Dependence of ! and " . Co-occurrence of # and $ . Mutual Information Pointwise Mutual Information HSIC Pointwise HSIC 34 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) PMI(, ; , ) = log (, ) () () <latexit 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sha1_base64="brvaGHiqW4ASZZmeoDha1J/A8O0=">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</latexit> MI(, ) = KL[ ‖ ] = E ( , ) log (, ) () () <latexit 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sha1_base64="GA5Ew+EeGw//AxnLgW338TsAVc4=">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</latexit> <latexit sha1_base64="GA5Ew+EeGw//AxnLgW338TsAVc4=">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</latexit> HSIC(, ; , ℓ ) = MMD ,ℓ [ , ] = ( , ) ( , ) [(, )ℓ(, )] <latexit 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<latexit 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<latexit 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<latexit 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PHSIC(, ; , , , ℓ ) = ( , ) [(, )ℓ(, )] <latexit 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" HSIC(!, ") is the expectation of PHSIC(#, $) PHSIC(#, $) is the contribution of (#, $) to HSIC(!, ") word-alignment based between a specific pair