변분 오토인코더

["\ubcc0\ubd84 \uc624\ud1a0\uc778\ucf54\ub354(VAE)\ub294 \uc0dd\uc131 \ubaa8\ub378\ub9c1\uc5d0 \uc0ac\uc6a9\ub418\ub294 \uc778\uacf5 \uc2e0\uacbd\ub9dd\uc758 \ud55c \uc720\ud615\uc73c\ub85c, 2013\ub144 Diederik P. Kingma\uc640 Max Welling\uc774 \uc18c\uac1c\ud588\ub2e4. \uc774\ub294 \ud655\ub960\uc801 \uadf8\ub798\ud53d \ubaa8\ub378 \ubc0f \ubcc0\ubd84 \ubca0\uc774\uc988 \ubc29\ubc95 \uacc4\uc5f4\uc5d0 \uc18d\ud55c\ub2e4. VAE\ub294 \uace0\ucc28\uc6d0 \ub370\uc774\ud130(\uc608: \uc774\ubbf8\uc9c0)\ub97c \uc800\ucc28\uc6d0 \uc7a0\uc7ac \uacf5\uac04\uc73c\ub85c \uc778\ucf54\ub529\ud55c \ub2e4\uc74c \ud574\ub2f9 \uc7a0\uc7ac \uacf5\uac04\uc758 \uc0d8\ud50c\uc744 \ub2e4\uc2dc \ub370\uc774\ud130\ub85c \ub514\ucf54\ub529\ud558\ub294 \ubc29\ubc95\uc744 \ud559\uc2b5\ud558\uba70, \uc774\ub97c \ud1b5\ud574 \ud6c8\ub828 \ub370\uc774\ud130\uc758 \uae30\ubcf8 \ud655\ub960 \ubd84\ud3ec\ub97c \ud6a8\uacfc\uc801\uc73c\ub85c \ud559\uc2b5\ud55c\ub2e4.\n\n## \uad6c\uc870 \ubc0f \uc791\ub3d9 \uac1c\uc694\n\nVAE\ub294 \uc778\ucf54\ub354\uc640 \ub514\ucf54\ub354\ub77c\ub294 \ub450 \uac00\uc9c0 \uc8fc\uc694 \uc2e0\uacbd\ub9dd \uad6c\uc131 \uc694\uc18c\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4. \uc778\ucf54\ub354\ub294 \uac01 \uc785\ub825 \ub370\uc774\ud130 \ud3ec\uc778\ud2b8 \\(x\\)\ub97c \uc7a0\uc7ac \ubcc0\uc218 \\(z\\)\uc5d0 \ub300\ud55c \ubd84\ud3ec(\uc77c\ubc18\uc801\uc73c\ub85c \ud3c9\uade0 \\(\\mu(x)\\)\uc640 \ubd84\uc0b0 \\(\\sigma^2(x)\\)\ub97c \uac16\ub294 \ub2e4\ubcc0\ub7c9 \uac00\uc6b0\uc2dc\uc548 \ubd84\ud3ec)\ub85c \ub9e4\ud551\ud55c\ub2e4. \ub2e8\uc77c \ud3ec\uc778\ud2b8\ub97c \uc778\ucf54\ub529\ud558\ub294 \ub300\uc2e0 \ud655\ub960 \ubd84\ud3ec\uc5d0 \ub300\ud55c \ub9e4\uac1c\ubcc0\uc218\ub97c \ucd9c\ub825\ud558\ubbc0\ub85c, \ubaa8\ub378\uc774 \ubd88\ud655\uc2e4\uc131\uc744 \ud45c\ud604\ud558\uace0 \ub370\uc774\ud130\uc758 \uc5f0\uc18d\uc801 \ubcc0\uc774\ub97c \ud3ec\ucc29\ud560 \uc218 \uc788\ub2e4. \ub514\ucf54\ub354\ub294 \uc774 \uc7a0\uc7ac \ubd84\ud3ec\uc5d0\uc11c \uc0d8\ud50c \\(z\\)\ub97c \uac00\uc838\uc640 \uc6d0\ub798 \ub370\uc774\ud130 \uacf5\uac04\uc73c\ub85c \ub9e4\ud551\ud558\uc5ec \uc7ac\uad6c\uc131 \\(\\hat{x}\\)\uc744 \uc0dd\uc131\ud55c\ub2e4.