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A Schrödinger Tour of Data Sciences

Gabriel Peyré
September 16, 2021

A Schrödinger Tour of Data Sciences

Talk at "Schrödinger's problem and Optimal Transport" conference in Lisboa.

Gabriel Peyré

September 16, 2021
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  1. A Schrödinger Tour


    of


    Data Sciences
    Gabriel Peyré
    É C O L E N O R M A L E
    S U P É R I E U R E
    RESEARCH UNIVERSITY PARIS
    Joint work with:
    François-Xavier


    Vialard
    Lénaic


    Chizat
    Flavier


    Léger
    Pierre


    Roussillon

    View full-size slide

  2. Density Fitting and Generative Models

    Parametric model: ✓ 7! ↵✓
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    Observations:
    def.
    = 1
    n
    Pn
    i=1 xi
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  3. Density Fitting and Generative Models

    Parametric model: ✓ 7! ↵✓
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    Observations:
    def.
    = 1
    n
    Pn
    i=1 xi
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    Density fitting:
    Maximum
    likelihood (MLE)
    d↵✓(x) = ⇢✓(x)dx
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  4. Density Fitting and Generative Models

    Parametric model: ✓ 7! ↵✓
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    Observations:
    def.
    = 1
    n
    Pn
    i=1 xi
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    Density fitting:
    Maximum
    likelihood (MLE)
    d↵✓(x) = ⇢✓(x)dx
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    g✓
    X
    Z

    Generative model fit:
    ! MLE undefined.
    ! Need a weaker metric.
    ↵✓ = g✓,]⇣
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  5. Schrödinger
    and kernels
    dimensionality
    Curse of
    meets Schrödinger
    Gromov
    X
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