{"id":2655,"date":"2023-03-28T10:38:50","date_gmt":"2023-03-28T09:38:50","guid":{"rendered":"https:\/\/cafe2sach.com\/?p=2655"},"modified":"2024-10-03T19:06:36","modified_gmt":"2024-10-03T18:06:36","slug":"gioi-thieu-ve-dinh-ly-bayes-cho-hoc-may-co-ban","status":"publish","type":"post","link":"https:\/\/cafe2sach.com\/index.php\/2023\/03\/28\/gioi-thieu-ve-dinh-ly-bayes-cho-hoc-may-co-ban\/","title":{"rendered":"Gi\u1edbi thi\u1ec7u v\u1ec1 \u0111\u1ecbnh l\u00fd bayes cho H\u1ecdc m\u00e1y c\u01a1 b\u1ea3n"},"content":{"rendered":"<p><strong>\u0110\u1ecbnh l\u00fd Bayes<\/strong> cung c\u1ea5p m\u1ed9t nguy\u00ean t\u1eafc c\u01a1 b\u1ea3n \u0111\u1ec3 t\u00ednh <strong>x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/strong>, gi\u00fap ch\u00fang ta x\u00e1c \u0111\u1ecbnh x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t s\u1ef1 ki\u1ec7n d\u1ef1a tr\u00ean th\u00f4ng tin \u0111\u00e3 bi\u1ebft v\u1ec1 s\u1ef1 ki\u1ec7n kh\u00e1c. M\u1eb7c d\u00f9 c\u00f3 v\u1ebb nh\u01b0 l\u00e0 m\u1ed9t ph\u00e9p t\u00ednh \u0111\u01a1n gi\u1ea3n, \u0111\u1ecbnh l\u00fd Bayes l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd, \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong h\u1ecdc m\u00e1y v\u00e0 th\u1ed1ng k\u00ea.<\/p>\n<p>\u0110\u1ecbnh l\u00fd Bayes kh\u00f4ng ch\u1ec9 h\u1eefu \u00edch trong vi\u1ec7c t\u00ednh to\u00e1n x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n m\u00e0 c\u00f2n l\u00e0 n\u1ec1n t\u1ea3ng cho c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u1ed1i \u01b0u h\u00f3a trong h\u1ecdc m\u00e1y nh\u01b0 <strong>t\u1ed1i \u0111a h\u1eadu nghi\u1ec7m<\/strong> (Maximum A Posteriori &#8211; MAP) v\u00e0 c\u00e1c m\u00f4 h\u00ecnh ph\u00e2n lo\u1ea1i nh\u01b0 <strong>tr\u00ecnh ph\u00e2n lo\u1ea1i t\u1ed1i \u01b0u Bayes<\/strong> (Bayes Optimal Classifier) v\u00e0 <strong>Naive Bayes<\/strong>.<\/p>\n<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">N\u1ed9i dung ch&iacute;nh<\/p><ul class=\"toc_list\"><ul><li><ul><li><ul><li><a href=\"#Xac_Suat_Co_Ban\"><span class=\"toc_number toc_depth_4\">0.0.0.1<\/span> X\u00e1c Su\u1ea5t C\u01a1 B\u1ea3n<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li><a href=\"#Dinh_Ly_Bayes\"><span class=\"toc_number toc_depth_1\">1<\/span> \u0110\u1ecbnh L\u00fd Bayes<\/a><\/li><li><a href=\"#Y_Nghia_Cac_Thuat_Ngu_Trong_Dinh_Ly_Bayes\"><span class=\"toc_number toc_depth_1\">2<\/span> \u00dd Ngh\u0129a C\u00e1c Thu\u1eadt Ng\u1eef Trong \u0110\u1ecbnh L\u00fd Bayes<\/a><ul><li><ul><li><ul><li><a href=\"#Vi_Du_Thuc_Tien\"><span class=\"toc_number toc_depth_4\">2.0.0.1<\/span> V\u00ed D\u1ee5 Th\u1ef1c Ti\u1ec5n<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li><a href=\"#Ung_Dung_Dinh_Ly_Bayes_Trong_Hoc_May\"><span class=\"toc_number toc_depth_1\">3<\/span> \u1ee8ng D\u1ee5ng \u0110\u1ecbnh L\u00fd Bayes Trong H\u1ecdc M\u00e1y<\/a><\/li><li><a href=\"#Bo_Phan_Loai_Naive_Bayes\"><span class=\"toc_number toc_depth_1\">4<\/span> B\u1ed9 Ph\u00e2n Lo\u1ea1i Naive Bayes<\/a><ul><li><ul><li><ul><li><a href=\"#Ket_Luan\"><span class=\"toc_number toc_depth_4\">4.0.0.1<\/span> K\u1ebft Lu\u1eadn<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/div>\n<h4><span