{"id":1073,"date":"2025-06-09T10:22:54","date_gmt":"2025-06-09T01:22:54","guid":{"rendered":"https:\/\/naomaeda.jp\/?p=1073"},"modified":"2025-06-22T15:17:58","modified_gmt":"2025-06-22T06:17:58","slug":"%e6%83%85%e5%a0%b1","status":"publish","type":"post","link":"https:\/\/naomaeda.jp\/?p=1073","title":{"rendered":"\u60c5\u5831\u3068\u30e2\u30c7\u30ea\u30f3\u30b0"},"content":{"rendered":"\n<p>\u3053\u308c\u3082\u307e\u3060\u7de8\u96c6\u4e2d\uff08\u5b8c\u5168\u306b\u8da3\u5473\u306e\u9818\u57df\uff09<\/p>\n\n\n\n<p>\u30af\u30ed\u30fc\u30c9\u30fb\u30b7\u30e3\u30ce\u30f3\u306f1948\u5e74\u306b\u767a\u8868\u3057\u305f\u300e\u901a\u4fe1\u306e\u6570\u5b66\u7684\u7406\u8ad6\u300f\u3067\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\uff08entropy\uff09\u3092\u300c\u4e0d\u78ba\u5b9f\u6027\u3001\u9a5a\u304d\u300d\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u3001\u3055\u3089\u306b\u7d50\u5408\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\uff08joint entropy\uff09\u3084\u76f8\u4e92\u60c5\u5831\u91cf\uff08mutual information\uff09\u3092\u5b9a\u5f0f\u5316\u3057\u305f\u3002\u305d\u3057\u3066\u5f7c\u306f\u3001typicality\uff08\u5178\u578b\u6027\uff09\u3001i.i.d.\uff08\u72ec\u7acb\u540c\u5206\u5e03\uff09\u3001LLN\uff08\u5927\u6570\u306e\u6cd5\u5247\uff09\u3092\u7528\u3044\u3066\u30012\u3064\u306e\u5b9a\u7406\u2015\u60c5\u5831\u6e90\u7b26\u53f7\u5316\u5b9a\u7406\uff08source coding theorem\uff09\u3068\u901a\u4fe1\u8def\u7b26\u53f7\u5316\u5b9a\u7406<strong>\uff08<\/strong>channel coding theorem\uff09\u2015\u3092\u8a3c\u660e\u3057\u305f\uff08\u306a\u305c\u82f1\u8a9e\u3092\u65e5\u672c\u8a9e\u306b\u3059\u308b\u3068\u7a81\u7136\u96e3\u3057\u304f\u306a\u308b\u306e\u3060\u308d\u3046&#8230;\uff09\u3002<\/p>\n\n\n\n<p>\u901a\u4fe1\u306f\u60c5\u5831\u6e90\u306b\u3042\u308b\u60c5\u5831\u3092\u7b26\u53f7\u5316\uff08\u30b3\u30fc\u30c9\u5316\uff09\u3057\u3001\u901a\u4fe1\u8def\uff08\u30c1\u30e3\u30cd\u30eb\uff09\u3092\u901a\u3063\u3066\u9001\u3089\u308c\u305f\u60c5\u5831\u3092\u76ee\u7684\u5730\u3067\u518d\u5ea6\u7b26\u53f7\u5316\uff08\u30c7\u30a3\u30b3\u30fc\u30c9\uff09\u3059\u308b\u4f5c\u696d\u306a\u306e\u3060\u304c\u3001\u305d\u306e\u969b\u306b\u3001\u901a\u4fe1\u8def\uff08\u30c1\u30e3\u30cd\u30eb\uff09\u306b\u306f\u30ce\u30a4\u30ba\u304c\u6df7\u3058\u3063\u3066\u3057\u307e\u3046\u3002\uff12\u3064\u306e\u5b9a\u7406\u304c\u793a\u3057\u305f\u306e\u306f\u30af\u30ec\u30d0\u30fc\uff08\u5de7\u5999\uff09\u306a\u30b3\u30fc\u30c9\u3055\u3048\u3042\u308c\u3070\u3001\u60c5\u5831\u6e90\u3092\u5b8c\u5168\u306b\u30b3\u30fc\u30c9\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u30c1\u30e3\u30cd\u30eb\u306b\u30ce\u30a4\u30ba\u304c\u3042\u3063\u3066\u3082\u7406\u8ad6\u4e0a\u5b8c\u5168\u306b\u60c5\u5831\u6e90\u306e\u60c5\u5831\u3092\u76ee\u7684\u5730\u307e\u3067\u901a\u4fe1\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