\n\nVAE\uc758 \ud6c8\ub828 \ubaa9\ud45c\ub294 \ub370\uc774\ud130\uc758 \ub85c\uadf8 \uc6b0\ub3c4\uc5d0 \ub300\ud55c \uc99d\uac70 \ud558\ud55c(ELBO)\uc744 \ucd5c\ub300\ud654\ud558\ub294 \uac83\uc774\ub2e4. \uc5ec\uae30\uc5d0\ub294 \ub450 \uac00\uc9c0 \ud56d\uc774 \ud3ec\ud568\ub41c\ub2e4: \ub514\ucf54\ub354\uac00 \uc7a0\uc7ac \uc0d8\ud50c\uc5d0\uc11c \uc785\ub825\uc744 \uc5bc\ub9c8\ub098 \uc798 \uc7ac\uad6c\uc131\ud558\ub294\uc9c0 \uce21\uc815\ud558\ub294 \uc7ac\uad6c\uc131 \uc190\uc2e4\uacfc, \uc778\ucf54\ub354\uc758 \ucd9c\ub825 \ubd84\ud3ec\uc640 \\(z\\)\uc5d0 \ub300\ud55c \uc0ac\uc804 \ubd84\ud3ec(\uc77c\ubc18\uc801\uc73c\ub85c \ud45c\uc900 \uc815\uaddc \ubd84\ud3ec) \uc0ac\uc774\uc758 \ucfe8\ubc31-\ub77c\uc774\ube14\ub7ec \ubc1c\uc0b0(KL \ubc1c\uc0b0)\uc774\ub2e4. KL \ud56d\uc740 \uc815\uaddc\ud654 \uc5ed\ud560\uc744 \ud558\uc5ec \uc7a0\uc7ac \uacf5\uac04\uc774 \ub9e4\ub044\ub7fd\uace0 \uc5f0\uc18d\uc801\uc774\ub3c4\ub85d \uc7a5\ub824\ud55c\ub2e4.\n\n\ubb34\uc791\uc704 \uc0d8\ud50c\ub9c1 \ub2e8\uacc4\ub97c \ud1b5\ud55c \uc5ed\uc804\ud30c\ub97c \uac00\ub2a5\ud558\uac8c \ud558\uae30 \uc704\ud574, VAE\ub294 \uc7ac\ub9e4\uac1c\ubcc0\uc218\ud654 \ud2b8\ub9ad\uc744 \uc0ac\uc6a9\ud55c\ub2e4: \\(q_\\phi(z|x)\\)\uc5d0\uc11c \uc9c1\uc811 \\(z\\)\ub97c \uc0d8\ud50c\ub9c1\ud558\ub294 \ub300\uc2e0, \ubaa8\ub378\uc740 \ubcf4\uc870 \uc7a1\uc74c \ubcc0\uc218 \\(\\epsilon \\sim \\mathcal{N}(0, I)\\)\ub97c \uc0d8\ud50c\ub9c1\ud558\uace0 \\(z = \\mu(x) + \\sigma(x) \\odot \\epsilon\\)\uc744 \uacc4\uc0b0\ud55c\ub2e4. \uc774\ub294 \uc0d8\ud50c\ub9c1 \uc5f0\uc0b0\uc774 \uc778\ucf54\ub354 \ub9e4\uac1c\ubcc0\uc218\uc5d0 \ub300\ud574 \ubbf8\ubd84 \uac00\ub2a5\ud558\uac8c \ub9cc\ub4e0\ub2e4.