id=\"Xac_Suat_Co_Ban\">X\u00e1c Su\u1ea5t C\u01a1 B\u1ea3n<\/span><\/h4>\n<p>Tr\u01b0\u1edbc khi \u0111i s\u00e2u v\u00e0o \u0111\u1ecbnh l\u00fd Bayes, c\u1ea7n \u00f4n l\u1ea1i m\u1ed9t s\u1ed1 kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n v\u1ec1 x\u00e1c su\u1ea5t:<\/p>\n<ul>\n<li>\n<p><strong>X\u00e1c su\u1ea5t c\u1eadn bi\u00ean (Marginal Probability)<\/strong>: L\u00e0 x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t s\u1ef1 ki\u1ec7n x\u1ea3y ra m\u00e0 kh\u00f4ng quan t\u00e2m \u0111\u1ebfn c\u00e1c s\u1ef1 ki\u1ec7n kh\u00e1c, ch\u1eb3ng h\u1ea1n nh\u01b0 x\u00e1c su\u1ea5t P(A) c\u1ee7a m\u1ed9t bi\u1ebfn ng\u1eabu nhi\u00ean A.<\/p>\n<\/li>\n<li>\n<p><strong>X\u00e1c su\u1ea5t chung (Joint Probability)<\/strong>: L\u00e0 x\u00e1c su\u1ea5t c\u1ee7a hai ho\u1eb7c nhi\u1ec1u s\u1ef1 ki\u1ec7n x\u1ea3y ra \u0111\u1ed3ng th\u1eddi, ch\u1eb3ng h\u1ea1n P(A v\u00e0 B), bi\u1ec3u th\u1ecb x\u00e1c su\u1ea5t c\u1ee7a c\u1ea3 hai s\u1ef1 ki\u1ec7n A v\u00e0 B c\u00f9ng x\u1ea3y ra.<\/p>\n<\/li>\n<li>\n<p><strong>X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n (Conditional Probability)<\/strong>: L\u00e0 x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t s\u1ef1 ki\u1ec7n x\u1ea3y ra khi bi\u1ebft s\u1ef1 ki\u1ec7n kh\u00e1c \u0111\u00e3 x\u1ea3y ra, \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 P(A|B), t\u1ee9c x\u00e1c su\u1ea5t c\u1ee7a A khi bi\u1ebft r\u1eb1ng B \u0111\u00e3 x\u1ea3y ra.<\/p>\n<\/li>\n<\/ul>\n<p>X\u00e1c su\u1ea5t chung c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n theo c\u00f4ng th\u1ee9c:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(A,B)=P(A\u2223B)\u00d7P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<p>X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb x\u00e1c su\u1ea5t chung:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(A\u2223B)=P(A,B)P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Tuy nhi\u00ean, x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng \u0111\u1ed1i x\u1ee9ng, ngh\u0129a l\u00e0 P(A|B) kh\u00f4ng b\u1eb1ng P(B|A).<\/p>\n<h1><span id=\"Dinh_Ly_Bayes\">\u0110\u1ecbnh L\u00fd Bayes<\/span><\/h1>\n<p>\u0110\u1ecbnh l\u00fd Bayes cho ph\u00e9p t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n theo x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n ng\u01b0\u1ee3c l\u1ea1i. C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n c\u1ee7a \u0111\u1ecbnh l\u00fd Bayes l\u00e0:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(A\u2223B)=P(B\u2223A)\u00d7P(A)P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span>\u2223<span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li>P(A|B) l\u00e0 x\u00e1c su\u1ea5t c\u1ee7a A khi bi\u1ebft B \u0111\u00e3 x\u1ea3y ra (<strong>x\u00e1c su\u1ea5t h\u1eadu nghi\u1ec7m<\/strong>).<\/li>\n<li>P(B|A) l\u00e0 x\u00e1c su\u1ea5t c\u1ee7a B khi bi\u1ebft A \u0111\u00e3 x\u1ea3y ra (<strong>kh\u1ea3 n\u0103ng x\u1ea3y ra<\/strong>).<\/li>\n<li>P(A) l\u00e0 x\u00e1c su\u1ea5t tr\u01b0\u1edbc c\u1ee7a A (<strong>x\u00e1c su\u1ea5t ti\u00ean nghi\u1ec7m<\/strong>).<\/li>\n<li>P(B) l\u00e0 x\u00e1c su\u1ea5t c\u1ee7a B (<strong>b\u1eb1ng ch\u1ee9ng<\/strong>).