/strong> HMC s\u1eed d\u1ee5ng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton, \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh b\u1edfi c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a Hamilton. H\u00e0m Hamilton k\u1ebft h\u1ee3p th\u1ebf n\u0103ng (li\u00ean quan \u0111\u1ebfn ph\u00e2n b\u1ed1 m\u1ee5c ti\u00eau) v\u00e0 \u0111\u1ed9ng n\u0103ng (li\u00ean quan \u0111\u1ebfn c\u00e1c bi\u1ebfn \u0111\u1ed9ng l\u01b0\u1ee3ng).<\/p>\n<\/li>\n

  2. \n

    T\u00edch h\u1ee3p nh\u1ea3y v\u1ecdt:<\/strong> \u0110\u1ec3 m\u00f4 ph\u1ecfng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton, s\u01a1 \u0111\u1ed3 t\u00edch ph\u00e2n b\u01b0\u1edbc nh\u1ea3y v\u1ecdt \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng. N\u00f3 r\u1eddi r\u1ea1c h\u00f3a c\u00e1c b\u01b0\u1edbc th\u1eddi gian, cho ph\u00e9p gi\u1ea3i ph\u00e1p s\u1ed1 hi\u1ec7u qu\u1ea3 v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n<\/li>\n

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    B\u01b0\u1edbc ch\u1ea5p nh\u1eadn c\u1ee7a Metropolis:<\/strong> Sau khi m\u00f4 ph\u1ecfng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton cho m\u1ed9t s\u1ed1 b\u01b0\u1edbc nh\u1ea5t \u0111\u1ecbnh, b\u01b0\u1edbc ch\u1ea5p nh\u1eadn Metropolis-Hastings \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n. N\u00f3 x\u00e1c \u0111\u1ecbnh xem n\u00ean ch\u1ea5p nh\u1eadn hay t\u1eeb ch\u1ed1i tr\u1ea1ng th\u00e1i \u0111\u1ec1 xu\u1ea5t, d\u1ef1a tr\u00ean \u0111i\u1ec1u ki\u1ec7n c\u00e2n b\u1eb1ng chi ti\u1ebft.<\/p>\n<\/li>\n

  4. \n

    Thu\u1eadt to\u00e1n Hamilton Monte Carlo:<\/strong> Thu\u1eadt to\u00e1n HMC bao g\u1ed3m vi\u1ec7c l\u1ea5y m\u1eabu nhi\u1ec1u l\u1ea7n c\u00e1c bi\u1ebfn \u0111\u1ed9ng l\u01b0\u1ee3ng t\u1eeb ph\u00e2n b\u1ed1 Gaussian v\u00e0 m\u00f4 ph\u1ecfng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton. B\u01b0\u1edbc ch\u1ea5p nh\u1eadn \u0111\u1ea3m b\u1ea3o r\u1eb1ng c\u00e1c m\u1eabu k\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c l\u1ea5y t\u1eeb ph\u00e2n ph\u1ed1i m\u1ee5c ti\u00eau.<\/p>\n<\/li>\n<\/ol>\n

    Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a Hamiltonian Monte Carlo.<\/h2>\n

    Hamiltonian Monte Carlo c\u00f3 m\u1ed9t s\u1ed1 \u01b0u \u0111i\u1ec3m ch\u00ednh so v\u1edbi c\u00e1c ph\u01b0\u01a1ng ph\u00e1p l\u1ea5y m\u1eabu truy\u1ec1n th\u1ed1ng:<\/p>\n

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      Th\u0103m d\u00f2 hi\u1ec7u qu\u1ea3:<\/strong> HMC c\u00f3 kh\u1ea3 n\u0103ng kh\u00e1m ph\u00e1 c\u00e1c ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t ph\u1ee9c t\u1ea1p v\u00e0 nhi\u1ec1u chi\u1ec1u hi\u1ec7u qu\u1ea3 h\u01a1n nhi\u1ec1u k\u1ef9 thu\u1eadt Monte Carlo chu\u1ed7i Markov (MCMC) kh\u00e1c.<\/p>\n<\/li>\n

