more naïve bayes

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More Naïve Bayes

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Page 1: More Naïve Bayes

More Naïve Bayes

Page 2: More Naïve Bayes

Previously on CSCI 4622

2

Probabilistic Classification:

Generative Models estimate these probabilities from Bayes Rule:

Throw out denominator and compare numerators:

Make Naïve Conditional Independence assumption:

Estimate likelihoods and priors from text, multiply to get scores, and make predictions

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p(y | x) = p(x | y)p(y)p(x)

<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><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>

p(SPAM | x) / p(x | SPAM)p(SPAM) =<latexit sha1_base64="z1+SUi6fhS2MHjo8Pp0XyqEzAJ0=">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</latexit><latexit sha1_base64="z1+SUi6fhS2MHjo8Pp0XyqEzAJ0=">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</latexit><latexit sha1_base64="z1+SUi6fhS2MHjo8Pp0XyqEzAJ0=">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</latexit><latexit sha1_base64="z1+SUi6fhS2MHjo8Pp0XyqEzAJ0=">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</latexit>

p(x = [buy, viagra] | SPAM) = p(buy | SPAM) · p(viagra | SPAM)<latexit sha1_base64="w/IPFRjtij8HzK+fWd1aYegCglc=">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</latexit><latexit sha1_base64="w/IPFRjtij8HzK+fWd1aYegCglc=">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</latexit><latexit sha1_base64="w/IPFRjtij8HzK+fWd1aYegCglc=">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</latexit><latexit sha1_base64="w/IPFRjtij8HzK+fWd1aYegCglc=">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</latexit>

p(term | Class) = # instances of term in Class + 1

# total words in Class + |V |<latexit sha1_base64="UlKOL6lMZOwaJA0cPViHg3O768c=">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</latexit><latexit sha1_base64="UlKOL6lMZOwaJA0cPViHg3O768c=">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</latexit><latexit sha1_base64="UlKOL6lMZOwaJA0cPViHg3O768c=">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</latexit><latexit sha1_base64="UlKOL6lMZOwaJA0cPViHg3O768c=">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</latexit>

p(Class) =# emails from Class + 1

# total emails in training data + |C|<latexit sha1_base64="oy4aLWTPGqzGRSuG4pbOD2CywzY=">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</latexit><latexit sha1_base64="oy4aLWTPGqzGRSuG4pbOD2CywzY=">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</latexit><latexit sha1_base64="oy4aLWTPGqzGRSuG4pbOD2CywzY=">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</latexit><latexit sha1_base64="oy4aLWTPGqzGRSuG4pbOD2CywzY=">AAACYnicbVFBb9MwGHUCjJEBy9gRDhYt0hBSlezCdkCa1AvHIVE2qamqL86X1prtRPYXRJflT3LjxoX/gdN20th4kqWn996nz37OayUdJcmvIHz0+MnO091n0d7zFy/344NX31zVWIETUanKXubgUEmDE5Kk8LK2CDpXeJFfjXv/4jtaJyvzlVY1zjQsjCylAPLSPL4eDqNsCdTW3VFG+IOsbscKnOve8088K0oLor01sgFHDVI5XtpK802Of+BpdzdCFYG6DUrDyYI00ix4AQR9/GZ800XD4TweJKNkDf6QpFsyYFucz+OfWVGJRqMh0a+epklNsxYsSaGwi7LGYQ3iChY49dSARjdr1x11/J1XCl5W1h9DfK3enWhBO7fSuU9qoKW77/Xi/7xpQ+XJrJWmbgiN2CwqG+Vr4H3hvJAWBamVJyCs9HflYgm+VvLfEvkS0vtPfkgmx6PTUfrleHB2sm1jl71mb9kRS9lHdsY+s3M2YYL9DnaC/SAO/oR74UF4uImGwXbmkP2D8M1f9/+1rA==</latexit>

_

÷-

Page 3: More Naïve Bayes

Slightly Different Warm-Up Exercise

3

Example: Consider the following binary labeled training set where labels are + and –

Question: What are the features?

Page 4: More Naïve Bayes

Slightly Different Warm-Up Exercise

4

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?

