Previously on CSCI 4622

More Naïve Bayes

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sha1_base64="wmyupxmvxzvbplyyugixem1wino=">aaacknicbvdlssnafj3uv42vqks3g63qbkrsjqokrtcuk1hbaekztcbt0mmdmykyqv7hjb/iqhda3pohttoa2npg4hdoudy5x4kyfdiwplppzxvtfao8qw9t7+zuvfyp7kuyc0y6ogqh7ztieeyd0pvumtkpoeg+w0jpmvzp/n4d4ykgwz1miml7abrqj2ikltssxnvqelrplj+6mlucdz5mdxgjldfjckdrvdbghkgaktrifurgptdqw0rvabo54dixc1ifbtrdyqvlhjj2ssaxq0imtcosdoq4pjirtldiqskej2heboogycfctvnbm3iifbd6ivcvkdbxf0+kybci8r2v9jeci0vvjv7ndwlpndkpdajykgdpf3kxgzkes+kgsznbkiwkimyp+ivey6rakqpexzvglp68tlqt5nntvg1v2xdfg2vwbi5bhzjgfltbdeialsdgcbyad/chpwtv2lt7nedlwjfzcp5a+/ogyd2kjw==</latexit> <latexit sha1_base64="wmyupxmvxzvbplyyugixem1wino=">aaacknicbvdlssnafj3uv42vqks3g63qbkrsjqokrtcuk1hbaekztcbt0mmdmykyqv7hjb/iqhda3pohttoa2npg4hdoudy5x4kyfdiwplppzxvtfao8qw9t7+zuvfyp7kuyc0y6ogqh7ztieeyd0pvumtkpoeg+w0jpmvzp/n4d4ykgwz1miml7abrqj2ikltssxnvqelrplj+6mlucdz5mdxgjldfjckdrvdbghkgaktrifurgptdqw0rvabo54dixc1ifbtrdyqvlhjj2ssaxq0imtcosdoq4pjirtldiqskej2heboogycfctvnbm3iifbd6ivcvkdbxf0+kybci8r2v9jeci0vvjv7ndwlpndkpdajykgdpf3kxgzkes+kgsznbkiwkimyp+ivey6rakqpexzvglp68tlqt5nntvg1v2xdfg2vwbi5bhzjgfltbdeialsdgcbyad/chpwtv2lt7nedlwjfzcp5a+/ogyd2kjw==</latexit> <latexit sha1_base64="wmyupxmvxzvbplyyugixem1wino=">aaacknicbvdlssnafj3uv42vqks3g63qbkrsjqokrtcuk1hbaekztcbt0mmdmykyqv7hjb/iqhda3pohttoa2npg4hdoudy5x4kyfdiwplppzxvtfao8qw9t7+zuvfyp7kuyc0y6ogqh7ztieeyd0pvumtkpoeg+w0jpmvzp/n4d4ykgwz1miml7abrqj2ikltssxnvqelrplj+6mlucdz5mdxgjldfjckdrvdbghkgaktrifurgptdqw0rvabo54dixc1ifbtrdyqvlhjj2ssaxq0imtcosdoq4pjirtldiqskej2heboogycfctvnbm3iifbd6ivcvkdbxf0+kybci8r2v9jeci0vvjv7ndwlpndkpdajykgdpf3kxgzkes+kgsznbkiwkimyp+ivey6rakqpexzvglp68tlqt5nntvg1v2xdfg2vwbi5bhzjgfltbdeialsdgcbyad/chpwtv2lt7nedlwjfzcp5a+/ogyd2kjw==</latexit> Probabilistic Classification: Previously on CSCI 4622 ŷ = arg max c p(y = c x) Generative Models estimate these probabilities from Bayes Rule: Throw out denominator and compare numerators: Make Naïve Conditional Independence assumption: p(y x) = Estimate likelihoods and priors from text, multiply to get scores, and make predictions p(x y)p(y) p(x) p(spam x) / p(x SPAM)p(SPAM) p(x = [buy, viagra] SP AM) =p(buy SPAM) p(viagra SPAM) _ - ˆp(term Class) = # instances of term in Class + 1 # total words in Class + V ˆp(Class) = # emails from Class + 1 # total emails in training data + C 2

Example: Consider the following binary labeled training set where labels are + and Question: What are the features? 3

Example: Consider the following binary labeled training set where labels are + and Question: What are the features? Answer: Shapes and Colors Question: What are the feature vocabs? 4

