Pointwise HSIC: A Linear-Time Kernelized Co-occurrence Norm for Sparse Linguistic Expressions

0fee20d8bbb7283e1887e7075f638f59?s=47 Sho Yokoi
November 03, 2018

Pointwise HSIC: A Linear-Time Kernelized Co-occurrence Norm for Sparse Linguistic Expressions

EMNLP 2018

0fee20d8bbb7283e1887e7075f638f59?s=128

Sho Yokoi

November 03, 2018
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  1. Pointwise HSIC: A Linear-Time Kernelized Co-occurrence Norm for Sparse Linguistic

    Expressions Sho Yokoi1,2, Sosuke Kobayashi3, Kenji Fukumizu4, Jun Suzuki1,2, Kentaro Inui1,2 1Tohoku University, 2RIKEN AIP, 3Preferred Networks, 4The Institute of Statistical Mathematics 1 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) github.com/cl-tohoku/phsic pip install phsic-cli Nov. 03, 2018. EMNLP 2018 @Brussels, Belgium. Special Thanks to Ryo Takahashi
  2. Summary •Purpose : Computing co-occurrence strength between sentences with short

    learning time 2 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) Applicable to Sentences Requires Short Learning Time PMI log (|) () <latexit sha1_base64="ccrkicOcP0jMJiIleKtAa2XOwJI=">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</latexit> <latexit 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  3. Summary •Purpose : Computing co-occurrence strength between sentences with short

    learning time •Proposal : PHSIC, “a smoothed variant of PMI” by kernels 3 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) Applicable to Sentences Requires Short Learning Time PMI PHSIC log (|) () <latexit sha1_base64="ccrkicOcP0jMJiIleKtAa2XOwJI=">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</latexit> <latexit 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  4. Brief Recap: Computing Co-occurrence Strength by PMI 4 Nov. 03,

    2018 Pointwise HSIC (EMNLP 2018)
  5. Computing Co-occurrence Strength in NLP New York in the 5

    Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) task: compute co-occurrence strength of word bigrams to extract collocations Example 1: Collocation Extraction [Manning&Schütze,’99] Have you you ever York ? … observed data: word bigrams from corpora
  6. Computing Co-occurrence Strength in NLP 6 Nov. 03, 2018 Pointwise

    HSIC (EMNLP 2018) task: compute co-occurrence strength of input-response sentence pairs to rank the candidate responses I've lost my wallet I saw it at the … I've lost my wallet I’m so sleepy I've lost my wallet I don’t know input by users response candidates Example 2: Dialogue Response Selection [Lowe+,’15] observed data: input-response message pairs from dialogue corpora I'm hungry! Let’s have lunch Will it rain today? It’s about to rain I love this manga I don’t know …
  7. Computing Co-occurrence Strength in NLP !" … 7 Nov. 03,

    2018 Pointwise HSIC (EMNLP 2018) observed: paired data task: compute co-occurrence strength of a pair #" !$ #$ !% #% &'( ~ ! # General Settings ?
  8. De-facto Measure: PMI [Church&Hanks,’89] Nov. 03, 2018 Pointwise HSIC (EMNLP

    2018) 8 co-occurrence by chance co-occurrence actual !" … #" !$ #$ !% #% &'( ~ ! # ? Task: Computing Co-occurrence Strength PMI(, ) = log (, ) () () <latexit sha1_base64="QRL6XwvZhHCptyxZ10ClzfytHqE=">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</latexit> <latexit sha1_base64="QRL6XwvZhHCptyxZ10ClzfytHqE=">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</latexit> <latexit sha1_base64="QRL6XwvZhHCptyxZ10ClzfytHqE=">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</latexit> <latexit sha1_base64="QRL6XwvZhHCptyxZ10ClzfytHqE=">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</latexit>
  9. Estimating PMI easy to learn cannot be applied to sparse

    expressions 9 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="8J8nlmkRzEYQ/hGx73TYH8/olB0=">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</latexit> <latexit 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New York … just counting word bigrams from corpora Example 1: Collocation Extraction by PMI learn parameters compute co-occurrence strength ?
  10. Estimating PMI input-response pairs from dialogue corpora input by users