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      K\u00edch th\u01b0\u1edbc b\u01b0\u1edbc th\u00edch \u1ee9ng:<\/strong> Thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 \u0111i\u1ec1u ch\u1ec9nh k\u00edch th\u01b0\u1edbc b\u01b0\u1edbc c\u1ee7a n\u00f3 m\u1ed9t c\u00e1ch th\u00edch \u1ee9ng trong qu\u00e1 tr\u00ecnh m\u00f4 ph\u1ecfng, cho ph\u00e9p n\u00f3 kh\u00e1m ph\u00e1 c\u00e1c v\u00f9ng c\u00f3 \u0111\u1ed9 cong kh\u00e1c nhau m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/p>\n<\/li>\n

    3. \n

      Kh\u00f4ng \u0111i\u1ec1u ch\u1ec9nh b\u1eb1ng tay:<\/strong> Kh\u00f4ng gi\u1ed1ng nh\u01b0 m\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p MCMC y\u00eau c\u1ea7u \u0111i\u1ec1u ch\u1ec9nh ph\u00e2n ph\u1ed1i \u0111\u1ec1 xu\u1ea5t theo c\u00e1ch th\u1ee7 c\u00f4ng, HMC th\u01b0\u1eddng y\u00eau c\u1ea7u \u00edt tham s\u1ed1 \u0111i\u1ec1u ch\u1ec9nh h\u01a1n.<\/p>\n<\/li>\n

    4. \n

      Gi\u1ea3m hi\u1ec7n t\u01b0\u1ee3ng t\u1ef1 t\u01b0\u01a1ng quan:<\/strong> HMC c\u00f3 xu h\u01b0\u1edbng t\u1ea1o ra c\u00e1c m\u1eabu c\u00f3 \u0111\u1ed9 t\u1ef1 t\u01b0\u01a1ng quan th\u1ea5p h\u01a1n, cho ph\u00e9p h\u1ed9i t\u1ee5 nhanh h\u01a1n v\u00e0 \u01b0\u1edbc t\u00ednh ch\u00ednh x\u00e1c h\u01a1n.<\/p>\n<\/li>\n

    5. \n

      Tr\u00e1nh h\u00e0nh vi \u0111i b\u1ed9 ng\u1eabu nhi\u00ean:<\/strong> Kh\u00f4ng gi\u1ed1ng nh\u01b0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p MCMC truy\u1ec1n th\u1ed1ng, HMC s\u1eed d\u1ee5ng \u0111\u1ed9ng l\u1ef1c x\u00e1c \u0111\u1ecbnh \u0111\u1ec3 h\u01b0\u1edbng d\u1eabn vi\u1ec7c th\u0103m d\u00f2, gi\u1ea3m h\u00e0nh vi b\u01b0\u1edbc \u0111i ng\u1eabu nhi\u00ean v\u00e0 kh\u1ea3 n\u0103ng tr\u1ed9n ch\u1eadm.<\/p>\n<\/li>\n<\/ol>\n