Page 5: More Naïve Bayes

Slightly Different Warm-Up Exercise

5

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:

xc 2 {red, blue, green}<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>

xs 2 {square, circle}<latexit sha1_base64="2uS7mrXuLebyvkwy5bUs1tz6Bms=">AAACHXicbVBNS8NAEN34bfyKevSy2AoepCQFsd4ELx4VrBWaUjbbaV3cbOLuRCyhv8SLf8WLBxUPXsR/46YtqNUHA4/3ZnZnXpRKYdD3P52p6ZnZufmFRXdpeWV1zVvfuDBJpjnUeSITfRkxA1IoqKNACZepBhZHEhrR9XHhN25BG5Goc+yn0IpZT4mu4Ayt1Pb2y2X3rp2HCHeo49wMBjQUiobfyk3GNOxRLjSXYN2BWy63vZJf8Yegf0kwJiUyxmnbew87Cc9iUMglM6YZ+Cm2cqZRFK+6YWYgZfya9aBpqWIxmFY+PG9Ad6zSod1E21JIh+rPiZzFxvTjyHbGDK/MpFeI/3nNDLu1Vi5UmiEoPvqom0mKCS2yoh2hgaPsW8K4FnZXyq+YZhxtoq4NIZg8+S+pVyuHleCsWjqqjdNYIFtkm+ySgByQI3JCTkmdcHJPHskzeXEenCfn1XkbtU4545lN8gvOxxf9BqHt</latexit><latexit sha1_base64="2uS7mrXuLebyvkwy5bUs1tz6Bms=">AAACHXicbVBNS8NAEN34bfyKevSy2AoepCQFsd4ELx4VrBWaUjbbaV3cbOLuRCyhv8SLf8WLBxUPXsR/46YtqNUHA4/3ZnZnXpRKYdD3P52p6ZnZufmFRXdpeWV1zVvfuDBJpjnUeSITfRkxA1IoqKNACZepBhZHEhrR9XHhN25BG5Goc+yn0IpZT4mu4Ayt1Pb2y2X3rp2HCHeo49wMBjQUiobfyk3GNOxRLjSXYN2BWy63vZJf8Yegf0kwJiUyxmnbew87Cc9iUMglM6YZ+Cm2cqZRFK+6YWYgZfya9aBpqWIxmFY+PG9Ad6zSod1E21JIh+rPiZzFxvTjyHbGDK/MpFeI/3nNDLu1Vi5UmiEoPvqom0mKCS2yoh2hgaPsW8K4FnZXyq+YZhxtoq4NIZg8+S+pVyuHleCsWjqqjdNYIFtkm+ySgByQI3JCTkmdcHJPHskzeXEenCfn1XkbtU4545lN8gvOxxf9BqHt</latexit><latexit sha1_base64="2uS7mrXuLebyvkwy5bUs1tz6Bms=">AAACHXicbVBNS8NAEN34bfyKevSy2AoepCQFsd4ELx4VrBWaUjbbaV3cbOLuRCyhv8SLf8WLBxUPXsR/46YtqNUHA4/3ZnZnXpRKYdD3P52p6ZnZufmFRXdpeWV1zVvfuDBJpjnUeSITfRkxA1IoqKNACZepBhZHEhrR9XHhN25BG5Goc+yn0IpZT4mu4Ayt1Pb2y2X3rp2HCHeo49wMBjQUiobfyk3GNOxRLjSXYN2BWy63vZJf8Yegf0kwJiUyxmnbew87Cc9iUMglM6YZ+Cm2cqZRFK+6YWYgZfya9aBpqWIxmFY+PG9Ad6zSod1E21JIh+rPiZzFxvTjyHbGDK/MpFeI/3nNDLu1Vi5UmiEoPvqom0mKCS2yoh2hgaPsW8K4FnZXyq+YZhxtoq4NIZg8+S+pVyuHleCsWjqqjdNYIFtkm+ySgByQI3JCTkmdcHJPHskzeXEenCfn1XkbtU4545lN8gvOxxf9BqHt</latexit><latexit sha1_base64="2uS7mrXuLebyvkwy5bUs1tz6Bms=">AAACHXicbVBNS8NAEN34bfyKevSy2AoepCQFsd4ELx4VrBWaUjbbaV3cbOLuRCyhv8SLf8WLBxUPXsR/46YtqNUHA4/3ZnZnXpRKYdD3P52p6ZnZufmFRXdpeWV1zVvfuDBJpjnUeSITfRkxA1IoqKNACZepBhZHEhrR9XHhN25BG5Goc+yn0IpZT4mu4Ayt1Pb2y2X3rp2HCHeo49wMBjQUiobfyk3GNOxRLjSXYN2BWy63vZJf8Yegf0kwJiUyxmnbew87Cc9iUMglM6YZ+Cm2cqZRFK+6YWYgZfya9aBpqWIxmFY+PG9Ad6zSod1E21JIh+rPiZzFxvTjyHbGDK/MpFeI/3nNDLu1Vi5UmiEoPvqom0mKCS2yoh2hgaPsW8K4FnZXyq+YZhxtoq4NIZg8+S+pVyuHleCsWjqqjdNYIFtkm+ySgByQI3JCTkmdcHJPHskzeXEenCfn1XkbtU4545lN8gvOxxf9BqHt</latexit>