    PMI(, ) = log (|) () <latexit sha1_base64="iZm2t2viqgME5d2mBcyJL6SmJMc=">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</latexit> <latexit sha1_base64="iZm2t2viqgME5d2mBcyJL6SmJMc=">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</latexit> <latexit sha1_base64="iZm2t2viqgME5d2mBcyJL6SmJMc=">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</latexit> <latexit sha1_base64="iZm2t2viqgME5d2mBcyJL6SmJMc=">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</latexit> response candidates 10 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) using RNNs Example 2: Dialogue Response Selection by PMI [Li+’16] tough to learn can be applied to sparse expressions learn parameters compute co-occurrence strength ? I've lost my wallet I saw it at the … I'm hungry! Let’s have lunch Will it rain today? It’s about to rain I love this manga I don’t know … sentences
  11. PMI Has a Trade-off between Two Properties 11 Nov. 03,

    2018 Pointwise HSIC (EMNLP 2018) Applicable to Sentences Requires Short Learning Time PMI log (|) () <latexit sha1_base64="ccrkicOcP0jMJiIleKtAa2XOwJI=">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</latexit> <latexit 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  12. PMI Has a Trade-off between Two Properties 12 PHSIC Meets

    Both Properties Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) Applicable to Sentences Requires Short Learning Time PMI PHSIC log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="piIdIgFlP9rjJ6Vaj6HD7Z5Iv0k=">AAACynicbZHNatwwEMe17kdS92vTHnsRXRYSSIPdBNpjIJceWkihmwTWyyLL411hWRLSuK0xSy95iTxNr+0j9G0qe13YTTog+PObGY00/9RI4TCK/gyCe/cfPNzZfRQ+fvL02fPh3osLpyvLYcK11PYqZQ6kUDBBgRKujAVWphIu0+KszV9+BeuEVl+wNjAr2UKJXHCGHs2Hx4nUiyS3jDeKJjzTSJPR/vfD+mDVdKJjB152ouXhfDiKjqIu6F0R92JE+jif7w1+JJnmVQkKuWTOTePI4KxhFgWXsAqTyoFhvGALmHqpWAlu1nS/W9GxJxnNtfVHIe3oZkfDSufqMvWVJcOlu51r4f9y0wrz97NGKFMhKL4elFeSoqbtqmgmLHCUtReMW+HfSvmS+VWhX+jWlEoJrjN4sx61lWrf7Axw/0kHWDKhWtKceYusYGvqmHI9lcLjf7W43Kyln9rbQzqmRn8Da7TotlEab6W3OxzTzblF235IC7CFcCtvWXzboLvi4u1R7PXnk9HpSW/eLnlFXpN9EpN35JR8IOdkQji5IT/JL/I7+BjYoA6adWkw6Htekq0Irv8CONPgkA==</latexit> <latexit 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sha1_base64="piIdIgFlP9rjJ6Vaj6HD7Z5Iv0k=">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</latexit> <latexit sha1_base64="piIdIgFlP9rjJ6Vaj6HD7Z5Iv0k=">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</latexit> Proposed Measure log (|) () <latexit 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  13. Pointwise HSIC 13 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018)

  14. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 14 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  15. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 15 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  16. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 16 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  17. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 17 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  18. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 18 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) +1 #(!, ") observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit>
  19. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 19 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) +1 observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  20. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 20 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) +1 observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit>
  21. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 21 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  22. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 22 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  23. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 23 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  24. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 24 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.7 observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> similar similar
  25. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 25 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.7 +0.3 observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> similar similar
  26. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 26 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">AAAC6HicbVLLahRBFK1pH4nta6JLN4XDQAIxdIsYN0IgG10EJuAkgelhqK6+PVPpelFVbRyaxl9wJ279Cb/FhVv9Dat7WphJvFBwOOfeunXvqVRzZl0U/ewFt27fubu1fS+8/+Dho8f9nSdnVpWGwpgqrsxFSixwJmHsmONwoQ0QkXI4T4vjRj//CMYyJT+4pYapIHPJckaJ89Ssf5pcsQwWxFWJIG5hRDU6eV/Xu5/2l3v4LU64mie5IbSSOKGZcjgZtFpdtaDl9jxsQcOHs/4gOojawDdB3IEB6mI02+l9TjJFSwHSUU6sncSRdtOKGMcohzpMSgua0ILMYeKhJALstGpnr/HQMxnOlfFHOtyy6xUVEdYuReozmwHtda0h/6dNSpe/mVZM6tKBpKtGecmxU7hZJM6YAer40gNCDfNvxXRB/KqcX/dGl1IyqjJ4sWq1ITVvthqoH9KCE4TJhqmOvYGGkRVribQdy5mn/+W6xXouPmluD/EQa3UFRivWbkNob7T/DOEQr/ctmvJ9XIApmK29ZfF1g26Cs5cHscenrwZHrzvzttEz9BztohgdoiP0Do3QGFH0A/1Cv9Gf4DL4EnwNvq1Sg15X8xRtRPD9L4C27KY=</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.3 +0.7 +1.0 observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> similar similar
  27. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 27 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.3 +0.7 +1.0 observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  28. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 28 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.3 +0.7 +1.0 +0.2 observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> similar similar
  29. 1. Intuitive Explanation Why PHSIC is Robust to Sparsity: Nov.