      C\u00e1c lo\u1ea1i Hamiltonian Monte Carlo<\/h2>\n

      C\u00f3 m\u1ed9t s\u1ed1 bi\u1ebfn th\u1ec3 v\u00e0 ph\u1ea7n m\u1edf r\u1ed9ng c\u1ee7a Hamiltonian Monte Carlo \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111\u1ec1 xu\u1ea5t \u0111\u1ec3 gi\u1ea3i quy\u1ebft nh\u1eefng th\u00e1ch th\u1ee9c c\u1ee5 th\u1ec3 ho\u1eb7c \u0111i\u1ec1u ch\u1ec9nh ph\u01b0\u01a1ng ph\u00e1p cho c\u00e1c t\u00ecnh hu\u1ed1ng c\u1ee5 th\u1ec3. M\u1ed9t s\u1ed1 lo\u1ea1i HMC \u0111\u00e1ng ch\u00fa \u00fd bao g\u1ed3m:<\/p>\n\n\n\n\n\n\n\n\n
      Lo\u1ea1i h\u00ecnh HMC<\/strong><\/th>\nS\u1ef1 mi\u00eau t\u1ea3<\/strong><\/th>\n<\/tr>\n<\/thead>\n
      B\u1ed9 l\u1ea5y m\u1eabu kh\u00f4ng quay \u0111\u1ea7u (NUTS)<\/strong><\/td>\nNUTS l\u00e0 ph\u1ea7n m\u1edf r\u1ed9ng c\u1ee7a HMC, t\u1ef1 \u0111\u1ed9ng x\u00e1c \u0111\u1ecbnh s\u1ed1 b\u01b0\u1edbc nh\u1ea3y v\u1ecdt trong qu\u00e1 tr\u00ecnh m\u00f4 ph\u1ecfng. N\u00f3 t\u1ef1 \u0111\u1ed9ng d\u1eebng m\u00f4 ph\u1ecfng khi qu\u1ef9 \u0111\u1ea1o quay \u0111\u1ea7u, d\u1eabn \u0111\u1ebfn vi\u1ec7c kh\u00e1m ph\u00e1 hi\u1ec7u qu\u1ea3 h\u01a1n.<\/td>\n<\/tr>\n
      HMC Riemannian<\/strong><\/td>\nRiemannian HMC \u0111i\u1ec1u ch\u1ec9nh thu\u1eadt to\u00e1n HMC cho ph\u00f9 h\u1ee3p v\u1edbi c\u00e1c \u0111a t\u1ea1p, cho ph\u00e9p l\u1ea5y m\u1eabu hi\u1ec7u qu\u1ea3 t\u1eeb ph\u00e2n b\u1ed1 x\u00e1c su\u1ea5t \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean c\u00e1c kh\u00f4ng gian cong. \u0110i\u1ec1u n\u00e0y \u0111\u1eb7c bi\u1ec7t h\u1eefu \u00edch trong c\u00e1c m\u00f4 h\u00ecnh Bayesian v\u1edbi c\u00e1c r\u00e0ng bu\u1ed9c ho\u1eb7c tham s\u1ed1 h\u00f3a tr\u00ean \u0111a t\u1ea1p.<\/td>\n<\/tr>\n
      \u0110\u1ed9 d\u1ed1c ng\u1eabu nhi\u00ean HMC<\/strong><\/td>\nBi\u1ebfn th\u1ec3 n\u00e0y k\u1ebft h\u1ee3p c\u00e1c gradient ng\u1eabu nhi\u00ean v\u00e0o m\u00f4 ph\u1ecfng, l\u00e0m cho n\u00f3 ph\u00f9 h\u1ee3p v\u1edbi c\u00e1c b\u00e0i to\u00e1n suy lu\u1eadn Bayesian quy m\u00f4 l\u1edbn, ch\u1eb3ng h\u1ea1n nh\u01b0 nh\u1eefng b\u00e0i to\u00e1n g\u1eb7p ph\u1ea3i trong c\u00e1c \u1ee9ng d\u1ee5ng h\u1ecdc m\u00e1y.<\/td>\n<\/tr>\n
      HMC t\u1ed5ng qu\u00e1t<\/strong><\/td>\nHMC t\u1ed5ng qu\u00e1t m\u1edf r\u1ed9ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y \u0111\u1ec3 bao g\u1ed3m \u0111\u1ed9ng l\u1ef1c h\u1ecdc phi Hamilton, m\u1edf r\u1ed9ng kh\u1ea3 n\u0103ng \u1ee9ng d\u1ee5ng c\u1ee7a n\u00f3 cho nhi\u1ec1u v\u1ea5n \u0111\u1ec1 h\u01a1n.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      C\u00e1c c\u00e1ch s\u1eed d\u1ee5ng Hamiltonian Monte Carlo, 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

      Hamiltonian Monte Carlo t\u00ecm th\u1ea5y c\u00e1c \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m:<\/p>\n

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        Suy lu\u1eadn Bayes:<\/strong> HMC \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i cho c\u00e1c nhi\u1ec7m v\u1ee5 \u01b0\u1edbc l\u01b0\u1ee3ng tham s\u1ed1 Bayes v\u00e0 l\u1ef1a ch\u1ecdn m\u00f4 h\u00ecnh. Hi\u1ec7u qu\u1ea3 c\u1ee7a n\u00f3 trong vi\u1ec7c kh\u00e1m ph\u00e1 c\u00e1c ph\u00e2n ph\u1ed1i h\u1eadu nghi\u1ec7m ph\u1ee9c t\u1ea1p khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t l\u1ef1a ch\u1ecdn h\u1ea5p d\u1eabn cho ph\u00e2n t\u00edch d\u1eef li\u1ec7u Bayes.<\/p>\n<\/li>\n