=Vs IVSKZ

=Vc IVCI =3

Page 6: More Naïve Bayes

Slightly Different Warm-Up Exercise

6

Question: How would we classify ?

Need to compute p(+ | x = [blue, square]) /<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>

p(blue | +) · p(square | +) · p(+) =<latexit sha1_base64="q7UUYH++v4w8b9t7hRgPnzpR8lQ=">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</latexit><latexit sha1_base64="q7UUYH++v4w8b9t7hRgPnzpR8lQ=">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</latexit><latexit sha1_base64="q7UUYH++v4w8b9t7hRgPnzpR8lQ=">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</latexit><latexit sha1_base64="q7UUYH++v4w8b9t7hRgPnzpR8lQ=">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</latexit>

In . F. Fz= 0.179

Page 7: More Naïve Bayes

Slightly Different Warm-Up Exercise

7

Question: How would we classify ?

Need to compute

p(blue | �) · p(square | �) · p(�) =<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>

p(� | x = [blue, square]) /<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><latexit sha1_base64="JnT8Rt0HWskKgxuk5GqGJapcT28=">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</latexit>

I. ÷ . ÷=0.167

Page 8: More Naïve Bayes

Slightly Different Warm-Up Exercise

8

Question: How would we classify ?

So we have:

So we predict __________________

p(+ | x = [blue, square]) / 0.179<latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">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</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">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</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">AAACKHicbVDLSgMxFM34dnxVXboJtoKilJlu1IVQcONSwarQGUomvaPBZCYmd8Qy9Hfc+CtuFFTc+iWmtQtfBwKHc+7l5pxES2ExCN69sfGJyanpmVl/bn5hcamyvHJm88JwaPFc5uYiYRakyKCFAiVcaANMJRLOk+vDgX9+C8aKPDvFnoZYsctMpIIzdFKn0qzVfL25TSMlurSMkpTe9ekBbUcId2hUmcgCdqi9KZiBfrxFI21yjTkN6uHuPvVrtU6lGtSDIehfEo5IlYxw3Kk8R92cFwoy5JJZ2w4DjXHJDAouoe9HhQXN+DW7hLajGVNg43KYtE83nNKlaW7cy5AO1e8bJVPW9lTiJhXDK/vbG4j/ee0C0724FJkuEDL+dSgtJHVRB7XRrjDAUfYcYdwI91fKr5hhHF25vish/B35L2k16vv18KRRbe6N2pgha2SdbJKQ7JImOSLHpEU4uSeP5IW8eg/ek/fmvX+NjnmjnVXyA97HJz//ox4=</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">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</latexit>

p(� | x = [blue, square]) / 0.167<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>

>

positive

Page 9: More Naïve Bayes

Slightly Different Warm-Up Exercise

9

Question: How would we classify ?

So we have:

So we predict positive .