    03, 2018 Pointwise HSIC (EMNLP 2018) 29 PMI(, ) = log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> <latexit sha1_base64="/irJKxcQJnq31bHv/tF6hQgEvmQ=">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</latexit> ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … PHSIC Smoothes the Matching by Kernels (Similarity Functions) Exact Match +1 ! " !# "# !$ "$ !% "% !& "& !' "' !( "( … +0.3 +0.7 +1.0 +0.2 smoothes the matching by kernels observed pairs observed pairs PHSIC(, ; , ℓ )= 1 (, )ℓ(, ) <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">AAAFNHictVPdahNBFN7YqHX9a/XSm4khkEgs2bRaoQQKEWxBJWL/IBvDZPZsMuzuzDoz2zQO66P4GL6L4J146zM4k6TYtBVEcfZiz37n5/vm7DmDNKZSNRpfCleWilevXV++4d68dfvO3ZXVeweSZ4LAPuExF0cDLCGmDPYVVTEcpQJwMojhcBC1rf/wGISknO2pSQq9BA8ZDSnBykD9lU/+mAYwwkr7CVYjkejOztvddp5XT+qTLb/k+pCkI3jPYKhzHeX185APcZy7NeSXWtYVCkyQh5j59mWW9Cn6RWANReMAUGTLn/Rp7RLntGB1Up8Yd6W/Um6sNaYHXTS8uVF25qfTX1366AecZAkwRWIsZddrpKqnsVCUxJC7fiYhxSTCQ+gak+EEZD04pqmcmj19Mm3qQqDGiZSTZJCjim2SPO+z4GW+bqbCZz1NWZopYMSEGF+YxUhxZH8GCqgAouKJMTAR1EhEZIRNC5X5ZQssGaOEB/B4RrXgCjlTMgViJEtQCabMIrpthkBQPEMlZnKOxtTAp7FqdDYWvbLVXVRBKR+DSDllChGepGZYzEC5FXSWN7LpdRSBiKjMXdd/DePn89a3eZJgFvgdwQc6QTzXFVebdAUnSqqJqeXbhoa6k/e1X9JlL8/faaNqNzzAcQZ7utzMdbXcrOWufc7yKhp9MAiDMZmx6PlAplzm3WbPUCHDZKK6p5vRswgz/euGNI5bL2kCLwQAK208qSPBMxZAYC4qmGl7az1VdYQZGXHRsgVscrXs1czLMDGZCbA3twrzrd8J+Qstm/9Fi9nSPxMyFHhSWm/8qwazsd75/bxoHDTXPGO/2ShvP53v7rLzwHnoVB3P2XS2nR2n4+w7pFAsPCqsFzaKn4tfi9+K32ehVwrznPvOwin++AkpsLzm</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit> <latexit sha1_base64="DTWFpTptIruQrvYwHi5dz5kJI10=">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</latexit>
  30. Kernels (Sentence Similarities) for PHSIC are Available! Nov. 03, 2018

    Pointwise HSIC (EMNLP 2018) 30 • Cosine Similarity between Sentence Vectors o Sentence vectors [Kiros+,’15; Dai&Le,’15; Iyyer+,’15; Hill+,’16; Cer+,’18] o Sum of word vectors [Mikolov+,’13; Pennington+,’14; Bojanowski+,’17] o Many pre-trained models are off-the-shelf! • Structured Kernels o [Collins&Duffy,’02; Bunescu&Mooney,’06; Moschitti,’06] • Combinations o We can freely combine (sum, product) kernels PHSIC(, ; , ℓ ) <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit>
  31. 2. Definition — MI : PMI :: HSIC : PHSIC