<latexit sha1_base64="r1r9sgqjlafx9jfqbmqf3iecl9c=">aaach3icbvbns8naen34wenx1aoxxvbwuerirb0vvhisykzqlllztuvszsbstsqs8lo8+fe8efarb/03bj8qvx4mpn6bywzeleph0ppgzsli0vlkamnnxd/y3nou7+xemytthakeyetfrmyafaocfcjhjtxa4khckxqet/zwhwgjenwfoxq6mrso0recozw65znq1b3v5ihcpeo450vbq6fo+kvo6nvojdoo0yegunyv3gq1w654dw8k+pf4c1ihczs75y+wl/asbovcmmpavpdij2cabzdqugfmigv8yabqtlsxgewnnz5y0eor9gg/0byu0qn6fsjnstgjolkdmcnb89ubip957qz7p51cqdrduhy2qj9jigmdpev7qgnhobkecs3srztfms042kxdg4l/++w/jdiun9x9y+nk43seronskwnyrhxyqhrkgjrjqdh5ie/khbw6j86z8+a8z1oxnpnmhvkbz/wjqr6ilg==</latexit> <latexit sha1_base64="r1r9sgqjlafx9jfqbmqf3iecl9c=">aaach3icbvbns8naen34wenx1aoxxvbwuerirb0vvhisykzqlllztuvszsbstsqs8lo8+fe8efarb/03bj8qvx4mpn6bywzeleph0ppgzsli0vlkamnnxd/y3nou7+xemytthakeyetfrmyafaocfcjhjtxa4khckxqet/zwhwgjenwfoxq6mrso0recozw65znq1b3v5ihcpeo450vbq6fo+kvo6nvojdoo0yegunyv3gq1w654dw8k+pf4c1ihczs75y+wl/asbovcmmpavpdij2cabzdqugfmigv8yabqtlsxgewnnz5y0eor9gg/0byu0qn6fsjnstgjolkdmcnb89ubip957qz7p51cqdrduhy2qj9jigmdpev7qgnhobkecs3srztfms042kxdg4l/++w/jdiun9x9y+nk43seronskwnyrhxyqhrkgjrjqdh5ie/khbw6j86z8+a8z1oxnpnmhvkbz/wjqr6ilg==</latexit> <latexit sha1_base64="r1r9sgqjlafx9jfqbmqf3iecl9c=">aaach3icbvbns8naen34wenx1aoxxvbwuerirb0vvhisykzqlllztuvszsbstsqs8lo8+fe8efarb/03bj8qvx4mpn6bywzeleph0ppgzsli0vlkamnnxd/y3nou7+xemytthakeyetfrmyafaocfcjhjtxa4khckxqet/zwhwgjenwfoxq6mrso0recozw65znq1b3v5ihcpeo450vbq6fo+kvo6nvojdoo0yegunyv3gq1w654dw8k+pf4c1ihczs75y+wl/asbovcmmpavpdij2cabzdqugfmigv8yabqtlsxgewnnz5y0eor9gg/0byu0qn6fsjnstgjolkdmcnb89ubip957qz7p51cqdrduhy2qj9jigmdpev7qgnhobkecs3srztfms042kxdg4l/++w/jdiun9x9y+nk43seronskwnyrhxyqhrkgjrjqdh5ie/khbw6j86z8+a8z1oxnpnmhvkbz/wjqr6ilg==</latexit> <latexit sha1_base64="r1r9sgqjlafx9jfqbmqf3iecl9c=">aaach3icbvbns8naen34wenx1aoxxvbwuerirb0vvhisykzqlllztuvszsbstsqs8lo8+fe8efarb/03bj8qvx4mpn6bywzeleph0ppgzsli0vlkamnnxd/y3nou7+xemytthakeyetfrmyafaocfcjhjtxa4khckxqet/zwhwgjenwfoxq6mrso0recozw65znq1b3v5ihcpeo450vbq6fo+kvo6nvojdoo0yegunyv3gq1w654dw8k+pf4c1ihczs75y+wl/asbovcmmpavpdij2cabzdqugfmigv8yabqtlsxgewnnz5y0eor9gg/0byu0qn6fsjnstgjolkdmcnb89ubip957qz7p51cqdrduhy2qj9jigmdpev7qgnhobkecs3srztfms042kxdg4l/++w/jdiun9x9y+nk43seronskwnyrhxyqhrkgjrjqdh5ie/khbw6j86z8+a8z1oxnpnmhvkbz/wjqr6ilg==</latexit> Example: Consider the following binary labeled training set where labels are + and Question: What are the features? Answer: Shapes and Colors Question: What are the feature vocabs? Answer: x s 2 {square, circle} = Vs IVSKZ x c 2 {red, blue, green} =Vc IVCI =3 5

<latexit sha1_base64="q7uuyh++v4w8b9t7hrgpnzpr8lq=">aaacrhicdva9swnbfnyl3+dx1njmmreiqrhloxacygopyftihbc395is2b07d9+j4cifs7g38x/ywkjyipuyqqmopbhm5rh7jkylmoh5j05hanpmdm5+wv1cwl5zla6tx5gk0xzqpjgjvgqzasliqknacvepbqzcczdh73jox96anikjz7gfqloxtizagjo0uqsylmtu0gwyp4nkghclwuwhzgbaayuiurtdax4lsccz5jpj+t+ufq7dcrlvlhlvbwt6m/hjuijjnlakd0gu8exbjfwyyxq+l2izzxoflzbwg8xaynipdabhacwumgy+amfat60s0xai7crir+r3jzwpy/oqtenfsgsmvah4l9fisl3fzewczggx/3qonumkcr1wsiohgapsw8k4fvavlhezzhxt8a4twz88+tep16ohvf+svjrah7cxtzbjfqkqn+yri3jctkmdchjhnsglexxunwfnzxn/ihac8c4g+qhn4xnkg6/k</latexit> <latexit sha1_base64="q7uuyh++v4w8b9t7hrgpnzpr8lq=">aaacrhicdva9swnbfnyl3+dx1njmmreiqrhloxacygopyftihbc395is2b07d9+j4cifs7g38x/ywkjyipuyqqmopbhm5rh7jkylmoh5j05hanpmdm5+wv1cwl5zla6tx5gk0xzqpjgjvgqzasliqknacvepbqzcczdh73jox96anikjz7gfqloxtizagjo0uqsylmtu0gwyp4nkghclwuwhzgbaayuiurtdax4lsccz5jpj+t+ufq7dcrlvlhlvbwt6m/hjuijjnlakd0gu8exbjfwyyxq+l2izzxoflzbwg8xaynipdabhacwumgy+amfat60s0xai7crir+r3jzwpy/oqtenfsgsmvah4l9fisl3fzewczggx/3qonumkcr1wsiohgapsw8k4fvavlhezzhxt8a4twz88+tep16ohvf+svjrah7cxtzbjfqkqn+yri3jctkmdchjhnsglexxunwfnzxn/ihac8c4g+qhn4xnkg6/k</latexit> <latexit sha1_base64="q7uuyh++v4w8b9t7hrgpnzpr8lq=">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</latexit> <latexit sha1_base64="q7uuyh++v4w8b9t7hrgpnzpr8lq=">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</latexit> <latexit sha1_base64="onu36eniyshcfsjtyxwqp/srufw=">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</latexit> <latexit sha1_base64="onu36eniyshcfsjtyxwqp/srufw=">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</latexit> <latexit sha1_base64="onu36eniyshcfsjtyxwqp/srufw=">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</latexit> <latexit sha1_base64="onu36eniyshcfsjtyxwqp/srufw=">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</latexit> Question: How would we classify? Need to compute p(+ x = [blue, square]) / ˆp(blue +) ˆp(square +) ˆp(+) = In. F. Fz = 0.179 6