Question: Is this what you would have predicted for ?

p(+ | x = [blue, square]) / 0.179<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>

p(� | x = [blue, square]) / 0.167<latexit sha1_base64="51Mpu9vUme9rChImnNtEjuAWguc=">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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>

Page 10: More Naïve Bayes

Slightly Different Warm-Up Exercise

10

Question: How would we classify ?

So we have:

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

p(+ | x = [blue, square]) / 0.179<latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">AAACKHicbVDLSgMxFM34dnxVXboJtoKilJlu1IVQcONSwarQGUomvaPBZCYmd8Qy9Hfc+CtuFFTc+iWmtQtfBwKHc+7l5pxES2ExCN69sfGJyanpmVl/bn5hcamyvHJm88JwaPFc5uYiYRakyKCFAiVcaANMJRLOk+vDgX9+C8aKPDvFnoZYsctMpIIzdFKn0qzVfL25TSMlurSMkpTe9ekBbUcId2hUmcgCdqi9KZiBfrxFI21yjTkN6uHuPvVrtU6lGtSDIehfEo5IlYxw3Kk8R92cFwoy5JJZ2w4DjXHJDAouoe9HhQXN+DW7hLajGVNg43KYtE83nNKlaW7cy5AO1e8bJVPW9lTiJhXDK/vbG4j/ee0C0724FJkuEDL+dSgtJHVRB7XRrjDAUfYcYdwI91fKr5hhHF25vish/B35L2k16vv18KRRbe6N2pgha2SdbJKQ7JImOSLHpEU4uSeP5IW8eg/ek/fmvX+NjnmjnVXyA97HJz//ox4=</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">AAACKHicbVDLSgMxFM34dnxVXboJtoKilJlu1IVQcONSwarQGUomvaPBZCYmd8Qy9Hfc+CtuFFTc+iWmtQtfBwKHc+7l5pxES2ExCN69sfGJyanpmVl/bn5hcamyvHJm88JwaPFc5uYiYRakyKCFAiVcaANMJRLOk+vDgX9+C8aKPDvFnoZYsctMpIIzdFKn0qzVfL25TSMlurSMkpTe9ekBbUcId2hUmcgCdqi9KZiBfrxFI21yjTkN6uHuPvVrtU6lGtSDIehfEo5IlYxw3Kk8R92cFwoy5JJZ2w4DjXHJDAouoe9HhQXN+DW7hLajGVNg43KYtE83nNKlaW7cy5AO1e8bJVPW9lTiJhXDK/vbG4j/ee0C0724FJkuEDL+dSgtJHVRB7XRrjDAUfYcYdwI91fKr5hhHF25vish/B35L2k16vv18KRRbe6N2pgha2SdbJKQ7JImOSLHpEU4uSeP5IW8eg/ek/fmvX+NjnmjnVXyA97HJz//ox4=</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">AAACKHicbVDLSgMxFM34dnxVXboJtoKilJlu1IVQcONSwarQGUomvaPBZCYmd8Qy9Hfc+CtuFFTc+iWmtQtfBwKHc+7l5pxES2ExCN69sfGJyanpmVl/bn5hcamyvHJm88JwaPFc5uYiYRakyKCFAiVcaANMJRLOk+vDgX9+C8aKPDvFnoZYsctMpIIzdFKn0qzVfL25TSMlurSMkpTe9ekBbUcId2hUmcgCdqi9KZiBfrxFI21yjTkN6uHuPvVrtU6lGtSDIehfEo5IlYxw3Kk8R92cFwoy5JJZ2w4DjXHJDAouoe9HhQXN+DW7hLajGVNg43KYtE83nNKlaW7cy5AO1e8bJVPW9lTiJhXDK/vbG4j/ee0C0724FJkuEDL+dSgtJHVRB7XRrjDAUfYcYdwI91fKr5hhHF25vish/B35L2k16vv18KRRbe6N2pgha2SdbJKQ7JImOSLHpEU4uSeP5IW8eg/ek/fmvX+NjnmjnVXyA97HJz//ox4=</latexit><latexit sha1_base64="hgrOQerWHl44iQeD9G2u4XoUBwg=">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</latexit>

p(� | x = [blue, square]) / 0.167<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>

Page 11: More Naïve Bayes

Slightly Different Warm-Up Exercise

11

Question: How would we classify ?