    Dependence Measure Co-occurrence Measure Mutual Information Pointwise Mutual Information HSIC Pointwise HSIC 31 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) ? kernelize kernelize 1 2 3
  32. 2. Definition — MI : PMI :: HSIC : PHSIC

    Dependence of ! and " . Co-occurrence of # and $ . Mutual Information Pointwise Mutual Information 32 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> contribute # $ ! " between all possible pairs between a specific pair PMI(#, $) is the contribution of (#, $) to MI(!, ") MI(!, ") is the expectation of PMI(#, $)
  33. 2. Definition — MI : PMI :: HSIC : PHSIC

    Dependence of ! and " . Co-occurrence of # and $ . Mutual Information Pointwise Mutual Information HSIC 33 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 sha1_base64="GA5Ew+EeGw//AxnLgW338TsAVc4=">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</latexit> <latexit sha1_base64="GA5Ew+EeGw//AxnLgW338TsAVc4=">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</latexit> <latexit sha1_base64="GA5Ew+EeGw//AxnLgW338TsAVc4=">AAAExnicrVPdbtMwFE5HgRH+Blxy41GGOqlM7RgCCU1CDMSAgYbYxqYkTK5z0lp17GA7bMVY4sl4D96CR+CkzSYKXHCBb3z8nZ/v+Pz0C8GN7Xa/N+bONM+eOz9/Ibx46fKVqwvXru8ZVWoGu0wJpff71IDgEnYttwL2Cw007wt43x9tVPr3n0AbruSOHReQ5HQgecYZtQgdLny7Q+Kc2qHO3esXvr3fOVgm66fQqy0fxdta9d3+gSfxF1I//PQ+8Ekch3fQvpQpkoB17ePOeNm7SYB+Rp75+AkfDEQUxpAXQ/goYeBQnXJTCDo2diwgjIUaxJmmzJ1yRRgm8SdvfCYnjBHioQ8nYXVyuNDqrnQnh/wp9GqhFdRn+/Da3I84VazMQVomqDFRr1vYxFFtOROAgUsDBWUjOoAIRUlzMJ30Ey/MREzc8aToM4aO5saM874nS9W/ze+6CvybLipt9jBxXBalBcnQBHVZKYhVpGoWSbkGZsUYBco0xxQJG1KslMVqz7CUkjOVwt0p1YwqU9KaAhimjB3KKZcV4jZwSDSnU9RQaWpUcIRPbO3wV1vyuooekiVSqCPQheLSEqbyAocJBy5cIr/yjir3DhmBHnGDAd/A0dO68hsqz6lMpz3NifJuKXTobeHY1jNR1TNz2/7QxYuu1fP+g8MYL7I9KkrYca1V79qt1eVqFmZ7YfnoMyISjtiUxdWjVyjjo9UEqQgyoVV0sjhJhUgsX5RxIda3eA7PNYBcXLvfIVpVw53iP7XEqq/fK2yHUMmGSq9XASrndqu3jBcySVNqqD5eZegf/TUR3IF/S0RD+h9SwB3p/b4Rfwp7qys9lN+utR7fq7dlPrgZ3AraQS94EDwONoPtYDdgjduNl413jZ3mZlM2y+bR1HSuUfvcCGZO8+tPYe+YJg==</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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HSIC [Gretton+’05] is another dependence measure HSIC uses kernels! %: '×' → ℝ ℓ: ,×, → ℝ replace (kernelize) # $ ! "
  34. 2. Definition — MI : PMI :: HSIC : PHSIC

    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> HSIC(, ; , ℓ ) = MMD ,ℓ [ , ] = ( , ) ( , ) [(, )ℓ(, )] <latexit 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<latexit 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<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
  35. 2. Definition — MI : PMI :: HSIC : PHSIC