      2. \n

        H\u1ecdc m\u00e1y:<\/strong> Trong b\u1ed1i c\u1ea3nh h\u1ecdc s\u00e2u Bayesian v\u00e0 h\u1ecdc m\u00e1y x\u00e1c su\u1ea5t, HMC cung c\u1ea5p m\u1ed9t ph\u01b0\u01a1ng ti\u1ec7n \u0111\u1ec3 l\u1ea5y m\u1eabu t\u1eeb c\u00e1c ph\u00e2n b\u1ed1 sau c\u1ee7a tr\u1ecdng s\u1ed1 m\u1ea1ng th\u1ea7n kinh, cho ph\u00e9p \u01b0\u1edbc t\u00ednh \u0111\u1ed9 kh\u00f4ng \u0111\u1ea3m b\u1ea3o trong d\u1ef1 \u0111o\u00e1n v\u00e0 hi\u1ec7u ch\u1ec9nh m\u00f4 h\u00ecnh.<\/p>\n<\/li>\n

      3. \n

        T\u1ed1i \u01b0u h\u00f3a:<\/strong> HMC c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh cho c\u00e1c nhi\u1ec7m v\u1ee5 t\u1ed1i \u01b0u h\u00f3a, trong \u0111\u00f3 n\u00f3 c\u00f3 th\u1ec3 l\u1ea5y m\u1eabu t\u1eeb ph\u00e2n ph\u1ed1i sau c\u1ee7a c\u00e1c tham s\u1ed1 m\u00f4 h\u00ecnh v\u00e0 kh\u00e1m ph\u00e1 b\u1ed1i c\u1ea3nh t\u1ed1i \u01b0u h\u00f3a m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/p>\n<\/li>\n<\/ol>\n

        Nh\u1eefng th\u00e1ch th\u1ee9c li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng HMC bao g\u1ed3m:<\/p>\n

          \n
        1. \n

          Th\u00f4ng s\u1ed1 \u0111i\u1ec1u ch\u1ec9nh:<\/strong> M\u1eb7c d\u00f9 HMC y\u00eau c\u1ea7u \u00edt tham s\u1ed1 \u0111i\u1ec1u ch\u1ec9nh h\u01a1n so v\u1edbi m\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p MCMC kh\u00e1c, vi\u1ec7c \u0111\u1eb7t k\u00edch th\u01b0\u1edbc b\u01b0\u1edbc v\u00e0 s\u1ed1 b\u01b0\u1edbc nh\u1ea3y v\u1ecdt ph\u00f9 h\u1ee3p v\u1eabn c\u00f3 th\u1ec3 r\u1ea5t quan tr\u1ecdng \u0111\u1ec3 kh\u00e1m ph\u00e1 hi\u1ec7u qu\u1ea3.<\/p>\n<\/li>\n

        2. \n

          T\u00ednh to\u00e1n chuy\u00ean s\u00e2u:<\/strong> M\u00f4 ph\u1ecfng \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton li\u00ean quan \u0111\u1ebfn vi\u1ec7c gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh vi ph\u00e2n, c\u00f3 th\u1ec3 t\u1ed1n k\u00e9m v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u ho\u1eb7c v\u1edbi b\u1ed9 d\u1eef li\u1ec7u l\u1edbn.<\/p>\n<\/li>\n

        3. \n

          L\u1eddi nguy\u1ec1n c\u1ee7a chi\u1ec1u k\u00edch:<\/strong> Nh\u01b0 v\u1edbi b\u1ea5t k\u1ef3 k\u1ef9 thu\u1eadt l\u1ea5y m\u1eabu n\u00e0o, l\u1eddi nguy\u1ec1n v\u1ec1 s\u1ed1 chi\u1ec1u \u0111\u1eb7t ra nh\u1eefng th\u00e1ch th\u1ee9c khi s\u1ed1 chi\u1ec1u c\u1ee7a ph\u00e2n b\u1ed1 m\u1ee5c ti\u00eau tr\u1edf n\u00ean qu\u00e1 cao.<\/p>\n<\/li>\n<\/ol>\n