First: Do you see any difficulties with. ?

Page 12: More Naïve Bayes

Slightly Different Warm-Up Exercise

12

Question: How would we classify ?

Need to compute p(+ | x = [green, circle]) /<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><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><latexit sha1_base64="gyPcozssWtrnpPqI1ClNXoelPJY=">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</latexit>

p(green | +) · p(circle | +) · p(+) =<latexit sha1_base64="ldFrQOgMSr+dQLDwRYf3xwl9k0k=">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</latexit><latexit sha1_base64="ldFrQOgMSr+dQLDwRYf3xwl9k0k=">AAACRXicdVA9SytBFJ3146mr7xm1tBlMBOVB2E2jFoJgY6lgVMguYXb2JhmcmV1m7ophya+zsbbzJ9hYqNjqJKbQqAcGDuecy71zklwKi0Fw701Nz8z+mZtf8BeX/v5brqysntmsMByaPJOZuUiYBSk0NFGghIvcAFOJhPPk8nDon1+BsSLTp9jPIVasq0VHcIZOalfiWs2PegzLfLAVIVyjUWXXAOgBjZRI6f9tGvE0QzoZ4sJwCb+lnLDv12rtSjWoByPQ7yQckyoZ47hduYvSjBcKNHLJrG2FQY5xyQyK4TY/KizkjF+yLrQc1UyBjctRDQO66ZSUdjLjnkY6Uj9PlExZ21eJSyqGPTvpDcWfvFaBnd24FDovEDT/WNQpJMWMDjulqTDAUfYdYdwIdyvlPWYYR9e870oIJ7/8nTQb9b16eNKoHuyO25gn62SDbJGQ7JADckSOSZNwckMeyBN59m69R+/Fe/2ITnnjmTXyBd7bOxp1sDg=</latexit><latexit sha1_base64="ldFrQOgMSr+dQLDwRYf3xwl9k0k=">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</latexit><latexit sha1_base64="ldFrQOgMSr+dQLDwRYf3xwl9k0k=">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</latexit>

# 7+1

¥tDFzI

a a%DP - one / = To . 5g . Fy = 0.032

THREE colors - two SHAPES

Page 13: More Naïve Bayes

Slightly Different Warm-Up Exercise

13

Question: How would we classify ?

Need to compute

p(green | �) · p(circle | �) · p(�) =<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="QPWRgsNjgZUHl/FNoO1DvPIuZGE=">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</latexit><latexit sha1_base64="QPWRgsNjgZUHl/FNoO1DvPIuZGE=">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</latexit>

p(� | x = [green, circle]) /<latexit sha1_base64="HGfbeiF+moOaynIhMm/c9zAE62g=">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</latexit><latexit sha1_base64="HGfbeiF+moOaynIhMm/c9zAE62g=">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</latexit><latexit sha1_base64="HGfbeiF+moOaynIhMm/c9zAE62g=">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</latexit><latexit sha1_base64="HGfbeiF+moOaynIhMm/c9zAE62g=">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</latexit>

¥5 . 5¥ . Fee= Zg

° ¥ . Fy = • 023

Page 14: More Naïve Bayes

Slightly Different Warm-Up Exercise

14

Question: How would we classify ?

So we have:

So we predict __________________

p(+ | x = [green, circle]) / 0.032<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>

p(� | x = [green, circle]) / 0.023<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=">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>

>

positive

Page 15: More Naïve Bayes

Slightly Different Warm-Up Exercise

15

Question: How would we classify ?

So we have:

So we predict positive .

p(+ | x = [green, circle]) / 0.032<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>

p(� | x = [green, circle]) / 0.023<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><latexit sha1_base64="Koo5m31GLgb3EtZpCLPrFx+WdNA=">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</latexit>

Page 16: More Naïve Bayes

Slightly Different Warm-Up Exercise

16

Question: How would we classify ?