<\/li>\n<\/ul>\n<p>Khi kh\u00f4ng c\u00f3 th\u00f4ng tin tr\u1ef1c ti\u1ebfp v\u1ec1 P(B), ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c m\u1edf r\u1ed9ng \u0111\u1ec3 t\u00ednh n\u00f3:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(B)=P(B\u2223A)\u00d7P(A)+P(B\u2223\u00acA)\u00d7P(\u00acA)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223\u00ac<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<p>Do \u0111\u00f3, c\u00f4ng th\u1ee9c m\u1edf r\u1ed9ng c\u1ee7a \u0111\u1ecbnh l\u00fd Bayes l\u00e0:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(A\u2223B)=P(B\u2223A)\u00d7P(A)P(B\u2223A)\u00d7P(A)+P(B\u2223\u00acA)\u00d7P(\u00acA)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span>\u2223<span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span>\u2223\u00ac<span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span>\u00ac<span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">B<\/span>\u2223<span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h1><span id=\"Y_Nghia_Cac_Thuat_Ngu_Trong_Dinh_Ly_Bayes\">\u00dd Ngh\u0129a C\u00e1c Thu\u1eadt Ng\u1eef Trong \u0110\u1ecbnh L\u00fd Bayes<\/span><\/h1>\n<p>C\u00e1c thu\u1eadt ng\u1eef trong \u0111\u1ecbnh l\u00fd Bayes th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng theo ng\u1eef c\u1ea3nh c\u1ee5 th\u1ec3:<\/p>\n<ul>\n<li><strong>X\u00e1c su\u1ea5t h\u1eadu nghi\u1ec7m (Posterior Probability)<\/strong>: X\u00e1c su\u1ea5t c\u1ee7a gi\u1ea3 thuy\u1ebft sau khi c\u00f3 th\u00f4ng tin t\u1eeb d\u1eef li\u1ec7u (P(A|B)).<\/li>\n<li><strong>X\u00e1c su\u1ea5t ti\u00ean nghi\u1ec7m (Prior Probability)<\/strong>: X\u00e1c su\u1ea5t c\u1ee7a gi\u1ea3 thuy\u1ebft tr\u01b0\u1edbc khi c\u00f3 d\u1eef li\u1ec7u (P(A)).<\/li>\n<li><strong>Kh\u1ea3 n\u0103ng x\u1ea3y ra (Likelihood)<\/strong>: X\u00e1c su\u1ea5t d\u1eef li\u1ec7u x\u1ea3y ra v\u1edbi m\u1ed9t gi\u1ea3 thuy\u1ebft nh\u1ea5t \u0111\u1ecbnh (P(B|A)).<\/li>\n<li><strong>B\u1eb1ng ch\u1ee9ng (Evidence)<\/strong>: X\u00e1c su\u1ea5t c\u1ee7a d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c quan s\u00e1t (P(B)).<\/li>\n<\/ul>\n<h4><span id=\"Vi_Du_Thuc_Tien\">V\u00ed D\u1ee5 Th\u1ef1c Ti\u1ec5n<\/span><\/h4>\n<p>M\u1ed9t v\u00ed d\u1ee5 ph\u1ed5 bi\u1ebfn l\u00e0 x\u00e1c \u0111\u1ecbnh kh\u1ea3 n\u0103ng c\u00f3 l\u1eeda khi c\u00f3 kh\u00f3i:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(L\u1eeda\u2223Kho\u02cai)=P(Kho\u02cai\u2223L\u1eeda)\u00d7P(L\u1eeda)P(Kho\u02cai)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord\">\u1eed<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">K<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">o<\/span><span class=\"accent-body\"><span class=\"mord\">\u02ca<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">K<\/span><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"accent-body\">\u02ca<\/span><\/span><\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">K<\/span><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"accent-body\">\u02ca<\/span><\/span><\/span><span class=\"mord mathnormal mtight\">i<\/span>\u2223<span class=\"mord mathnormal mtight\">L<\/span>\u1eed<span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">L<\/span>\u1eed<span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li>P(L\u1eeda|Kh\u00f3i) l\u00e0 x\u00e1c su\u1ea5t c\u00f3 l\u1eeda khi th\u1ea5y kh\u00f3i.