          Gi\u1ea3i ph\u00e1p cho nh\u1eefng th\u00e1ch th\u1ee9c n\u00e0y li\u00ean quan \u0111\u1ebfn vi\u1ec7c t\u1eadn d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p th\u00edch \u1ee9ng, s\u1eed d\u1ee5ng c\u00e1c b\u01b0\u1edbc l\u1eb7p kh\u1edfi \u0111\u1ed9ng v\u00e0 s\u1eed d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n chuy\u00ean d\u1ee5ng nh\u01b0 NUTS \u0111\u1ec3 t\u1ef1 \u0111\u1ed9ng \u0111i\u1ec1u ch\u1ec9nh tham s\u1ed1.<\/p>\n

          C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 c\u00e1c so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1 d\u01b0\u1edbi d\u1ea1ng b\u1ea3ng v\u00e0 danh s\u00e1ch.<\/h2>\n\n\n\n\n\n\n\n\n\n
          \u0111\u1eb7c tr\u01b0ng<\/strong><\/th>\nSo s\u00e1nh v\u1edbi Metropolis-Hastings<\/strong><\/th>\n<\/tr>\n<\/thead>\n
          Hi\u1ec7u qu\u1ea3 th\u0103m d\u00f2<\/strong><\/td>\nHMC th\u1ec3 hi\u1ec7n hi\u1ec7u qu\u1ea3 th\u0103m d\u00f2 cao h\u01a1n, cho ph\u00e9p h\u1ed9i t\u1ee5 nhanh h\u01a1n v\u00e0 l\u1ea5y m\u1eabu ch\u00ednh x\u00e1c h\u01a1n so v\u1edbi h\u00e0nh vi \u0111i b\u1ed9 ng\u1eabu nhi\u00ean c\u1ee7a Metropolis-Hastings.<\/td>\n<\/tr>\n
          \u0110i\u1ec1u ch\u1ec9nh \u0111\u1ed9 ph\u1ee9c t\u1ea1p<\/strong><\/td>\nHMC th\u01b0\u1eddng y\u00eau c\u1ea7u \u00edt tham s\u1ed1 \u0111i\u1ec1u ch\u1ec9nh h\u01a1n Metropolis-Hastings, gi\u00fap s\u1eed d\u1ee5ng d\u1ec5 d\u00e0ng h\u01a1n trong th\u1ef1c t\u1ebf.<\/td>\n<\/tr>\n
          X\u1eed l\u00fd kh\u00f4ng gian ph\u1ee9c t\u1ea1p<\/strong><\/td>\nHMC c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 c\u00e1c kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u ph\u1ee9c t\u1ea1p m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3, trong khi Metropolis-Hastings c\u00f3 th\u1ec3 g\u1eb7p kh\u00f3 kh\u0103n trong nh\u1eefng t\u00ecnh hu\u1ed1ng nh\u01b0 v\u1eady.<\/td>\n<\/tr>\n
          T\u1ef1 t\u01b0\u01a1ng quan<\/strong><\/td>\nHMC t\u1ea1o ra c\u00e1c m\u1eabu c\u00f3 \u0111\u1ed9 t\u1ef1 t\u01b0\u01a1ng quan th\u1ea5p h\u01a1n, d\u1eabn \u0111\u1ebfn \u00edt d\u01b0 th\u1eeba h\u01a1n trong chu\u1ed7i l\u1ea5y m\u1eabu.<\/td>\n<\/tr>\n
          Kh\u1ea3 n\u0103ng m\u1edf r\u1ed9ng<\/strong><\/td>\n\u0110\u1ed1i v\u1edbi c\u00e1c b\u00e0i to\u00e1n c\u00f3 chi\u1ec1u cao, HMC c\u00f3 xu h\u01b0\u1edbng ho\u1ea1t \u0111\u1ed9ng t\u1ed1t h\u01a1n Metropolis-Hastings do kh\u1ea3 n\u0103ng kh\u00e1m ph\u00e1 \u0111\u01b0\u1ee3c c\u1ea3i thi\u1ec7n v\u00e0 gi\u1ea3m h\u00e0nh vi b\u01b0\u1edbc \u0111i ng\u1eabu nhi\u00ean.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          Quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn Hamiltonian Monte Carlo.<\/h2>\n