Uhhh…

pcunkslt) = 0¥ =

17+2+110

PC LTH )= 3+1 - 4-7+2+110

putt ' '

yes.EE

Page 17: More Naïve Bayes

Slightly Different Warm-Up Exercise

17

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

Page 18: More Naïve Bayes

Slightly Different Warm-Up Exercise

18

Question: How would we classify ?

Need p(+ | x = [orange, square]) /<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>

p(orange | +) · p(square | +) · p(+)<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>

UNKCOLOR ) UNKSHAPE

0+1 3+1

# • 7+-3• f¥z

= 0.021 Vga { Cir , sqr , on KSAAPE }

Vc= § RED , green , BUUE , Unkcolor

Page 19: More Naïve Bayes

Slightly Different Warm-Up Exercise

19

Question: How would we classify ?

Need

p(orange | �) · p(square | �) · p(�)<latexit sha1_base64="xpW3VYkl5MjBgbqpZgZoZhrZxHg=">AAACRHicdVA9bxNBFNwLAZLjy0CZZhUbyS5s3bkhdJHSUAYJk0g+y3q392yvvB+X3XcI6+Q/R5Oejn9AkyIgWsTacUGcMNKTRjPztPsmL5X0lCTfo50Huw8fPd7bj588ffb8RePlq0/eVk7gQFhl3XkOHpU0OCBJCs9Lh6BzhWf5/GTln31G56U1H2lR4kjD1MiJFEBBGjeyVivOZkB1uWxnhF/I6do6MFNc8kzLgnc7PBOFJb6d8hcVuP+mup241Ro3mkkvWYPfJemGNNkGp+PGt6ywotJoSCjwfpgmJY1qcCSFwmWcVR5LEHOY4jBQAxr9qF63sORvglLwiXVhDPG1+u9GDdr7hc5DUgPN/La3Eu/zhhVNjka1NGVFaMTNQ5NKcbJ8VSkvpENBahEICCfDX7mYgQNBofg4lJBun3yXDPq9d730Q795fLRpY48dsEPWZil7y47Ze3bKBkywr+wHu2Y/o8voKvoV/b6J7kSbndfsFqI/fwErjLBh</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>

p(� | x = [orange, square]) /<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>

OH 5 H

-5+4 • Ft. 5¥tz- tg . 63 . hf, = 0.036

Page 20: More Naïve Bayes

Slightly Different Warm-Up Exercise

20

Question: How would we classify ?

So we have:

So we predict __________________

p(+ | x = [orange, square]) / 0.021<latexit sha1_base64="vLzMpw1vkvpKB4JioHFOllmduBE=">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</latexit><latexit sha1_base64="vLzMpw1vkvpKB4JioHFOllmduBE=">AAACKXicbVDLThtBEJzlEcBAcJIjlxE2ElGQtesL5hCJiAtHkDAgeVfW7LjXjJgXM70Ia+XvyYVfyYUDIbnmRzI2PvAqaaRSVbd6qnIrhcc4/hPNzS8sflhaXqmtrq1/3Kh/+nzmTek4dLmRxl3kzIMUGrooUMKFdcBULuE8vzqc+Oc34Lww+hRHFjLFhloUgjMMUr/+o9ms2Z1vNFViQKs0L+jtmH6nvRThFp2qjGN6CLvUX5fMwTj7SlPrjEVD41bcTmiz2a83Ap2CviXJjDTIDMf9+n06MLxUoJFL5n0viS1mFXMouIRxLS09WMav2BB6gWqmwGfVNOqYbgdlQAvjwtNIp+rzjYop70cqD5OK4aV/7U3E97xeiUUnq4S2JYLmT4eKUtKQdNIbHQgHHOUoEMadCH+l/JI5xjG0WwslJK8jvyXddmu/lZy0GwedWRvLZJNskR2SkD1yQI7IMekSTn6SX+SB/I7uovvoMfr7NDoXzXa+kBeI/v0HnJ6j5A==</latexit><latexit sha1_base64="vLzMpw1vkvpKB4JioHFOllmduBE=">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</latexit><latexit sha1_base64="vLzMpw1vkvpKB4JioHFOllmduBE=">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</latexit>

p(� | x = [orange, square]) / 0.036<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>

<

negative

Page 21: More Naïve Bayes

Slightly Different Warm-Up Exercise

21

Question: How would we classify ?