    Dependence of ! and " . Co-occurrence of # and $ . Mutual Information Pointwise Mutual Information HSIC Pointwise HSIC 35 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> <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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sha1_base64="O3tUIFA8yqBKwz9kWOKw7dB3e40=">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</latexit> contribute contribute replace (kernelize) # $ ! "
  36. 3. PHSIC Requires Very Short Computation Time Is Computing PHSIC

    costly? Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 36 1 (, )ℓ(, ) <latexit sha1_base64="vmlmdW9dFULuiGEgS7Uks2pLlkU=">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</latexit> <latexit sha1_base64="vmlmdW9dFULuiGEgS7Uks2pLlkU=">AAAEWHicrVPLbhMxFHXbQNvwasuSjcsoUiqFKhPKQ0KVKhUJkAAFqS8pEyLHcyexxo/B9jQJ1vwW/wJiC2s+AU+SSk3bBQs8izk693Guj+1+xpmxzeb3peWVyq3bq2vr1Tt3791/sLG5dWJUrikcU8WVPusTA5xJOLbMcjjLNBDR53DaTw/L+Ok5aMOUPLKTDLqCDCRLGCXWU72NdpRoQnGIJY62I5OLHsPRiMUwJNZNgWU8BpwW9XFj3GM7NwQj4LyoTxoTH671NoLmbnO68HUQzkGA5qvd21z+E8WK5gKkpZwY0wmbme06oi2jHIpqlBvICE3JADoeSiLANOJzlpkp7Lrx1IaFREeEMRPRL3BNEDs0V2MleVOsk9vkZdcxmeUWJPUpPpbkHFuFS/twzDRQyyceEKqZHxHTIfEWWm/ygkouGVUxPJlJLYQSJa3JgPqRDVhBmCwZd+iPTTMyYw2RZs5y5umLXDu8nIs/lN2ruIYzNQKdKSYtpkpk/nj9FajW8GXdtCxv4BR0yoxv+BFGr+fOHyohiIyjtlZ9J7AqXK3qfLWFsTV24ltFpZ+Jaxc9F227ICyKz873eJecEJ7DkQtahasHrZ2iWn6XZS1Lv3pGwojOVFwEIhvCl0yZotPqeinslXxW5+Iqd0tGevs6CeN8/z0T8EYDyO29Zw2sVS5jiP0+tfSu7z/NbAMTSYdK75cNyuJ6EO74n1eSJtdQbrycsHh14yASBv82iIb4P4zg30h49UVcByet3dDjT3vBwfP5a1lDj9BjVEcheoEO0FvURseIom/oJ/qFfq/8qKDKamV9lrq8NK95iBZWZesvB3lvHQ==</latexit> <latexit sha1_base64="vmlmdW9dFULuiGEgS7Uks2pLlkU=">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</latexit> <latexit sha1_base64="vmlmdW9dFULuiGEgS7Uks2pLlkU=">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</latexit> Learning !(#$) Prediction !(#) ? ? need construct the entire Gram matrices? need match with all observed pairs?
  37. 3. PHSIC Requires Very Short Computation Time Is Computing PHSIC

    costly? Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 37 No! reduced to simple matrix calculations when using cosine similarity can compute in feature space directly when using non-linear kernels can use a matrix decomposition technique 1 (, )ℓ(, ) <latexit 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Learning !(#) Prediction !(1)
  38. PMI Has a Trade-off between Two Properties 38 PHSIC Meets

    Both Properties Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) Applicable to Sentences Requires Short Learning Time PMI PHSIC log ⋅ #(, ) #(, ⋅)#(⋅, ) <latexit sha1_base64="piIdIgFlP9rjJ6Vaj6HD7Z5Iv0k=">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</latexit> <latexit 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Estimators are reduced to simple matrix calculations 1. PHSIC Smoothes the Matching by Kernels 2. Kernelize via MI and HSIC
  39. Experiments (Use Case) 39 Nov. 03, 2018 Pointwise HSIC (EMNLP

    2018)
  40. Kernels (Sentence Similarities) Used in Experiments • Cosine Similarity between

    Sum of Word Vectors • Gaussian Kernel between Sum of Word Vectors • Cosine Similarity between Sentence Vectors Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 40 PHSIC(, ; , ℓ ) <latexit 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  41. Kernels (Sentence Similarities) Used in Experiments • Cosine Similarity between