<\/li>\n<li>P(Kh\u00f3i|L\u1eeda) l\u00e0 x\u00e1c su\u1ea5t xu\u1ea5t hi\u1ec7n kh\u00f3i khi c\u00f3 l\u1eeda.<\/li>\n<li>P(L\u1eeda) l\u00e0 x\u00e1c su\u1ea5t ti\u00ean nghi\u1ec7m c\u1ee7a vi\u1ec7c c\u00f3 l\u1eeda.<\/li>\n<li>P(Kh\u00f3i) l\u00e0 x\u00e1c su\u1ea5t c\u1ee7a vi\u1ec7c c\u00f3 kh\u00f3i.<\/li>\n<\/ul>\n<h1><span id=\"Ung_Dung_Dinh_Ly_Bayes_Trong_Hoc_May\">\u1ee8ng D\u1ee5ng \u0110\u1ecbnh L\u00fd Bayes Trong H\u1ecdc M\u00e1y<\/span><\/h1>\n<p>Trong h\u1ecdc m\u00e1y, \u0111\u1ecbnh l\u00fd Bayes \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7 gi\u1eefa d\u1eef li\u1ec7u v\u00e0 gi\u1ea3 thuy\u1ebft. M\u00f4 h\u00ecnh h\u1ecdc m\u00e1y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c xem nh\u01b0 l\u00e0 m\u1ed9t gi\u1ea3 thuy\u1ebft v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa \u0111\u1ea7u v\u00e0o v\u00e0 \u0111\u1ea7u ra. Theo \u0111\u1ecbnh l\u00fd Bayes, x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t gi\u1ea3 thuy\u1ebft (m\u00f4 h\u00ecnh) v\u1edbi d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c quan s\u00e1t c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(h\u2223D)=P(D\u2223h)\u00d7P(h)P(D)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">D<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">D<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">D<\/span>\u2223<span class=\"mord mathnormal mtight\">h<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li>P(h|D) l\u00e0 x\u00e1c su\u1ea5t h\u1eadu nghi\u1ec7m c\u1ee7a gi\u1ea3 thuy\u1ebft h d\u1ef1a tr\u00ean d\u1eef li\u1ec7u D.<\/li>\n<li>P(D|h) l\u00e0 kh\u1ea3 n\u0103ng quan s\u00e1t d\u1eef li\u1ec7u D khi gi\u1ea3 thuy\u1ebft h \u0111\u00fang.<\/li>\n<li>P(h) l\u00e0 x\u00e1c su\u1ea5t ti\u00ean nghi\u1ec7m c\u1ee7a gi\u1ea3 thuy\u1ebft h.<\/li>\n<li>P(D) l\u00e0 x\u00e1c su\u1ea5t d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c quan s\u00e1t.<\/li>\n<\/ul>\n<h1><span id=\"Bo_Phan_Loai_Naive_Bayes\">B\u1ed9 Ph\u00e2n Lo\u1ea1i Naive Bayes<\/span><\/h1>\n<p>B\u1ed9 ph\u00e2n lo\u1ea1i <strong>Naive Bayes<\/strong> l\u00e0 m\u1ed9t \u1ee9ng d\u1ee5ng quan tr\u1ecdng c\u1ee7a \u0111\u1ecbnh l\u00fd Bayes trong ph\u00e2n lo\u1ea1i. N\u00f3 gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng c\u00e1c \u0111\u1eb7c tr\u01b0ng (bi\u1ebfn \u0111\u1ea7u v\u00e0o) l\u00e0 \u0111\u1ed9c l\u1eadp v\u1edbi nhau, \u0111i\u1ec1u n\u00e0y \u0111\u01a1n gi\u1ea3n h\u00f3a r\u1ea5t nhi\u1ec1u vi\u1ec7c t\u00ednh to\u00e1n. C\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n trong Naive Bayes l\u00e0:<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\">P(L\u1edbp\u2223X1,X2,&#8230;,Xn)=P(X1\u2223L\u1edbp)\u00d7P(X2\u2223L\u1edbp)\u00d7&#8230;\u00d7P(Xn\u2223L\u1edbp)\u00d7P(L\u1edbp)P(D\u1eefli\u1ec7u)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord\">\u1edb<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">&#8230;<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">D<\/span>\u1eef<span class=\"mord mathnormal mtight\">l<\/span><span class=\"mord mathnormal