So we have:

So we predict negative .

p(+ | x = [orange, square]) / 0.021<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>

p(� | x = [orange, square]) / 0.036<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>

Page 22: More Naïve Bayes

Naïve Bayes

22

o The Naïve Bayes classifier is a probabilistic classifier

o We compute the posterior score of message belonging to class c as

o Predicted class is the one with the highest posterior score

x<latexit 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><latexit 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>

y = arg maxc p(y = c | x) = arg maxc p(c)Y

k

p(xk | c)<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=">AAACYHicbVFBa9swFJa9bmu9tU2323Z5LBmkl2D30nUwKOyyYwfLWoiDkWU5EZFsIT0XG+P+yN566aV/ZHKSwdb2geDj+773nvQp1VJYDMM7z3+x8/LV69294M3b/YPDwdG737asDONTVsrSXKXUcikKPkWBkl9pw6lKJb9MV997/fKaGyvK4hc2ms8VXRQiF4yio5JBPRoF8ZJi23TwDWLkNRrVUrMAResuYXCjx41TGMRKZNDGaQ51d/ys9wY2o3Q3ZscQa1NmyQr+UnWP+xlOC0ajZDAMJ+G64CmItmBItnWRDG7jrGSV4gUySa2dRaHGuVuPgkneBXFluaZsRRd85mBBFbfzdp1QB58dk0FeGncKhDX7b0dLlbWNSp1TUVzax1pPPqfNKsy/zFtR6Ap5wTaL8koCltDHDZkwnKFsHKDMCHdXYEtqKEP3KYELIXr85KdgejI5m0Q/T4bnX7dp7JKP5BMZk4icknPyg1yQKWHk3tvx9r0D78Hf8w/9o43V97Y978l/5X/4A0M7sy8=</latexit><latexit sha1_base64="eBJJ3mQ6/WMOr/3y02uFm/eMN5A=">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</latexit>

p(y = c | x) / p(c)Y

k

p(xk | c)<latexit sha1_base64="q5Il4z+u6bm+ZTPZ1pxtjTbEtoQ=">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</latexit><latexit sha1_base64="q5Il4z+u6bm+ZTPZ1pxtjTbEtoQ=">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</latexit><latexit sha1_base64="q5Il4z+u6bm+ZTPZ1pxtjTbEtoQ=">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</latexit><latexit sha1_base64="q5Il4z+u6bm+ZTPZ1pxtjTbEtoQ=">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</latexit> = = =

= -

Page 23: More Naïve Bayes

Numerical Hiccup

23

For long messages, have to multiply a lot of probabilities together

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:

Predicted class becomes:

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y = arg maxc log p(c) +X

k

log p(xk | c)<latexit sha1_base64="85GSNIiZN4v3YGJ/bbsWeHhmnto=">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</latexit><latexit sha1_base64="85GSNIiZN4v3YGJ/bbsWeHhmnto=">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</latexit><latexit sha1_base64="85GSNIiZN4v3YGJ/bbsWeHhmnto=">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</latexit><latexit sha1_base64="85GSNIiZN4v3YGJ/bbsWeHhmnto=">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</latexit>

y = arg maxc p(c)Y

k

p(xk | c)<latexit sha1_base64="uTdDh4a239l8Qd/LGMbU/KtqY1M=">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</latexit><latexit sha1_base64="uTdDh4a239l8Qd/LGMbU/KtqY1M=">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</latexit><latexit sha1_base64="uTdDh4a239l8Qd/LGMbU/KtqY1M=">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</latexit><latexit sha1_base64="uTdDh4a239l8Qd/LGMbU/KtqY1M=">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</latexit>

F

Page 24: More Naïve Bayes

Training and Prediction Complexity

24

Question: How much does Naïve Bayes cost to train?

Page 25: More Naïve Bayes

Training and Prediction Complexity

25

Question: How much does Naïve Bayes cost to train?