\n\n## \uc218\ud559\uc801 \uacf5\uc2dd\ud654\n\n\ud655\ub960\uc801 \uad00\uc810\uc5d0\uc11c \ubaa9\ud45c\ub294 \uad00\uce21 \ub370\uc774\ud130\uc758 \uc8fc\ubcc0 \uc6b0\ub3c4 \\(p_\\theta(x) = \\int p_\\theta(x|z) p(z) dz\\)\ub97c \ucd5c\ub300\ud654\ud558\ub294 \uac83\uc774\ub2e4. \uadf8\ub7ec\ub098 \uc774 \uc801\ubd84\uc740 \uc885\uc885 \ub2e4\ub8e8\uae30 \uc5b4\ub835\ub2e4. VAE\ub294 \uadfc\uc0ac \uc0ac\ud6c4 \ubd84\ud3ec \\(q_\\phi(z|x)\\)\ub97c \ub3c4\uc785\ud558\uace0 ELBO\ub97c \uc720\ub3c4\ud55c\ub2e4:\n\n\\[\n\\log p_\\theta(x) \\geq \\mathbb{E}_{q_\\phi(z|x)}[\\log p_\\theta(x|z)] - D_{KL}(q_\\phi(z|x) \\| p(z))\n\\]\n\n\uccab \ubc88\uc9f8 \ud56d\uc740 \uc7ac\uad6c\uc131 \uc6b0\ub3c4\uc774\uace0, \ub450 \ubc88\uc9f8 \ud56d\uc740 KL \ubc1c\uc0b0\uc774\ub2e4. \uc7ac\ub9e4\uac1c\ubcc0\uc218\ud654 \ud2b8\ub9ad\uc744 \uc0ac\uc6a9\ud558\uba74 \ub450 \ud56d \ubaa8\ub450 \ub9e4\uac1c\ubcc0\uc218 \\(\\theta\\)\uc640 \\(\\phi\\)\uc5d0 \ub300\ud574 \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4.\n\n\uc0ac\uc804 \ubd84\ud3ec \\(p(z)\\)\uc640 \uc6b0\ub3c4 \\(p_\\theta(x|z)\\)\uc758 \uc120\ud0dd\uc740 \ub370\uc774\ud130 \uc720\ud615\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c4\ub2e4. \uc5f0\uc18d \ub370\uc774\ud130\uc758 \uacbd\uc6b0 \uac00\uc6b0\uc2dc\uc548 \uc6b0\ub3c4\uac00 \uc77c\ubc18\uc801\uc774\uace0, \uc774\uc9c4 \ub370\uc774\ud130(\uc608: \uc774\uc9c4\ud654\ub41c MNIST)\uc758 \uacbd\uc6b0 \ubca0\ub974\ub204\uc774 \uc6b0\ub3c4\uac00 \uc0ac\uc6a9\ub41c\ub2e4. \uc7a0\uc7ac \uc0ac\uc804 \ubd84\ud3ec\ub294 \uc77c\ubc18\uc801\uc73c\ub85c \ud45c\uc900 \uc815\uaddc \ubd84\ud3ec\uc774\ub2e4.\n\n## \ud6c8\ub828 \uc5ed\ud559\n\nVAE\ub294 ELBO\uc5d0 \ub300\ud55c \ud655\ub960\uc801 \uacbd\uc0ac \ud558\uac15\ubc95\uc73c\ub85c \ud6c8\ub828\ub41c\ub2e4. \uc7ac\uad6c\uc131 \uc190\uc2e4\uc740 \ub514\ucf54\ub354\uac00 \uc785\ub825\uc5d0 \uac00\uae4c\uc6b4 \ucd9c\ub825\uc744 \uc0dd\uc131\ud558\ub3c4\ub85d \uc7a5\ub824\ud558\uace0, KL \ubc1c\uc0b0\uc740 \uc778\ucf54\ub354\uc758 \uc0ac\ud6c4 \ubd84\ud3ec\ub97c \uc0ac\uc804 \ubd84\ud3ec\ub85c \ubc00\uc5b4\ub0b8\ub2e4. \uc774\ub294 \uc808\ucda9\uc744 \ub9cc\ub4e0\ub2e4: \uc7ac\uad6c\uc131\uc5d0 \ub108\ubb34 \ub9ce\uc740 \uac00\uc911\uce58\ub97c \ub450\uba74 \uacfc\uc801\ud569\uacfc \ub2e8\ud3b8\ud654\ub41c \uc7a0\uc7ac \uacf5\uac04\uc774 \ubc1c\uc0dd\ud558\uace0, KL\uc5d0 \ub108\ubb34 \ub9ce\uc740 \uac00\uc911\uce58\ub97c \ub450\uba74 \uc7a0\uc7ac \ubcc0\uc218\uac00 \uc815\ubcf4\ub97c \uc81c\uacf5\ud558\uc9c0 \ubabb\ud558\uace0 \ubaa8\ub378\uc774 \\(z\\)\ub97c \ubb34\uc2dc\ud558\ub294 \uc0ac\ud6c4 \ubd95\uad34 \ud604\uc0c1\uc774 \ubc1c\uc0dd\ud55c\ub2e4. KL \uc5b4\ub2d0\ub9c1\uc774\ub098 \ubca0\ud0c0-VAE\uc640 \uac19\uc740 \ub2e4\uc591\ud55c \uae30\ubc95\uc774 \uc774\ub7ec\ud55c \uade0\ud615\uc744 \uc870\uc815\ud55c\ub2e4.\n\n## \ubcc0\ud615 \ubc0f \ud655\uc7a5\n\nVAE\uc758 \uc5ec\ub7ec \ubcc0\ud615\uc774 \uac1c\ubc1c\ub418\uc5c8\ub2e4. \ubca0\ud0c0-VAE\ub294 KL \ud56d\uc5d0 \uac00\uc911\uce58\ub97c \uc8fc\ub294 \ud558\uc774\ud37c\ud30c\ub77c\ubbf8\ud130 \\(\\beta\\)\ub97c \ub3c4\uc785\ud558\uc5ec \ub354 \ubd84\ub9ac\ub41c \ud45c\ud604\uc744 \uac00\ub2a5\ud558\uac8c \ud55c\ub2e4. \uc870\uac74\ubd80 VAE(CVAE)\ub294 \ud074\ub798\uc2a4 \ub808\uc774\ube14\uc774\ub098 \uae30\ud0c0 \uc870\uac74 \uc815\ubcf4\ub97c \uc778\ucf54\ub354\uc640 \ub514\ucf54\ub354 \ubaa8\ub450\uc5d0 \ud1b5\ud569\ud55c\ub2e4. \ubca1\ud130 \uc591\uc790\ud654 VAE(VQ-VAE)\ub294 \uc774\uc0b0 \uc7a0\uc7ac \ucf54\ub4dc\ub97c \uc0ac\uc6a9\ud558\uba70, \uace0\ucda9\uc2e4\ub3c4 \uc774\ubbf8\uc9c0 \uc0dd\uc131\uc5d0 \ud2b9\ud788 \ud6a8\uacfc\uc801\uc774\ub2e4. \ub2e4\ub978 \ud655\uc7a5\uc5d0\ub294 \uacc4\uce35\uc801 VAE, \uc815\uaddc\ud654 \ud750\ub984, \uc801\ub300\uc801 \uc624\ud1a0\uc778\ucf54\ub354\uac00 \ud3ec\ud568\ub41c\ub2e4.\n\n## \uc751\uc6a9 \ubd84\uc57c\n\nVAE\ub294 \ub2e4\uc591\ud55c \uc601\uc5ed\uc5d0\uc11c \ub110\ub9ac \uc801\uc6a9\ub418\uc5c8\ub2e4. \ucef4\ud4e8\ud130 \ube44\uc804\uc5d0\uc11c\ub294 \uc774\ubbf8\uc9c0 \uc0dd\uc131, \ub178\uc774\uc988 \uc81c\uac70, \uc778\ud398\uc778\ud305\uc5d0 \uc0ac\uc6a9\ub41c\ub2e4. \uc790\uc5f0\uc5b4 \ucc98\ub9ac\uc5d0\uc11c\ub294 \ud14d\uc2a4\ud2b8 \uc0dd\uc131 \ubc0f \ubb38\uc7a5 \ud45c\ud604 \ud559\uc2b5\uc5d0 \uc801\uc6a9\ub418\uc5c8\ub2e4. \uc758\ub8cc \uc601\uc0c1\uc5d0\uc11c\ub294 \uc774\uc0c1 \ud0d0\uc9c0\uc5d0 \uc0ac\uc6a9\ub41c\ub2e4. VAE\ub294 \ub610\ud55c \uc2e0\uc57d \ubc1c\uacac \ubc0f \ubd84\uc790 \uc124\uacc4\uc5d0 \uc0ac\uc6a9\ub418\ub294 \uac83\uacfc \uac19\uc740 \ub354 \ubcf5\uc7a1\ud55c \uc0dd\uc131 \ubaa8\ub378\uc758 \uad6c\uc131 \uc694\uc18c \uc5ed\ud560\uc744 \ud55c\ub2e4.\n\n## \ub2e4\ub978 \uc0dd\uc131 \ubaa8\ub378\uacfc\uc758 \uad00\uacc4\n\nVAE\ub294 \uc0dd\uc131\uc801 \uc801\ub300 \uc2e0\uacbd\ub9dd(GAN) \ubc0f \uc790\uae30\ud68c\uadc0 \ubaa8\ub378\uacfc \ud568\uaed8 \ub525 \uc0dd\uc131 \ubaa8\ub378\uc758 \uc138 \uac00\uc9c0 \uc8fc\uc694 \uc720\ud615 \uc911 \ud558\ub098\uc774\ub2e4. \uc2e4\uc81c \uc0d8\ud50c\uacfc \uac00\uc9dc \uc0d8\ud50c\uc744 \uad6c\ubcc4\ud558\ub294 \ud310\ubcc4\uae30\ub97c \ud6c8\ub828\ud558\ub294 GAN\uacfc \ub2ec\ub9ac, VAE\ub294 \uc6b0\ub3c4 \uae30\ubc18 \ubaa9\ud45c\ub97c \ucd5c\uc801\ud654\ud558\ubbc0\ub85c \ud6c8\ub828\uc774 \ub354 \uc548\uc815\uc801\uc774\uc9c0\ub9cc \uc885\uc885 \ub354 \ud750\ub9bf\ud55c \ucd9c\ub825\uc744 \uc0dd\uc131\ud55c\ub2e4. PixelCNN\uacfc \uac19\uc740 \uc790\uae30\ud68c\uadc0 \ubaa8\ub378\uc740 \uacb0\ud569 \ubd84\ud3ec\ub97c \uc870\uac74\ubd80 \ubd84\ud3ec\uc758 \uacf1\uc73c\ub85c \ubaa8\ub378\ub9c1\ud558\uc9c0\ub9cc \uc800\ucc28\uc6d0 \uc7a0\uc7ac \uacf5\uac04\uc774 \ubd80\uc871\ud558\ub2e4. VAE\ub294 \ub2e4\ub8e8\uae30 \uc26c\uc6b4 \ucd94\ub860\uacfc \ud45c\ud604\ub825 \uc788\ub294 \uc0dd\uc131 \uc0ac\uc774\uc758 \uade0\ud615\uc744 \uc81c\uacf5\ud55c\ub2e4.\n\n## \ud55c\uacc4 \ubc0f \ud604\uc7ac \uc5f0\uad6c\n\n\uc131\uacf5\uc5d0\ub3c4 \ubd88\uad6c\ud558\uace0 VAE\uc5d0\ub294 \uc54c\ub824\uc9c4 \ud55c\uacc4\uac00 \uc788\ub2e4. \uac00\uc6b0\uc2dc\uc548 \uc6b0\ub3c4 \uac00\uc815\uc73c\ub85c \uc778\ud574 \uc0dd\uc131\ub41c \uc0d8\ud50c\uc740 \uc885\uc885 GAN\uc758 \uc0d8\ud50c\ubcf4\ub2e4 \ub35c \uc120\uba85\ud558\ub2e4. \uc7a0\uc7ac \uacf5\uac04\uc774 \uc644\uc804\ud788 \ubd84\ub9ac\ub418\uc9c0 \uc54a\uc744 \uc218 \uc788\uc73c\uba70, \uc0ac\ud6c4 \ubd95\uad34\ub294 \uc5ec\uc804\ud788 \ud65c\ubc1c\ud55c \uc5f0\uad6c \uc601\uc5ed\uc774\ub2e4. \ucd5c\uadfc \uc5f0\uad6c\ub294 \uc0ac\uc804 \ubc0f \uc0ac\ud6c4 \ubd84\ud3ec\uc758 \ud45c\ud604\ub825\uc744 \uac1c\uc120\ud558\uace0, \ub354 \uc720\uc5f0\ud55c \ubd84\ud3ec\ub97c \uc0ac\uc6a9\ud558\uba70, VAE\ub97c \ub2e4\ub978 \ubaa8\ub378\uacfc \uacb0\ud569\ud558\ub294 \ub370 \ucd08\uc810\uc744 \ub9de\ucd94\uace0 \uc788\ub2e4. \uc774 \ubd84\uc57c\ub294 \uacc4\uc18d \uc9c4\ud654\ud558\uace0 \uc788\uc73c\uba70, \uc751\uc6a9 \ubd84\uc57c\ub294 \uac15\ud654 \ud559\uc2b5 \ubc0f \ud45c\ud604 \ud559\uc2b5\uc73c\ub85c \ud655\uc7a5\ub418\uace0 \uc788\ub2e4.\n\n## \uac19\uc774 \ubcf4\uae30\n\n- \uc624\ud1a0\uc778\ucf54\ub354\n- \uc0dd\uc131\uc801 \uc801\ub300 \uc2e0\uacbd\ub9dd\n- \ubca0\uc774\uc988 \ucd94\ub860\n- \uc7a0\uc7ac \ubcc0\uc218 \ubaa8\ub378\n- \uc7ac\ub9e4\uac1c\ubcc0\uc218\ud654 \ud2b8\ub9ad\n- \uc99d\uac70 \ud558\ud55c\n- \ubca0\ud0c0-VAE\n- \uc870\uac74\ubd80 \ubcc0\ubd84 \uc624\ud1a0\uc778\ucf54\ub354\n- \ubca1\ud130 \uc591\uc790\ud654 \ubcc0\ubd84 \uc624\ud1a0\uc778\ucf54\ub354\n- \uc815\uaddc\ud654 \ud750\ub984\n- \ud655\ub960\uc801 \uadf8\ub798\ud53d \ubaa8\ub378\n- \ub525 \ub7ec\ub2dd\n- \ube44\uc9c0\ub3c4 \ud559\uc2b5\n- \ud655\ub960\uc801 \uacbd\uc0ac \ud558\uac15\ubc95\n- \ucfe8\ubc31-\ub77c\uc774\ube14\ub7ec \ubc1c\uc0b0\n- \uac00\uc6b0\uc2dc\uc548 \ubd84\ud3ec\n- \ubca0\ub974\ub204\uc774 \ubd84\ud3ec\n- MNIST \ub370\uc774\ud130\ubca0\uc774\uc2a4\n- \uc774\ubbf8\uc9c0 \uc0dd\uc131\n- \ud45c\ud604 \ud559\uc2b5\n\n## \ucc38\uace0 \ubb38\ud5cc\n\n- Kingma, D. P., & Welling, M. (2013). Auto-Encoding Variational Bayes. arXiv:1312.6114.\n- Doersch, C. (2016). Tutorial on Variational Autoencoders. arXiv:1606.05908.\n- Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational Inference: A Review for Statisticians. Journal of the American Statistical Association.\n- Higgins, I., et al. (2017). beta-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework. ICLR.", true]