there exists a measure di↵ering from such that OT" ( , ) < OT" ( , ). Consequently, minimizing the cost OT" (↵, ) with respect to ↵ does not all us to recover ↵ = , but rather drives ↵ towards a “median axis”-like structu of "-localized Fr´ echet means constructed from [FCVP17] – see Figure 1. (a) " = 0.01. (b) " = 0.10. (c) " = 1.00. Figure 1: Entropic bias in the OT" loss. Starting from an arbitrary Gauss sample, the positions of the red dots that make up a model distribution ↵ optimized to fit an empirical distribution (in blue) as we minimize OT" (↵, These registrations are performed in the unit square, with an Earth Move cost C(x, y) = kx yk. 5 " > 0 : in general, there exists a measure di↵ering from such that OT" ( , ) < OT" ( , ). (2) Consequently, minimizing the cost OT" (↵, ) with respect to ↵ does not allow us to recover ↵ = , but rather drives ↵ towards a “median axis”-like structure of "-localized Fr´ echet means constructed from [FCVP17] – see Figure 1. (a) " = 0.01. (b) " = 0.10. (c) " = 1.00. Figure 1: Entropic bias in the OT" loss. Starting from an arbitrary Gaussian sample, the positions of the red dots that make up a model distribution ↵ are optimized to fit an empirical distribution (in blue) as we minimize OT" (↵, ). These registrations are performed in the unit square, with an Earth Mover’s cost C(x, y) = kx yk. 5 " > 0 : in general, there exists a measure di↵ering from such that OT" ( , ) < OT" ( , ). (2) Consequently, minimizing the cost OT" (↵, ) with respect to ↵ does not allow us to recover ↵ = , but rather drives ↵ towards a “median axis”-like structure of "-localized Fr´ echet means constructed from [FCVP17] – see Figure 1. (a) " = 0.01. (b) " = 0.10. (c) " = 1.00. Figure 1: Entropic bias in the OT" loss. Starting from an arbitrary Gaussian sample, the positions of the red dots that make up a model distribution ↵ are optimized to fit an empirical distribution (in blue) as we minimize OT" (↵, ). These registrations are performed in the unit square, with an Earth Mover’s cost C(x, y) = kx yk. 5 Problem: <latexit 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" <latexit 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min ⇡1=↵,⇡2= R X2 d(x, y)pd⇡(x, y) + " KL(⇡|↵ ⌦ ) <latexit 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W" p (↵, ) def. = <latexit 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⇡(") "!0 ! ↵ ⌦ <latexit sha1_base64="iAvjwgilPahhMA7Jt0rycZ4xuuI=">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</latexit> for k(x, y) = d(x, y)p and <latexit sha1_base64="Gp6WNxgbw+WZiDhK1JeM+2KyYQw=">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</latexit> h↵, ik def. = R k(x, y)d↵(x)d (y) <latexit 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W" p (↵, )p "!0 ! h↵, ik <latexit 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Prop.: Kernel norms (MMD): <latexit 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||↵ ||2 k def. = h↵ , ↵ ik Arthur Gretton <latexit 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||↵ ||2 k = 1 n2 X i,i0 k(xi, xi0 ) + 1 m2 X j,j0 k(yj, yj0 ) 2 nm X i,j k(xi, yj) <latexit 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k must be: <latexit sha1_base64="wDht3jJeopX8B4AeU9IOoUl+dQ8=">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</latexit> conditionally positive <latexit 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universal <latexit 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xi ↵ <latexit 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yj