          Hamiltonian Monte Carlo \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh l\u00e0 m\u1ed9t k\u1ef9 thu\u1eadt l\u1ea5y m\u1eabu c\u00f3 gi\u00e1 tr\u1ecb trong th\u1ed1ng k\u00ea Bayes, v\u1eadt l\u00fd t\u00ednh to\u00e1n v\u00e0 h\u1ecdc m\u00e1y. Tuy nhi\u00ean, nghi\u00ean c\u1ee9u v\u00e0 ti\u1ebfn b\u1ed9 \u0111ang di\u1ec5n ra trong l\u0129nh v\u1ef1c n\u00e0y ti\u1ebfp t\u1ee5c ho\u00e0n thi\u1ec7n v\u00e0 m\u1edf r\u1ed9ng kh\u1ea3 n\u0103ng c\u1ee7a ph\u01b0\u01a1ng ph\u00e1p.<\/p>\n

          M\u1ed9t s\u1ed1 l\u0129nh v\u1ef1c ph\u00e1t tri\u1ec3n \u0111\u1ea7y h\u1ee9a h\u1eb9n c\u1ee7a HMC bao g\u1ed3m:<\/p>\n

            \n
          1. \n

            Song song h\u00f3a v\u00e0 GPU:<\/strong> C\u00e1c k\u1ef9 thu\u1eadt song song h\u00f3a v\u00e0 vi\u1ec7c s\u1eed d\u1ee5ng B\u1ed9 x\u1eed l\u00fd \u0111\u1ed3 h\u1ecda (GPU) c\u00f3 th\u1ec3 \u0111\u1ea9y nhanh qu\u00e1 tr\u00ecnh t\u00ednh to\u00e1n \u0111\u1ed9ng l\u1ef1c h\u1ecdc Hamilton, gi\u00fap HMC tr\u1edf n\u00ean kh\u1ea3 thi h\u01a1n \u0111\u1ed1i v\u1edbi c\u00e1c v\u1ea5n \u0111\u1ec1 quy m\u00f4 l\u1edbn.<\/p>\n<\/li>\n

          2. \n

            Ph\u01b0\u01a1ng ph\u00e1p HMC th\u00edch \u1ee9ng:<\/strong> Nh\u1eefng c\u1ea3i ti\u1ebfn trong thu\u1eadt to\u00e1n HMC th\u00edch \u1ee9ng c\u00f3 th\u1ec3 l\u00e0m gi\u1ea3m nhu c\u1ea7u \u0111i\u1ec1u ch\u1ec9nh th\u1ee7 c\u00f4ng v\u00e0 th\u00edch \u1ee9ng hi\u1ec7u qu\u1ea3 h\u01a1n v\u1edbi c\u00e1c ph\u00e2n ph\u1ed1i m\u1ee5c ti\u00eau ph\u1ee9c t\u1ea1p.<\/p>\n<\/li>\n

          3. \n

            H\u1ecdc s\u00e2u Bayes:<\/strong> Vi\u1ec7c t\u00edch h\u1ee3p HMC v\u00e0o c\u00e1c khung h\u1ecdc s\u00e2u Bayesian c\u00f3 th\u1ec3 mang l\u1ea1i nh\u1eefng \u01b0\u1edbc t\u00ednh kh\u00f4ng ch\u1eafc ch\u1eafn m\u1ea1nh m\u1ebd h\u01a1n v\u00e0 c\u00e1c d\u1ef1 \u0111o\u00e1n \u0111\u01b0\u1ee3c hi\u1ec7u ch\u1ec9nh t\u1ed1t h\u01a1n.<\/p>\n<\/li>\n

          4. \n

            T\u0103ng t\u1ed1c ph\u1ea7n c\u1ee9ng:<\/strong> Vi\u1ec7c s\u1eed d\u1ee5ng ph\u1ea7n c\u1ee9ng chuy\u00ean d\u1ee5ng, ch\u1eb3ng h\u1ea1n nh\u01b0 b\u1ed9 x\u1eed l\u00fd tensor (TPU) ho\u1eb7c b\u1ed9 t\u0103ng t\u1ed1c HMC chuy\u00ean d\u1ee5ng, c\u00f3 th\u1ec3 n\u00e2ng cao h\u01a1n n\u1eefa hi\u1ec7u su\u1ea5t c\u1ee7a c\u00e1c \u1ee9ng d\u1ee5ng d\u1ef1a tr\u00ean HMC.<\/p>\n<\/li>\n<\/ol>\n