<latexit sha1_base64="bnvx6ss2rjzyqn5parub3nk01wu=">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</latexit> <latexit sha1_base64="bnvx6ss2rjzyqn5parub3nk01wu=">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</latexit> <latexit sha1_base64="bnvx6ss2rjzyqn5parub3nk01wu=">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</latexit> <latexit sha1_base64="bnvx6ss2rjzyqn5parub3nk01wu=">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</latexit> <latexit sha1_base64="jnt8rt0hwskkgxuk5gqgjapct28=">aaacixicbvbnswmxfmz6wetx1aoxycsoann1oh6eghepclyl3avk07cathzj8lyss3+lf/+kfw8q3sq/y1p70opayjh5j5ezweth0fc/vinjqemz2djcex5hcwm5srj6ybpccgjytgamftmluqtqrieswtoau7gey/jmeobf3ogxikvpsachuuwqfyngdj3uqrzwamw9tutdjbq0cooe3vfpew2hcpdovbhlhhaovc2zgx60tuntmo0zrdu6lapf94egf0kwiluywmmn8h52m54rsjflzm078dvgbtmouir+ocwtamzv2bw0hu2zahsvw4h9uumulk0y416kdkj+3ciysranyjepgf7bcw8g/ue1c0wookkkokdi+fehjjfuzrz0rbvcaefzc4rxi9xfkb9mhnf0rzzdccf45l+kuvc/radne9xgwainelkng2slbgsfnmgjosvnwskdesiv5nv79j69n+/9e3tcg+2skv/wpr8a8oohsq==</latexit> <latexit sha1_base64="jnt8rt0hwskkgxuk5gqgjapct28=">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</latexit> <latexit sha1_base64="jnt8rt0hwskkgxuk5gqgjapct28=">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</latexit> <latexit sha1_base64="jnt8rt0hwskkgxuk5gqgjapct28=">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</latexit> Question: How would we classify? Need to compute p( x = [blue, square]) / ˆp(blue ) ˆp(square ) ˆp( )= I. 0.167. = 7

<latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> Question: How would we classify? So we have: p(+ x = [blue, square]) / 0.179 p( x = [blue, square]) / 0.167 > positive So we predict 8

<latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">aaacj3icbvdlsgmxfm34tr6qlt0ew0fby4wlhwtrconswarqguomvaohyuxm7ohl6oe48vfcikjo0j8xrv34oha4nhmvn+fewgqlvv/udq2pji6nt0ywpqznzufk8wtnnssnhzrpzgyuymzbihtqkfdchtbavczhpg4f9vzzgzbwzokpdjreil2mihgcozoa5f1qtarxn2ioriswyzzq2y7do40q4rankmkzwzq11zkz0i3wakhnpjgjfi3y2qbvarnc8wt+h/qvcqakqgy4bpafwlbgcwupcsmsbqs+xqhgbgwx0c2fuqxnejtdqsprlcmwudep2qurtmnrjdpupuj76vengilroyp2k4rhlf3t9ct/veaoyu5uiftnccn/optkkrqkvdzosxjgkduomg6e+yvlv8wwjq7bkish+b35l6lv1nzrwclm5wbn0myewsllzjuezjsckcnytoqekzvyqj7ji3fvpxqv3tvx6ja32fkkp+b9fal2tkmj</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> Question: How would we classify? So we have: p(+ x = [blue, square]) / 0.179 p( x = [blue, square]) / 0.167 So we predict positive. Question: Is this what you would have predicted for? 9

<latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="hgroqerwhl44iqed9g2u4xoubwg=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> <latexit sha1_base64="51mpu9vume9rchimnntejuawguc=">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</latexit> Question: How would we classify? So we have: p(+ x = [blue, square]) / 0.179 p( x = [blue, square]) / 0.167 So we predict positive. Question: Is this what you would have predicted for? Observation: If we had only looked at the class-likelihood, it would have indicated negative, but there are several more positive examples, so the prior pushes the prediction to positive 10