Answer: It’s linear in the number of features and number of training examples!

o Single pass over training data to do frequency counts

o Another pass over recorded frequencies to normalize and take logs

Question: How much does Naïve Bayes cost to make a prediction?

Page 26: More Naïve Bayes

Training and Prediction Complexity

26

Question: How much does Naïve Bayes cost to train?

Answer: It’s linear in the number of features and number of training examples!

o Single pass over training data to do frequency counts

o 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!

Page 27: More Naïve Bayes

Naïve Bayes with Continuous Features

27

Example: Predict Iris species from sepal length and sepal width.

Features are now continuous values instead offrequencies…

What do we do?!

Page 28: More Naïve Bayes

Naïve Bayes with Continuous Features

28

Example: Predict Iris species from sepal length and sepal width.

Features are now continuous values instead offrequencies…

Idea: Discretize the Continuous Features

Now just pretend features are frequency counts

xk =

8>><

>>:

0 if xk < Q1

1 if xk 2 [Q1, Q2]2 if xk 2 [Q2, Q3]3 if xk > Q3

<latexit sha1_base64="sdM0kE53nVHR9+N/pBmdlayen+k=">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</latexit><latexit sha1_base64="sdM0kE53nVHR9+N/pBmdlayen+k=">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</latexit><latexit sha1_base64="sdM0kE53nVHR9+N/pBmdlayen+k=">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</latexit><latexit sha1_base64="sdM0kE53nVHR9+N/pBmdlayen+k=">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</latexit>

¥111

Page 29: More Naïve Bayes

Gaussian Naïve Bayes

29

Idea: Assume features follow a normal dist

o Priors don’t change.

o Likelihoods are computed from Gaussian pdf

p(y = c) =1

n

nX

i=1

I(yi = c)<latexit sha1_base64="cT4GYfCwUP+Qo40gOWmqHGLuoXU=">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</latexit><latexit sha1_base64="cT4GYfCwUP+Qo40gOWmqHGLuoXU=">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</latexit><latexit sha1_base64="cT4GYfCwUP+Qo40gOWmqHGLuoXU=">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</latexit><latexit sha1_base64="cT4GYfCwUP+Qo40gOWmqHGLuoXU=">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</latexit>

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<latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit>

p(Xk = x | Y = c) =<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><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>

s.net#

Page 30: More Naïve Bayes

Gaussian Naïve Bayes

30

o Likelihoods are computed from Gaussian pdf

o Get MLE estimates of params from training set

1p2⇡�kc

exp

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2

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<latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit><latexit sha1_base64="UEwKNGba4JiktpjpkwMOGU18qcU=">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</latexit>

p(Xk = x | Y = c) =<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><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>

µkc =1Pn

i=1 I(yi = c)

nX

i=1

xikI(yi = c)<latexit sha1_base64="us1bcFBYnEwDctr1HuGSRUP+EXk=">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</latexit><latexit sha1_base64="us1bcFBYnEwDctr1HuGSRUP+EXk=">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</latexit><latexit sha1_base64="us1bcFBYnEwDctr1HuGSRUP+EXk=">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</latexit><latexit sha1_base64="us1bcFBYnEwDctr1HuGSRUP+EXk=">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</latexit>

�2kc =

1Pni=1 I(yi = c)

nX

i=1

(xik � µkc)2I(yi = c)

<latexit sha1_base64="+UQlxJ2NKLI3n9w+XHGKlhwsPY8=">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</latexit><latexit sha1_base64="+UQlxJ2NKLI3n9w+XHGKlhwsPY8=">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</latexit><latexit sha1_base64="+UQlxJ2NKLI3n9w+XHGKlhwsPY8=">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</latexit><latexit sha1_base64="+UQlxJ2NKLI3n9w+XHGKlhwsPY8=">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</latexit>

µ|BW:TpzuE

= =

-1I I I I 11111111

*

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Gaussian Naïve Bayes

31

P ( • / SL = 6.5,Sw =3 -25 ) -

L PC . ) ×p(sL=6-51• ) ×p( Swiss -251

• )

Mx!÷expFHas#)yDue#

Page 32: More Naïve Bayes

32

a pla It ) =

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33

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34