            C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi Hamiltonian Monte Carlo.<\/h2>\n

            M\u00e1y ch\u1ee7 proxy \u0111\u00f3ng vai tr\u00f2 trung gian gi\u1eefa ng\u01b0\u1eddi d\u00f9ng v\u00e0 internet. Ch\u00fang c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c li\u00ean k\u1ebft v\u1edbi Hamiltonian Monte Carlo theo hai c\u00e1ch ch\u00ednh:<\/p>\n

              \n
            1. \n

              T\u0103ng c\u01b0\u1eddng quy\u1ec1n ri\u00eang t\u01b0 v\u00e0 b\u1ea3o m\u1eadt:<\/strong> Gi\u1ed1ng nh\u01b0 Hamiltonian Monte Carlo c\u00f3 th\u1ec3 c\u1ea3i thi\u1ec7n t\u00ednh ri\u00eang t\u01b0 v\u00e0 b\u1ea3o m\u1eadt c\u1ee7a d\u1eef li\u1ec7u th\u00f4ng qua l\u1ea5y m\u1eabu hi\u1ec7u qu\u1ea3 v\u00e0 \u01b0\u1edbc t\u00ednh \u0111\u1ed9 kh\u00f4ng \u0111\u1ea3m b\u1ea3o, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 cung c\u1ea5p th\u00eam m\u1ed9t l\u1edbp b\u1ea3o v\u1ec7 quy\u1ec1n ri\u00eang t\u01b0 b\u1eb1ng c\u00e1ch che gi\u1ea5u \u0111\u1ecba ch\u1ec9 IP c\u1ee7a ng\u01b0\u1eddi d\u00f9ng v\u00e0 m\u00e3 h\u00f3a vi\u1ec7c truy\u1ec1n d\u1eef li\u1ec7u.<\/p>\n<\/li>\n

            2. \n

              C\u00e2n b\u1eb1ng t\u1ea3i v\u00e0 t\u1ed1i \u01b0u h\u00f3a:<\/strong> M\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n ph\u1ed1i y\u00eau c\u1ea7u gi\u1eefa nhi\u1ec1u m\u00e1y ch\u1ee7 ph\u1ee5 tr\u1ee3, t\u1ed1i \u01b0u h\u00f3a vi\u1ec7c s\u1eed d\u1ee5ng t\u00e0i nguy\u00ean v\u00e0 c\u1ea3i thi\u1ec7n hi\u1ec7u qu\u1ea3 chung c\u1ee7a h\u1ec7 th\u1ed1ng. Kh\u00eda c\u1ea1nh c\u00e2n b\u1eb1ng t\u1ea3i n\u00e0y c\u00f3 nh\u1eefng \u0111i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng v\u1edbi c\u00e1ch HMC kh\u00e1m ph\u00e1 hi\u1ec7u qu\u1ea3 c\u00e1c kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u v\u00e0 tr\u00e1nh b\u1ecb k\u1eb9t \u1edf m\u1ee9c c\u1ef1c ti\u1ec3u c\u1ee5c b\u1ed9 trong c\u00e1c t\u00e1c v\u1ee5 t\u1ed1i \u01b0u h\u00f3a.<\/p>\n<\/li>\n<\/ol>\n

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

              \u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 Hamiltonian Monte Carlo, b\u1ea1n c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n