Question: How would we classify? First: Do you see any difficulties with.? 11

<latexit sha1_base64="ldfrqogmsr+dqldwryf3xwl9k0k=">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</latexit> <latexit sha1_base64="ldfrqogmsr+dqldwryf3xwl9k0k=">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</latexit> <latexit sha1_base64="ldfrqogmsr+dqldwryf3xwl9k0k=">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</latexit> <latexit sha1_base64="ldfrqogmsr+dqldwryf3xwl9k0k=">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</latexit> <latexit sha1_base64="gypcozsswtrnppqi1clnxoelpjy=">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</latexit> <latexit sha1_base64="gypcozsswtrnppqi1clnxoelpjy=">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</latexit> <latexit sha1_base64="gypcozsswtrnppqi1clnxoelpjy=">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</latexit> <latexit sha1_base64="gypcozsswtrnppqi1clnxoelpjy=">aaacinicbvbntxsxfprckrbocexixwqclkpvtjslaaksui8cqsinunyvez23wcl2wvzbrltkf+hcx+hcgqinjh4mzsehjr3j0mjmpdszqzhcyri+bevlh1y+rq6tvzy2p33eqm5/+e3ywnlo8fzm9jxldqtq0egbes6nbazscd308tfe716bdslxzzgykcg21citnkgx+txder1igt9prmsalnga0esx/ul7mci1wluolyd+qbmwxmi4+uzjy3odoa3x+9va2aynoiskmpmameokx32kbzkvfgjkkjnxi0kdscksisnllbhwybi/zepoeaqzapeu04xjuuevac1y649golx/3iizcm6kuj+pgf64995e/j/xkzbrj6xqpkdqfpzqvkjqm04kownhgamceck4ff6vlf8wyzj6wiu+hoh95exsatupmtfpq3bunrexrnbjv9igedknr+synjao4esg3jeh8ie4de6dx+b5nrouzhd2yd8ixt8alu+iaw==</latexit> Question: How would we classify? Need to compute p(+ x = [green, circle]) / ˆp(green +) ˆp(circle +) ˆp(+) = # 7+1 tdfz I a a - one %DP - THREE colors two / = SHAPES To. 5g. Fy = 0.032 12

<latexit sha1_base64="qpwrgsnjgzuhl/fnoo1dvpiuzge=">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</latexit> <latexit sha1_base64="qpwrgsnjgzuhl/fnoo1dvpiuzge=">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</latexit> <latexit sha1_base64="qpwrgsnjgzuhl/fnoo1dvpiuzge=">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</latexit> <latexit sha1_base64="qpwrgsnjgzuhl/fnoo1dvpiuzge=">aaacrxicdva9sytbfj3146mr7xm1tblmbc1e2e2jfojgy6lgvmguyxb2jhmcmv1m7ophya+zsbbzj9hyqnjqjkbqqacgduecy71zklwki0fw701nz8z+mztf8bex/v5brqysntmsmbyapjozuuiybsk0nfgghivcafojhppk8ndon1+bssltp9jpivasq0vhcizoalfiws2pegzlflavivyjuwxxaogbjzri6f9tgve0qzoz4sjwcb+lnldv12rtsjwobypq7yqckyoz47hduyvsjbcknhljrg2fqy5xyqyk4ty/kizkjf+ylrqc1uybjctrdqo66zsudjljnky6uj9plexz21ejsyqgptvpdcwfvfabnd24fdovedt/wnqpjmwmdjulqtdaufydydwidyvlpwyyr9e870oij7/8ntqb9b16enkohuyo25gn62sdbjgq7jadcksosznwckmeybn59m69r+/fe/2itnnjmtxybd7boyq7sd4=</latexit> <latexit sha1_base64="hgfbeif+mooaynihmm/c9zae62g=">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</latexit> <latexit sha1_base64="hgfbeif+mooaynihmm/c9zae62g=">aaacinicbvbntxsxfprckrbocexixwqclepttjslaaksui8cqsinunyvez23wcl2wvzbrltkf+hcx+hcgqinjh4mzsehjr3j0mjmpdszqzhcyri+bevlh1y+rq6tvzy2p33eqm5/+e3ywnlo8fzm9jxldqtq0egbes6nbazscd308tfe716bdslxzzgykcg21citnkgx+txder1igj9ormsalnga0esx/ul7mci1wluolyd+trmwxmi4+uzjy3odoa3x+9va2aynoiskmpmameokx32kbzkvfgjkkjnxi0kdscksisnllbhwybi/zepoeaqzapeu04xjuuevac1y649golx/3iizcm6kuj+pgf64995e/j/xkzbrj6xqpkdqfpzqvkjqm04kownhgamceck4ff6vlf8wyzj6wiu+hoh95exsatupmtfpq3bunrexrnbjv9igedknr+synjao4esg3jeh8ie4de6dx+b5nrouzhd2yd8ixt8aml2ibq==</latexit> <latexit sha1_base64="hgfbeif+mooaynihmm/c9zae62g=">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</latexit> <latexit sha1_base64="hgfbeif+mooaynihmm/c9zae62g=">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</latexit> Question: How would we classify? Need to compute p( x = [green, circle]) / ˆp(green ) ˆp(circle ) ˆp( )= 5. 5. Fee = Zg. Fy = 023 13

<latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">aaacj3icbvbnsynbfozx2+i6uy9eghpbhd0wkz2ob1hw4lhbrejmcd2dn7gxu6fpfiogit/hi3/fi4ikhv0ndmiofmxbq1h1hq+ruiofwzb8csymp6znzufmkwulp5z+vpdx/rm8sbxapje5puuzayk0tfcghdnjgaluwml6ctd0ty/bophre+wbsbtrazejztblnepevv4xm39oresxlnga0asb3axtgoekrsp7fkd/plxylmgq/kkxsbnbnianspm3xu9ua56nql+taexqziyjtvu+7ua8ukcrs+zcowonjiwzkiyxknhhwdb+wxrq9lqzbs4pr0ehdmmrxzrl1j+ndkr+3cizcq6vuj+pgj67r95q/j/xljdbtkqhtygg+fuhrjdubx22rrvcakfz94rxk/xfkt9nlnh03vz8cdhxyn9jq9nyauthzdr+9rinobjg1skmicgw2seh5ii0ccfx5jy8kmfgjrglnoln99gjylyzsj4heh0dkbujkg==</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> Question: How would we classify? So we have: p(+ x = [green, circle]) / 0.032 p( x = [green, circle]) / 0.023 > positive So we predict 14

<latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="yl5aavi97qbpumaplutvqserrtc=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">aaacj3icbvbnsynbfozx2+i6uy9eghpbhd0wkz2ob1hw4lhbrejmcd2dn7gxu6fpfiogit/hi3/fi4ikhv0ndmiofmxbq1h1hq+ruiofwzb8csymp6znzufmkwulp5z+vpdx/rm8sbxapje5puuzayk0tfcghdnjgaluwml6ctd0ty/bophre+wbsbtrazejztblnepevv4xm39oresxlnga0asb3axtgoekrsp7fkd/plxylmgq/kkxsbnbnianspm3xu9ua56nql+taexqziyjtvu+7ua8ukcrs+zcowonjiwzkiyxknhhwdb+wxrq9lqzbs4pr0ehdmmrxzrl1j+ndkr+3cizcq6vuj+pgj67r95q/j/xljdbtkqhtygg+fuhrjdubx22rrvcakfz94rxk/xfkt9nlnh03vz8cdhxyn9jq9nyauthzdr+9rinobjg1skmicgw2seh5ii0ccfx5jy8kmfgjrglnoln99gjylyzsj4heh0dkbujkg==</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> <latexit sha1_base64="koo5m31glgb3etzpclprfx+wdna=">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</latexit> Question: How would we classify? So we have: p(+ x = [green, circle]) / 0.032 p( x = [green, circle]) / 0.023 So we predict positive. 15

Question: How would we classify? Uhhh ) = 0 = 10.EE putt ' 7+2+ 10 ' 17+2+1 4- pcunkslt PC LTH = ) 3+1 - yes 16

Question: How would we classify? Orange doesn t appear in training set Add UNKCOLOR feature value While we re at it, add UNKSHAPE feature too 17

<latexit sha1_base64="mr8yynwagn9eaukecxfxdnxvafa=">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</latexit> <latexit sha1_base64="mr8yynwagn9eaukecxfxdnxvafa=">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</latexit> <latexit sha1_base64="mr8yynwagn9eaukecxfxdnxvafa=">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</latexit> <latexit sha1_base64="mr8yynwagn9eaukecxfxdnxvafa=">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</latexit> <latexit sha1_base64="xt5gu7v3g8x3vvugg28srhs9kz0=">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</latexit> <latexit sha1_base64="xt5gu7v3g8x3vvugg28srhs9kz0=">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</latexit> <latexit sha1_base64="xt5gu7v3g8x3vvugg28srhs9kz0=">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</latexit> <latexit sha1_base64="xt5gu7v3g8x3vvugg28srhs9kz0=">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</latexit> UNKCOLOR ) Question: How would we classify? UNKSHAPE Need p(+ x = [orange, square]) / ˆp(orange +) ˆp(square +) ˆp(+) 0+1 3+1 # 7+-3 f z = 0.021 Vga { Cir, sqr, on KSAAPE } Vc= RED, green, BUUE, Unkcolor 18

<latexit sha1_base64="dmo+vz6oyiipc6/w+wmhmrun3bm=">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</latexit> <latexit sha1_base64="dmo+vz6oyiipc6/w+wmhmrun3bm=">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</latexit> <latexit sha1_base64="dmo+vz6oyiipc6/w+wmhmrun3bm=">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</latexit> <latexit sha1_base64="dmo+vz6oyiipc6/w+wmhmrun3bm=">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</latexit> <latexit sha1_base64="xpw3vykl5mjbgbqpzgzozhrzxhg=">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</latexit> <latexit sha1_base64="xpw3vykl5mjbgbqpzgzozhrzxhg=">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</latexit> <latexit sha1_base64="xpw3vykl5mjbgbqpzgzozhrzxhg=">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</latexit> <latexit sha1_base64="xpw3vykl5mjbgbqpzgzozhrzxhg=">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</latexit> Question: How would we classify? Need p( x = [orange, square]) / ˆp(orange ) ˆp(square ) ˆp( ) OH -5+4 5 H Ft5 tz. - tg. 63. hf, = 0.036 19

<latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">aaackxicbvdlshxbfk02juokxolzuimccriiq7ecj4wgumlswvfhuhmqa26phfwy6nzwaoz7svfxsnhhi1t/xjpxfr4ofbzouzdb5+rwco9xfb9nfzj++glmdq72+cv814x6t8vjb0rhoc2nno40zx6k0nbggrjorqomcgkn+fn+yd/5a84lo49wycftrk9fitjdihxre81mza6s0lsjhq3svkcxq7pdoyncjtpvgcd0h35rf1eyb8psj02tmxynjvvx+gztnrv1rqbj0lckmzagmecgw79oe4axcjryybzvjlhfrgiobzcwrkwlb8v4oetdj1dnfpisgkcd0h9b6dhcupa00rh6fkniyvubysokynjmx3sj8t2vu2kxlvvc2xjb86ddrslpsdrqjfaea45yeajjtos/un7ghomy2q2feplxkd+s9lpru5ucrjv2tyztzjilskxwsei2ys75tq5im3dyl/wjn+q2uoquo7vo/9povdtz+u5eihp4bkk/o+w=</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">aaackxicbvdlshxbfk02juokxolzuimccriiq7ecj4wgumlswvfhuhmqa26phfwy6nzwaoz7svfxsnhhi1t/xjpxfr4ofbzouzdb5+rwco9xfb9nfzj++glmdq72+cv814x6t8vjb0rhoc2nno40zx6k0nbggrjorqomcgkn+fn+yd/5a84lo49wycftrk9fitjdihxre81mza6s0lsjhq3svkcxq7pdoyncjtpvgcd0h35rf1eyb8psj02tmxynjvvx+gztnrv1rqbj0lckmzagmecgw79oe4axcjryybzvjlhfrgiobzcwrkwlb8v4oetdj1dnfpisgkcd0h9b6dhcupa00rh6fkniyvubysokynjmx3sj8t2vu2kxlvvc2xjb86ddrslpsdrqjfaea45yeajjtos/un7ghomy2q2feplxkd+s9lpru5ucrjv2tyztzjilskxwsei2ys75tq5im3dyl/wjn+q2uoquo7vo/9povdtz+u5eihp4bkk/o+w=</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> Question: How would we classify? So we have: p(+ x = [orange, square]) / 0.021 p( x = [orange, square]) / 0.036 < negative So we predict 20

<latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="q+zqik11tyfav50pg/tcqe9ws8y=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> <latexit sha1_base64="vlzmpw1vkvpkb4jiohfollmdube=">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</latexit> Question: How would we classify? So we have: p(+ x = [orange, square]) / 0.021 p( x = [orange, square]) / 0.036 So we predict negative. 21

<latexit sha1_base64="ebjj3mq6/wmor/3y02ufm/emn5a=">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</latexit> <latexit sha1_base64="ebjj3mq6/wmor/3y02ufm/emn5a=">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</latexit> <latexit sha1_base64="ebjj3mq6/wmor/3y02ufm/emn5a=">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</latexit> <latexit sha1_base64="ebjj3mq6/wmor/3y02ufm/emn5a=">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</latexit> <latexit sha1_base64="q5il4z+u6bm+ztpz1pxtjtbetoq=">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</latexit> <latexit 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sha1_base64="ezxhi2prtfy0vxyy/yealvhfblu=">aaab83icbvbnt8jaej3if9yv1koxjdtee2m5+hei8eireysk0jdtsoun223d3rjjw+/w4kgnv/+mn/+nc/sg4esmexlvjjpzwpqzpv332yqtrw9sbpw37z3dvf2dyuhrg0oysahpep7idogv5uxqxzpnatuvfmchp61wddpzw2mqfuvevz6knijxqlcieaynfdionxfdcd1nbcfpvapuzz0drrkvifuo0oxvvrr9hgqxfzpwrfthc1md5fhqrjid2t1m0rster7qjqecx1qf+fzoktozsh9fitqlnjqrvydyhcs1iuptgwm9vmvetpzp62q6ugxyjtjmu0ewi6kmi52gwqkozyqlmk8mwuqycysiqywx0syn24tglb+8svx67arm3dwrjesijtkcwcmcgwcx0ibbaiipbb7hgv7hzrpbl9a79bfolvnfzdh8gfx5a3nnkb4=</latexit> <latexit sha1_base64="ezxhi2prtfy0vxyy/yealvhfblu=">aaab83icbvbnt8jaej3if9yv1koxjdtee2m5+hei8eireysk0jdtsoun223d3rjjw+/w4kgnv/+mn/+nc/sg4esmexlvjjpzwpqzpv332yqtrw9sbpw37z3dvf2dyuhrg0oysahpep7idogv5uxqxzpnatuvfmchp61wddpzw2mqfuvevz6knijxqlcieaynfdionxfdcd1nbcfpvapuzz0drrkvifuo0oxvvrr9hgqxfzpwrfthc1md5fhqrjid2t1m0rster7qjqecx1qf+fzoktozsh9fitqlnjqrvydyhcs1iuptgwm9vmvetpzp62q6ugxyjtjmu0ewi6kmi52gwqkozyqlmk8mwuqycysiqywx0syn24tglb+8svx67arm3dwrjesijtkcwcmcgwcx0ibbaiipbb7hgv7hzrpbl9a79bfolvnfzdh8gfx5a3nnkb4=</latexit> Naïve Bayes o The Naïve Bayes classifier is a probabilistic classifier o We compute the posterior score of message belonging to class c as p(y = c x) / ˆp(c) Y k ˆp(x k c) <latexit sha1_base64="q5il4z+u6bm+ztpz1pxtjtbetoq=">aaacm3icbvdnssnagnzuvxr/qh69llzcvzskf+tbkhgrvfqwttcustls2qwbznndsevoq3nxqbyi4ehfq+/gpg2irqmlw8w3fpunxxmvyrjejmlk6tr6rnht3nre2d0r7r/cytgrmdg4zrhoeegsripikkoy6xbbuogx0vzgl5nfvidc0ji6vrnoeieardsggckt9uvxlyrjqxn4atf0q+rd1pucoj6eqpelmksyukokuj6t4rnk90c/0jjjwuh7zqxsl5wtmjudxcz2tsogr6tfenl9gcchirrmsmqubxhvs5fqfdmynd1eeo7wca1iv9mihut20tnru3iifr8gsdavuncm/k6kkjryenp6mkrqkbe9tpzp6yyqaprsgvfekqjpfwujg7qlrehou0gwyhnnebzu/xxiiriik92zquuwf09ejk69dl6zb+rlzinvowiowdgoahucgsa4ai3gaawewdn4a+/go/fqfbif89gckwcowr8yx98gcqem</latexit> = = = o Predicted class is the one with the highest posterior score ŷ = arg max c p(y = c x) = arg max c ˆp(c) Y = - k ˆp(x k c) 22

