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10-ot-generic-bio.pdf

 10-ot-generic-bio.pdf

Gabriel Peyré

January 14, 2024
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  1. Gabriel Peyré É C O L E N O R

    M A L E S U P É R I E U R E Optimal Transport for Machine Learning and Genomics Geert-Jan Huizing Laura Cantini
  2. Comparing Distributions for Learning <latexit sha1_base64="vT0xGll5ZYO8gmdwavYy0Ckm65g=">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</latexit> ATAC-seq

  3. Comparing Distributions for Learning Parametric model: ✓ 7! ↵✓ <latexit

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<latexit 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<latexit sha1_base64="YYkL6JTK2uYxh8MNcanIViL0GK4=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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<latexit 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↵✓ <latexit 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ATAC-seq
  4. Comparing Distributions for Learning min ✓ D(↵✓, ) <latexit sha1_base64="9IYkKnkiR+VYnIAjCg9CiCnhkKw=">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</latexit>

    <latexit 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Density fitting: <latexit 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<latexit 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<latexit 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<latexit 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Parametric model: ✓ 7! ↵✓ <latexit 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<latexit 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<latexit sha1_base64="YYkL6JTK2uYxh8MNcanIViL0GK4=">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</latexit> Observations: def. = 1 n Pn i=1 xi <latexit 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<latexit 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<latexit 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↵✓ <latexit 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ATAC-seq
  5. x <latexit 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<latexit 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<latexit 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<latexit

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d(x,y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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2. Entropic <latexit 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<latexit 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Regularization <latexit 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1. Optimal Transport <latexit 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<latexit 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4. Gromov Wasserstein <latexit sha1_base64="9fqK2kknFwBXfI8mtR1BkfiXw2M=">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</latexit> 3. Single cell genomics
  6. Monge’s Problem Monge optimal matching: <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit

    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<latexit 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[Monge 1784] <latexit 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<latexit sha1_base64="UVBrgZLymtr0d1RvatLpsl9X7ek=">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</latexit> Points (xi)i, (yj)j Permutation: <latexit 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<latexit 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<latexit 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: {1, . . . , n} ! {1, . . . , n} <latexit 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<latexit 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<latexit sha1_base64="htpgxAyMB7fa8Ak1IhsYtBIZXuE=">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</latexit> D(X, Y ) = min n X i=1 d(xi, y (i) )
  7. Monge’s Problem Monge optimal matching: <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit sha1_base64="cXrrsZJZuxRia1oYbgE1ijicFzU=">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</latexit> <latexit

    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<latexit 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[Monge 1784] <latexit 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<latexit sha1_base64="UVBrgZLymtr0d1RvatLpsl9X7ek=">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</latexit> Points (xi)i, (yj)j Permutation: <latexit 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<latexit 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<latexit 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: {1, . . . , n} ! {1, . . . , n} <latexit 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<latexit 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D(X, Y ) = min n X i=1 d(xi, y (i) ) ! Seems intractable: n! possibilities. <latexit 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<latexit 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<latexit 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<latexit 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! Di↵erent number of points?
  8. Kantorovitch’s Formulation ↵ = Pn i=1 ai xi = Pm