    Sum of Word Vectors • Gaussian Kernel between Sum of Word Vectors • Cosine Similarity between Sentence Vectors Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 41 PHSIC(, ; , ℓ ) <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> <latexit sha1_base64="rpCR4umr+BS2iuel0ydKBLrI120=">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</latexit> fastText [Bojanowski+,’17; Grave+,‘18] Universal Sentence Encoder [Cer+’18] w/Deep Averaging Network [Iyyer+,’15] Useful pre-trained models are off-the-shelf!! 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  42. (Re-)Ranking: Dialogue Response Selection Nov. 03, 2018 Pointwise HSIC (EMNLP

    2018) 42 task: compute co-occurrence strength of input-response sentence pairs to rank the candidate responses observed data: input-response sentence pairs from dialogue corpora use PHSIC I've lost my wallet I saw it at the … I've lost my wallet I’m so sleepy I've lost my wallet I don’t know input by users response candidates I'm hungry! Let’s have lunch Will it rain today? It’s about to rain I love this manga I don’t know … corpus: Twitter (following [Sordoni+,’15])
  43. (Re-)Ranking: Dialogue Response Selection — Results •Learning Time [s] •Predictive

    Performance [R@2] Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 43 13054.9 1.8 thousands of times faster! while outperforming PMI 0.52 0.57 PMI (w/RNN) PHSIC (cos of USE) ! = 5×10'
  44. (Re-)Ranking: Dialogue Response Selection — Results •Learning Time [s] •Predictive

    Performance [R@2] Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 44 13054.9 1.8 thousands of times faster! while outperforming PMI 0.52 0.57 PMI (w/RNN) PHSIC (cos of USE) ! = 5×10' •Learning Time [s] •Predictive Performance [R@2] 49.0 0.0 much more robust to data sparsity 0.21 0.56 PMI (w/RNN) PHSIC (cos of USE) ! = 10(
  45. Data Selection: Noisy Parallel Corpus Filtering [NLP4TM’16, WMT’18] Nov. 03,

    2018 Pointwise HSIC (EMNLP 2018) 45 task: compute co-occurrence strength of source-target sentence pairs to filter noisy parallel corpora source sentence target sentence observed data: noisy source-target sentence pairs (noisy parallel corpora) PHSIC gives high (low) scores to consistent (inconsistent) pairs !" … #" !$ #$ !% #% !" … #" !$ #$ !% #% for reducing learning time of NMT for increasing translation quality
  46. Data Selection: Noisy Parallel Corpus Filtering — Results •BLEU score

    after filtering (3M ⟼ 1M) Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 46 39.82 (-1.20) 40.56 (-0.46) PHSIC reduces # of training data to 1/3, almost without sacrificing BLEU random fast_align PHSIC (RBF kernel of fastText) 40.95 (-0.07) 41.02 (using all (3M) training data) Corpus: ASPEC-JE corpus [WMT’14] Model: Transformer [Vaswani+,’17] on fairSeq baseline using word alignment [Dyer+,’13]
  47. Summary: Computing Co-occurrence Strength, Robust and Fast •Proposal: PHSIC, “a

    smoothed variant of PMI” by kernels o applicable to sentences (PHSIC “smoothes” the matching by kernels) o allows various similarity metrics to be plugged in as kernels o requires very short learning time (Estimators are reduced to matrix calculations) •Experiments (Use Case) o (Re-)Ranking — Dialogue Response Selection o Data Selection — Noisy Parallel Corpus Filtering Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 47 github.com/cl-tohoku/phsic pip install phsic-cli Special Thanks to Ryo Takahashi
  48. Appendix 48 Nov. 03, 2018 Pointwise HSIC (EMNLP 2018)

  49. (Re-)Ranking: Dialogue Response Selection Nov. 03, 2018 Pointwise HSIC (EMNLP

    2018) 49
  50. Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 50

  51. Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 51

  52. Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 52

  53. Data Selection: Noisy Parallel Corpus Filtering Nov. 03, 2018 Pointwise

    HSIC (EMNLP 2018) 53
  54. Data Selection: Noisy Parallel Corpus Filtering •Baseline: fast_align (one of

    the SotA word aligners) [Dyer+,’13] •1. word alignment on each (x i , y i ) with fast_align to get a set of aligned word pairs with its probabilities •2. compute co-occurrence score of (x i , y i ) with the average log probability of aligned word pairs Nov. 03, 2018 Pointwise HSIC (EMNLP 2018) 54