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sha1_base64="/x8avx4vjdge0zgaxzlibha1mie=">aaacc3icbzdlsgmxfiyz9vbhw9wlm2bhabhktddeqci4cvnbsyv2kjk0bumzyzbkhdl0adz4km5cqlj1bdz5nqadwwjrd4gp/5zdyfndmfglxffbkqysrq1vfdftre2d3b3s/sg9eonexmeccdkokskmcujrqhlpx5kgkgskfy6vz/xwa5gkcn6njzejijtkdeax0sbqlcqoy3ezgfzqwivxmmmqpm3ielbjmc635s4fl8hloqxynxulr25f4cqixgoglop4bqydfelnmsntu5soeim8rkpsmchrrfsqzo+zwhpj9ofaspo4hnp390skiqumuwg6i6rhare2m/+rdri9oa9syunee46zryoeqs3glbnyp5jgzsygejbu/bxieziia5ofbulwfk9ebr9eu6h5t/vy4zjpowiowdgoaa+cgqa4au3gawwewtn4bw/wk/vivvsfwwvbymcowr9znz866zbs</latexit> <latexit sha1_base64="/x8avx4vjdge0zgaxzlibha1mie=">aaacc3icbzdlsgmxfiyz9vbhw9wlm2bhabhktddeqci4cvnbsyv2kjk0bumzyzbkhdl0adz4km5cqlj1bdz5nqadwwjrd4gp/5zdyfndmfglxffbkqysrq1vfdftre2d3b3s/sg9eonexmeccdkokskmcujrqhlpx5kgkgskfy6vz/xwa5gkcn6njzejijtkdeax0sbqlcqoy3ezgfzqwivxmmmqpm3ielbjmc635s4fl8hloqxynxulr25f4cqixgoglop4bqydfelnmsntu5soeim8rkpsmchrrfsqzo+zwhpj9ofaspo4hnp390skiqumuwg6i6rhare2m/+rdri9oa9syunee46zryoeqs3glbnyp5jgzsygejbu/bxieziia5ofbulwfk9ebr9eu6h5t/vy4zjpowiowdgoaa+cgqa4au3gawwewtn4bw/wk/vivvsfwwvbymcowr9znz866zbs</latexit> Numerical Hiccup For long messages, have to multiply a lot of probabilities together ŷ = arg max c ˆp(c) Y k ˆp(x k c) F Probabilities are numbers less than 1. If you multiply enough of them, you could get underflow Fix: Compute and store the log of the term-class score estimates Recall: The log of a product is the sum of the logs: log(ab) = log(a) + log(b) Predicted class becomes: ŷ = arg max c log ˆp(c)+ X k log ˆp(x k c) 23

Training and Prediction Complexity Question: How much does Naïve Bayes cost to train? 24

Training and Prediction Complexity Question: How much does Naïve Bayes cost to train? Answer: It s linear in the number of features and number of training examples! o o Single pass over training data to do frequency counts Another pass over recorded frequencies to normalize and take logs Question: How much does Naïve Bayes cost to make a prediction? 25

Training and Prediction Complexity Question: How much does Naïve Bayes cost to train? Answer: It s linear in the number of features and number of training examples! o o Single pass over training data to do frequency counts Another pass over recorded frequencies to normalize and take logs Question: How much does Naïve Bayes cost to make a prediction? Answer: It s linear in the number of features present in the query point! 26

Naïve Bayes with Continuous Features Example: Predict Iris species from sepal length and sepal width. Features are now continuous values instead of frequencies What do we do?! 27

