(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

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(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼

.

(ii) Verify that the Wasserstein distance between πX1 and πX2 is given by

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(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

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(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

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(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

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Add Answer to: (i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers

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(i) Verify that the Kullback-Leibler divergence of two univariate Gaussians Xi ∼ N(¯xi, σ2 i ), i = 1, 2, is given by DKL(πX1 ||πX2) = ∫ R ln πX1(x) πX2(x) πX1(x)dx = 1 2 ( σ−2 2 σ2 1 + σ−2 2 (¯x2 − ¯x1)2 − 1 − 2 log σ1 σ2 ) . (ii) Verify that the Wassers