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Lecture 5 Jan-Willem van de Meent Conjugate Priors <latexit - PowerPoint PPT Presentation

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Unsupervised Machine Learning and Data Mining DS 5230 / DS 4420 - Fall 2018 Lecture 5 Jan-Willem van de Meent Conjugate Priors <latexit

  1. Unsupervised Machine Learning 
 and Data Mining DS 5230 / DS 4420 - Fall 2018 Lecture 5 Jan-Willem van de Meent

  2. Conjugate Priors

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  5. <latexit sha1_base64="z9jbK0C2B0bymVtEWNsdOrtQecg=">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</latexit> <latexit sha1_base64="m49vKTjt/uVv8k07CRg8QZKlH4=">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</latexit> Likelihood: Bernoulli (a discrete distribution with outcomes x=0 and x=1) µ x (1 − µ ) 1 − x Bern( x | µ ) = E [ x ] = µ var[ x ] = µ (1 − µ ) � 1 if µ � 0 . 5 , mode[ x ] = 0 otherwise H[ ] = ln (1 ) ln µ ∈ [0 , 1] that ariable x ∈ { 0 , 1 } by a single continuous

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