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sha1_base64="vbgbeqdtvmqoc1u4ryj2/fwkxhg=">aaacbnicbzbps8mwgmzt/876r+prkoaqzmtod3eehiexjxosm2ylpgm6havpsvjxjn28+fw8efdx6mfw5rcx23rqzrcsfjzp+5k8t5gxkpxjfbtlyyura+uldxnza3tn19rbv5vpljdxcmps0q6rjixy4imqgglngqakzkqvdi4nfuueceltfqoggfet1om0phgplqxwkw2bwauddoaffiddhebwtim+1zdp24fvdqrotoaiuawuqvhnwprqrinoe8ivzkjkjutkyh8hoshmzgx2c0kyhaeorzoaouqi9eftpcbwrcsrjfohd1dwqv6egkfeymes6s4eqb6c9ybif14nv3hdh1ge5ypwphsozhlukzyeaimqcfzsqafhqfvfie4jgbds0zk6bhd+5uxwatxzqntdkzfqrrolcaioqqw44aw0wbvoag9g8aiewst4m56mf+pd+ji1lhnfzah4u8bnd1uflkc=</latexit> <latexit sha1_base64="vbgbeqdtvmqoc1u4ryj2/fwkxhg=">aaacbnicbzbps8mwgmzt/876r+prkoaqzmtod3eehiexjxosm2ylpgm6havpsvjxjn28+fw8efdx6mfw5rcx23rqzrcsfjzp+5k8t5gxkpxjfbtlyyura+uldxnza3tn19rbv5vpljdxcmps0q6rjixy4imqgglngqakzkqvdi4nfuueceltfqoggfet1om0phgplqxwkw2bwauddoaffiddhebwtim+1zdp24fvdqrotoaiuawuqvhnwprqrinoe8ivzkjkjutkyh8hoshmzgx2c0kyhaeorzoaouqi9eftpcbwrcsrjfohd1dwqv6egkfeymes6s4eqb6c9ybif14nv3hdh1ge5ypwphsozhlukzyeaimqcfzsqafhqfvfie4jgbds0zk6bhd+5uxwatxzqntdkzfqrrolcaioqqw44aw0wbvoag9g8aiewst4m56mf+pd+ji1lhnfzah4u8bnd1uflkc=</latexit> <latexit sha1_base64="vbgbeqdtvmqoc1u4ryj2/fwkxhg=">aaacbnicbzbps8mwgmzt/876r+prkoaqzmtod3eehiexjxosm2ylpgm6havpsvjxjn28+fw8efdx6mfw5rcx23rqzrcsfjzp+5k8t5gxkpxjfbtlyyura+uldxnza3tn19rbv5vpljdxcmps0q6rjixy4imqgglngqakzkqvdi4nfuueceltfqoggfet1om0phgplqxwkw2bwauddoaffiddhebwtim+1zdp24fvdqrotoaiuawuqvhnwprqrinoe8ivzkjkjutkyh8hoshmzgx2c0kyhaeorzoaouqi9eftpcbwrcsrjfohd1dwqv6egkfeymes6s4eqb6c9ybif14nv3hdh1ge5ypwphsozhlukzyeaimqcfzsqafhqfvfie4jgbds0zk6bhd+5uxwatxzqntdkzfqrrolcaioqqw44aw0wbvoag9g8aiewst4m56mf+pd+ji1lhnfzah4u8bnd1uflkc=</latexit> Gaussian Naïve Bayes Idea: Assume features follow a normal dist o Priors don t change. ˆp(y = c) = 1 n nx I(y i = c) i=1 o Likelihoods are computed from Gaussian pdf p(x k = x Y = c) = s.net# " # 2 1 1 x µkc p exp 2 kc 2 kc 29

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sha1_base64="vbgbeqdtvmqoc1u4ryj2/fwkxhg=">aaacbnicbzbps8mwgmzt/876r+prkoaqzmtod3eehiexjxosm2ylpgm6havpsvjxjn28+fw8efdx6mfw5rcx23rqzrcsfjzp+5k8t5gxkpxjfbtlyyura+uldxnza3tn19rbv5vpljdxcmps0q6rjixy4imqgglngqakzkqvdi4nfuueceltfqoggfet1om0phgplqxwkw2bwauddoaffiddhebwtim+1zdp24fvdqrotoaiuawuqvhnwprqrinoe8ivzkjkjutkyh8hoshmzgx2c0kyhaeorzoaouqi9eftpcbwrcsrjfohd1dwqv6egkfeymes6s4eqb6c9ybif14nv3hdh1ge5ypwphsozhlukzyeaimqcfzsqafhqfvfie4jgbds0zk6bhd+5uxwatxzqntdkzfqrrolcaioqqw44aw0wbvoag9g8aiewst4m56mf+pd+ji1lhnfzah4u8bnd1uflkc=</latexit> <latexit sha1_base64="vbgbeqdtvmqoc1u4ryj2/fwkxhg=">aaacbnicbzbps8mwgmzt/876r+prkoaqzmtod3eehiexjxosm2ylpgm6havpsvjxjn28+fw8efdx6mfw5rcx23rqzrcsfjzp+5k8t5gxkpxjfbtlyyura+uldxnza3tn19rbv5vpljdxcmps0q6rjixy4imqgglngqakzkqvdi4nfuueceltfqoggfet1om0phgplqxwkw2bwauddoaffiddhebwtim+1zdp24fvdqrotoaiuawuqvhnwprqrinoe8ivzkjkjutkyh8hoshmzgx2c0kyhaeorzoaouqi9eftpcbwrcsrjfohd1dwqv6egkfeymes6s4eqb6c9ybif14nv3hdh1ge5ypwphsozhlukzyeaimqcfzsqafhqfvfie4jgbds0zk6bhd+5uxwatxzqntdkzfqrrolcaioqqw44aw0wbvoag9g8aiewst4m56mf+pd+ji1lhnfzah4u8bnd1uflkc=</latexit> Gaussian Naïve Bayes o o Likelihoods are computed from Gaussian pdf p(x k = x Y = c) = " 1 1 x p exp 2 kc 2 µkc Get MLE estimates of params from training set 2 kc = µ kc = 1 P n i=1 I(y i = c) 1 P n i=1 I(y i = c) kc 2 # nx x ik I(y i = c) i=1 = = nx (x ik µ kc ) 2 I(y i = c) i=1-1 I µ BW: TpzuE I I I 11111111 * 30