                \n
              1. Lai Monte Carlo<\/a> \u2013 Trang Wikipedia v\u1ec1 thu\u1eadt to\u00e1n Monte Carlo lai g\u1ed1c.<\/li>\n
              2. Hamiltonian Monte Carlo<\/a> \u2013 Trang Wikipedia d\u00e0nh ri\u00eang cho Hamiltonian Monte Carlo.<\/li>\n
              3. H\u01b0\u1edbng d\u1eabn s\u1eed d\u1ee5ng Stan<\/a> \u2013 H\u01b0\u1edbng d\u1eabn to\u00e0n di\u1ec7n v\u1ec1 vi\u1ec7c th\u1ef1c hi\u1ec7n Hamiltonian Monte Carlo \u1edf Stan.<\/li>\n
              4. NUTS: B\u1ed9 l\u1ea5y m\u1eabu kh\u00f4ng quay \u0111\u1ea7u<\/a> \u2013 B\u00e0i vi\u1ebft g\u1ed1c gi\u1edbi thi\u1ec7u ph\u1ea7n m\u1edf r\u1ed9ng No-U-Turn Sampler c\u1ee7a HMC.<\/li>\n
              5. L\u1eadp tr\u00ecnh x\u00e1c su\u1ea5t v\u00e0 ph\u01b0\u01a1ng ph\u00e1p Bayesian d\u00e0nh cho tin t\u1eb7c<\/a> \u2013 S\u00e1ch tr\u1ef1c tuy\u1ebfn v\u1edbi c\u00e1c v\u00ed d\u1ee5 th\u1ef1c t\u1ebf v\u1ec1 ph\u01b0\u01a1ng ph\u00e1p Bayesian, trong \u0111\u00f3 c\u00f3 HMC.<\/li>\n<\/ol>","protected":false},"featured_media":468513,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477408","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Hamiltonian Monte Carlo: A Powerful Sampling Technique for Efficient Proxy Server Operations<\/mark>","faq_items":[{"question":"What is Hamiltonian Monte Carlo (HMC)?","answer":"

                Hamiltonian Monte Carlo (HMC) is an advanced sampling technique used in Bayesian statistics and computational physics. It efficiently explores complex probability distributions by simulating Hamiltonian dynamics, offering faster convergence and more accurate results compared to traditional methods.<\/p>"},{"question":"How does Hamiltonian Monte Carlo work?","answer":"

                HMC introduces auxiliary momentum variables to the standard Metropolis-Hastings algorithm. These continuous variables interact with the position variables representing the parameters of interest, creating a hybrid system. The algorithm uses Hamiltonian dynamics to simulate the behavior of this hybrid system, and a Metropolis acceptance step ensures the resulting samples are drawn from the target distribution.<\/p>"},{"question":"What are the advantages of Hamiltonian Monte Carlo over other methods?","answer":"

                HMC boasts several key advantages, including efficient exploration of high-dimensional spaces, adaptive step size for varying curvature, reduced autocorrelation in samples, and fewer tuning parameters compared to some other MCMC methods.<\/p>"},{"question":"What are the different types of Hamiltonian Monte Carlo?","answer":"

                There are several variations of HMC, each designed to address specific challenges or tailor the method for different scenarios. Some notable types include the No-U-Turn Sampler (NUTS) for adaptive trajectory length, Riemannian HMC for manifolds, Stochastic Gradient HMC for large-scale problems, and Generalized HMC for non-Hamiltonian dynamics.<\/p>"},{"question":"In which fields is Hamiltonian Monte Carlo used?","answer":"

                HMC finds applications in various domains, such as Bayesian inference for parameter estimation and model selection, machine learning for uncertainty estimation and calibration, and optimization tasks to explore optimization landscapes effectively.<\/p>"},{"question":"What are the challenges associated with using Hamiltonian Monte Carlo?","answer":"

                While HMC requires fewer tuning parameters, setting the appropriate step size and number of leapfrog steps is crucial for efficient exploration. Additionally, simulating Hamiltonian dynamics can be computationally intensive, especially in high-dimensional spaces or with large datasets.<\/p>"},{"question":"How can Hamiltonian Monte Carlo be used with proxy servers?","answer":"

                Proxy servers, acting as intermediaries between users and the internet, can benefit from HMC's efficient exploration just as data analysis and optimization tasks do. Proxy servers enhance privacy and security by masking IP addresses and encrypting data, while HMC explores probability distributions effectively and avoids getting stuck in local minima during optimization tasks.<\/p>"},{"question":"Where can I find more information about Hamiltonian Monte Carlo?","answer":"

                For more information about Hamiltonian Monte Carlo, you can explore the Wikipedia page on \"Hamiltonian Monte Carlo,\" the Stan User's Guide for practical implementation, and the No-U-Turn Sampler (NUTS) paper for the NUTS extension. Additionally, the book \"Probabilistic Programming & Bayesian Methods for Hackers\" provides practical examples of Bayesian methods, including HMC.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/477408","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\/477408\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/468513"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=477408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}