    j=1 bj yj Points (xi)i, (yj)j Weights ai > 0, bj > 0. Pn i=1 ai = Pm j=1 bj = 1 xi <latexit 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sha1_base64="lHCrrCdLriSUoJxIcVw6BefNKNo=">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</latexit> Discrete distributions: <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mdlENPIKtv1PnSOEu/s/cH99nYI=">AABE+XictVzdctxIFe4sf0v4y8IFF9xo8YbKUiHYZikotqjaxJM43jiJkxk72Y2T1GhGniiRR5PRjPMz64ehuKEouOIBeA4egCq44hU4P93q1kxLp2VCVLZbrf7OOX3Uffqc063EkywtZuvr/zj33te+/o1vfuv9b5//zne/9/0fXPjghwdFPp8Okv1BnuXTh3G/SLJ0nOzP0lmWPJxMk/5xnCUP4hdb+PzBSTIt0nzcm72ZJI+P+6NxepQO+jOoenrhx520GEyTWRINgdk0jedYX/zu6YW19Svr9C9aLWzowprS//byDz78pzpUQ5WrgZqrY5WosZpBOVN9VcD1SG2odTWBusdqAXVTKKX0PFGn6jxg59AqgRZ9qH0Bv0dw90jXjuEeaRaEHgCXDH6mgIzURcDk0G4KZeQW0fM5UcbaOtoLoomyvYG/saZ1DLUz9QxqJZxpGYrDvszUkfot9SGFPk2oBns30FTmpBWUPHJ6NQMKE6jD8hCeT6E8IKTRc0SYgvqOuu3T839RS6zF+4FuO1f/JikvwhWpru59XlLoqxOiH9HbnMMzlicDziOgkOg+YukV6fqYej+G9guovwPXKZWMTmK4FlR72ojcgsuH3BKR23D5kNsichcuH3JXRO7B5UPuaSRip6RzP74Llw/fFTnfg8uHvCci78PlQ94XkQdw+ZAHIvJLuHzIL0XkDbh8yBsi8hZcPuQtEdmDy4fsich9uHzIfRF5HS4f8rpG1s/UKVw50UmFWXkVylUeaCkyqLkqyneNrKMPey1gTg9qsPKs7sBfP7YToNOkBns9YNwd1WDlkbcNNtKPlW3RTVpNfNibInYHRoAfuyNiP1fPa7CfB8y0FzVYea7tQjs/Vra+t+HOj70tYu9AyY+V16i7UOPH3g1YMSY12D0Re0+9rMGGWP1pDVa2+12wK36svE71oL0fG2JN5zVY2Z4egAfjx8qr1QOo9WMfiNiH6nUN9qGI/QKsux/7RcAK+7YGa9bY87SCjMgfSWDGNlHrl7MSSxOg1hf4Z+XakpFvHEO9hBmVmBFhjkXEdonYDkTslojdYLmK0o4W5O/KXLolohuIiMu1CUszsf2wbI+lLADRKRGdJUSTR4rv2vTlhLwLUyMhZ+XKhaWQPuWl/cZSosdDs+U1iLsVBI/tZzTyL1O0hBEUaqqJ2rNyjWdkRPdNiFcUvZleGh4yblZaBRf1WkTFHlQsot54UG9E1NyDmouoEw/qRETZme/iDgNGgNU/vosF3fEIYB+5/orAK7gKq85NmKMRjJ898ALvU81d+Nul2Fu6miTDaB7XScxyPK5Y4imUFmoN6m1U2KH4OqMZloBk3PKujvHxDnMbCz3n2Aqflit5VGZMwumkJM+opIPeYkTzqR2dW1RzSt4dl9rhb5bz3pTa4a+Txk/Ji+dSO/xMSz87g+w9je2dAduF2TTR2rfltjQ4/8I0TPk8rbpocfGtHusxg/Ret6S/o9/MzhneyxaVWD+23I5G4fSvqPSvDQ2r58LRczsq6D2x12tKUeuejHXca8ttZchpFR1rOexd2zeDbYb6zZhyOxp74HFtUcy9cMptR++k7I0tt6NxoDjveUqevCm3ozGie9aHLbejgdmWvo7zbbmtZUcNcOxsy22t+piywJgD4jHPNdYrmpKfNNfUUvIPmrM1rs+/uo5hzuZJGSM0U7K+bT2duFzLmiUy/kICVm3WUg70L+aOD1alsVCbYnzFMswq6/sqHbvGo+Z3QYsRzH7eA5By5hlIaHISaL0zoLghRl3VnhncpojDUXK0hDrUtTPRW7R8OWtUrXtKtVJcZntr9XhI9rqgsTchn3CXNCvpYbf2DddRlDS0W9GQTK+N7t7q+VrV/rqImywhJuVIG9COEO+kNcepPq13HR1f1Ls8M7h4z8eOX8w2H2lrgzFPTrYIZWni6bYzeSS3DtfVy8rmuPlZRG8U7dUJWY2UdqQKMQo12WL2xhd0b2nv054c8mAaA3iPkaYyUbxrhll0zKdHZFFdeyvxRn2ZDB2XC7K6xh43o0cOeuRBt49xtmDFuAOlHsQM+3DXC4hyzpe6yknjU/WLcnc0pzfYHNFnFQtpaLC9SSoWsinKflah8grQOBo4Sg+nsUzH4A9XKMlRv08eG7tWLf9F2rk1+9t9GuP1o7k+EzMkrpvENaJZw7u6fLfMgSVYeJ9skv/a3Evk14Yj2lCJ6xOHM+tlTDv+CUWwE/KMM5pt0uyotnbzU8tPDKc9ZfbOcTc7JwsZkf2LYH3KaUxG9OOeHTA76GwRMrKRIXYnLb0bn6+TimPM+nGp4lMNdrwlZMvmxN/QdWdXQWORIwZeB06XxrbRyS75gglxnWrrbud28+qDSHtOwh0lTNGOlUvE/2P6bX7MOFlbGRGoYXwDhbZ1vveRU8yCOurTKt9sg0xbV8qPShmeaKnt+mdl+qgiWYciLpQHV+shcB7QPfPCUTIluYuVNryONmVzkfJkSY/Y2yOK4tnuj/QKjHJfplVyjebcIY2SEYyCWRlFmLZSFnmZbzOvKvUw2sX/hbrVdVVrSDFSNoPLGpLy+wlFa66UGYxqHr8vaDb5tT5datXMZ0xj8diZy19B7Yfw28ht7sPoxBWrcI3GAFOwd1YjXBOttAjjda3Cy4xMQ8veW352TJpWbs1Z4mu2bjbGPmlNZY9GzWudtTDls9B47tB4HqjDHu01Wi2aemOJnoqxRU/vVobya8Ot14LyXKQse2QGlQZI6cZSYVSHIlU5xjeotyKtdZFWH2aruxvgzvkQpH+uL8/ur8rVPVI3yLcZkAfG8cuQZmlKPpepbY7UmAJy/kTbV3f2H1INco/JgiJlPseJM4Z3nQZ0nZaS/kyvbDnZeWsRzLmlV7qNsbGHVP7VCvKY5kRB89IgPqEWiZbflSNaskhXHJ8josx/n3wq9juaY2a3tX0nUcWfsPEmzyrLiyOFMelfyrztrESvO078GlFMONfedQy02r9hpMAYk0nwe5YFvSFc5XgngT3amOznqp3iXbyxI9EVknqhfh9gYzjqtWPdHVumx6ZvP4eWqHX71n0tZH5ZMEeJ31l29Pq0qh1rH3WxdH82Wn29ylXvm/QwX+Jr9TGnNm5kYaO8KuZQfRrMhSVqx4UxIVza9aKN/O0kbyMz706FUjatDeVqpoFtzDOKl6RzoIjweXeXvN7cx0I/4hV6MWFdalwjUcJsXK7zA66lxaxUtBQhufXSmpQ561HdemF5uKuGteNsKROygpmScjfc2u3DYSVakbMxTGGg+GRvXZzo0vwULvwdKV+UaDiG5BC74OdeVVvq+js4FfFSlzmzGVEN2oThUgze1/2stmjW0UuHuks/hEM4jxR0LUmf0oraVnamLEvuUg+n/4qswVQlovS2Zfs+uFzknqxyatOflCyc3JtUmW9y2vbFcAjpSZVLOB/e35B6caTMt03t+mCoyz2ocmjDw5xnCHvntnV7Xi6nZn2tcgnlweuA2XkxONwBrI9ZbLsQCzV13si754DW4aiBulkt/td+GD6WU3teodwK+ubsecBb53aJzsyiX9x+zlhuIaO5nmM4z7zsnfWa/PzY/4tavanc6c27p49+qR0DhtdCcT5Ulo7x7iiy8oZSwf0Bnwy5+o/6+zn5q4SXJY06OdpQMvsV9dRMC5ma+fLS1zvzLEQmS6dOpio1G0906WTsltpRN+Bnq/QA254S5W8q+S9i/d/RDqH2iKyHyaZzBuGQ6hLKgtjdtCHd23O0dRLjmV4+49uDGtwT36VaPO97h9rjmd9epW/1X5LwXL+tcjWsRCbLu3x2XsXQg+oOHOeCzPe+EZ2p52wWn0A7Dthj5HNUHCmZr58XhBhSXLgs6YIQZrQ0UY69lGM6k5TU0I4rfRvQCJ/onX7cd8Dz+f0yuxSpX1JdX68OuFJLUu15pHpEmYGY9L8OEdqv1WX4e1mX/ZLurUha0DuoSvTaedZ8EuzUOy7s14wXKQ9mMnUnul1OUb3dPWzOxHZqufCJ92b8qAE/cqTs0tt6QXH3VDXnDucNNOdaJnc/d6xM3pP1gNFsvxwfzfHzSQOvk4D+36pF33Ik3QZZYsq2R7SfNyV6mdbNdZKez1U2521vNkhrvtpkmvZkpR0H5oxk855Apsdd/eznc5BSriapoePOdT6RKZ0WSb2U5Pk5CTgN0Q/ordzXkJ5KVOaiJPOAL5FPAmQ5CaBzJEhzJFIYiZJo+/D0wtrG8v/1sVo42LyysX5l497m2mfX9P8D8r76ifqpugRr32/UZzD+99Q+eRl/VH9Rf+0sOn/o/KnzZ2763jmN+ZGq/Ov87b9Y2kmH</latexit>
  9. Kantorovitch’s Formulation ↵ = Pn i=1 ai xi = Pm

    j=1 bj yj Points (xi)i, (yj)j Weights ai > 0, bj > 0. Pn i=1 ai = Pm j=1 bj = 1 b <latexit sha1_base64="LhlbHqBkrxCDCHirUc/UdkhSooo=">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</latexit> <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Couplings: <latexit 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<latexit 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<latexit 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P j Pi,j = ai <latexit 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<latexit 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<latexit 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<latexit 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P i Pi,j = bj <latexit 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P > 0, P1m = a, P>1n = b <latexit 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