mtight\">i<\/span>\u1ec7<span class=\"mord mathnormal mtight\">u<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">X<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span>\u2223<span class=\"mord mathnormal mtight\">L<\/span>\u1edb<span class=\"mord mathnormal mtight\">p<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">X<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><span class=\"vlist-s\">\u200b<\/span><\/span>\u2223<span class=\"mord mathnormal mtight\">L<\/span>\u1edb<span class=\"mord mathnormal mtight\">p<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span>&#8230;<span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">X<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span>\u2223<span class=\"mord mathnormal mtight\">L<\/span>\u1edb<span class=\"mord mathnormal mtight\">p<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">L<\/span>\u1edb<span class=\"mord mathnormal mtight\">p<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Naive Bayes \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00e1c b\u00e0i to\u00e1n ph\u00e2n lo\u1ea1i v\u0103n b\u1ea3n, ph\u00e2n t\u00edch c\u1ea3m x\u00fac, v\u00e0 nhi\u1ec1u \u1ee9ng d\u1ee5ng kh\u00e1c nh\u1edd t\u00ednh hi\u1ec7u qu\u1ea3 v\u00e0 d\u1ec5 tri\u1ec3n khai.<\/p>\n<h4><span id=\"Ket_Luan\">K\u1ebft Lu\u1eadn<\/span><\/h4>\n<p>\u0110\u1ecbnh l\u00fd Bayes cung c\u1ea5p m\u1ed9t c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd \u0111\u1ec3 t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 li\u00ean quan \u0111\u1ebfn h\u1ecdc m\u00e1y, \u0111\u1eb7c bi\u1ec7t trong c\u00e1c m\u00f4 h\u00ecnh ph\u00e2n lo\u1ea1i. M\u1eb7c d\u00f9 c\u00f3 nh\u1eefng h\u1ea1n ch\u1ebf, nh\u01b0 gi\u1ea3 \u0111\u1ecbnh v\u1ec1 t\u00ednh \u0111\u1ed9c l\u1eadp c\u1ee7a c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o trong Naive Bayes, nh\u01b0ng c\u00e1c \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ecbnh l\u00fd n\u00e0y v\u1eabn r\u1ea5t r\u1ed9ng r\u00e3i v\u00e0 hi\u1ec7u qu\u1ea3 trong nhi\u1ec1u t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ecbnh l\u00fd Bayes cung c\u1ea5p m\u1ed9t nguy\u00ean t\u1eafc c\u01a1 b\u1ea3n \u0111\u1ec3 t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n, gi\u00fap ch\u00fang ta [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[714,233],"tags":[],"class_list":["post-2655","post","type-post","status-publish","format-standard","hentry","category-hoc-may-co-ban","category-tri-tue-nhan-tao"],"_links":{"self":[{"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/posts\/2655","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/comments?post=2655"}],"version-history":[{"count":4,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/posts\/2655\/revisions"}],"predecessor-version":[{"id":4070,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/posts\/2655\/revisions\/4070"}],"wp:attachment":[{"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/media?parent=2655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/categories?post=2655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cafe2sach.com\/index.php\/wp-json\/wp\/v2\/tags?post=2655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}