8003\u3048\u65b9\u3092\uff08\u79d1\u5b66\u7684\uff09\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u6587\u8108\u306b\u7f6e\u304d\u63db\u3048\u308b\u306a\u3089\u3070\u3001\u60c5\u5831\u6e90\u3092\u81ea\u7136\u305d\u306e\u3082\u306e\u3001\u3042\u308b\u3044\u306f\u771f\u306e\u5206\u5e03\u3068\u307f\u306a\u3057\u3001\u7b26\u53f7\u5316\uff08\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\uff09\u306f\u30e2\u30c7\u30ea\u30f3\u30b0\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u30e2\u30c7\u30ea\u30f3\u30b0\uff08\u5f97\u3089\u308c\u305f\u60c5\u5831\u304b\u3089\u306e\u4e16\u754c\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\uff09\u306f\u57fa\u672c\u7684\u306b\u306f\u60c5\u5831\u306e\u5727\u7e2e\u3067\u3042\u308b\uff08\u6700\u826f\u306e\u30e2\u30c7\u30eb\u306f\u6700\u3082\u60c5\u5831\u3092\u5727\u7e2e\u3057\u305f\u30e2\u30c7\u30eb\u3067\u3042\u308a\u3001\u6700\u5c0f\u8a18\u8ff0\u9577\uff08minimum description length, MDL\uff09\u3067\u8a18\u8ff0\u3055\u308c\u308b\u30e2\u30c7\u30eb\u3060\u3002\u3053\u306e\u8fba\u308a\u306f<a href=\"https:\/\/naomaeda.jp\/?p=985\">AIC<\/a>\u306a\u3069\u3068\u3082\u30ea\u30f3\u30af\u3057\u3066\u304f\u308b\uff09\u3002\u3053\u306e\u3088\u3046\u306b\u8003\u3048\u308b\u3068\u3001\u3082\u3057\u3053\u306e\u4e16\u754c\u304c\u78ba\u7387\u7684\uff08stochastic\uff09\u306b\u52d5\u3044\u3066\u304a\u308a\u3001\u304b\u3064\u305d\u306e\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u5b8c\u5168\u3067\uff08\u3059\u306a\u308f\u3061\u640d\u5931\u304c\u306a\u3044\uff08lossless\uff09\uff09\u3001\u5341\u5206\u306b\u9577\u3044\u30b9\u30b1\u30fc\u30eb\u3067\u898b\u305f\u3068\u304d\u306b\u306f\uff08\u6975\u9650\u306b\u304a\u3044\u3066\u306f\uff09\u3001\u305d\u306e\u30e2\u30c7\u30eb\u304c\u6301\u3064\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\uff08\uff1d\u4e0d\u78ba\u5b9f\u6027\uff09\u306f\u3001\u81ea\u7136\u304c\u6301\u3064\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u3044\u3046\u4e0b\u9650\uff08lower bound\uff09\u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u3053\u308c\u304c\u60c5\u5831\u6e90\u7b26\u53f7\u5316\u5b9a\u7406\u3060\u3002<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001\u901a\u4fe1\u8def\u7b26\u53f7\u5316\u5b9a\u7406\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u8003\u3048\u308b\u3068\u3001\u901a\u4fe1\u8def\u3092\u81ea\u7136\u3001\u3042\u308b\u3044\u306f\u771f\u306e\u5206\u5e03\u3068\u307f\u306a\u3057\u3001\u5fa9\u53f7\uff08decoding\uff09\u3092\u30e2\u30c7\u30ea\u30f3\u30b0\uff08\u5f97\u3089\u308c\u305f\u60c5\u5831\u304b\u3089\u306e\u4e16\u754c\u306e\u518d\u69cb\u7bc9\uff09\u3068\u8003\u3048\u308b\u306a\u3089\u3070\u3001\u3082\u3057\u5fa9\u53f7\u304c\u5b8c\u5168\uff08lossless\uff09\u3067\u3042\u308c\u3070\u3001\u30c1\u30e3\u30cd\u30eb\u5185\u306b\u30ce\u30a4\u30ba\u304c\u3042\u3063\u305f\u3068\u3057\u3066\u3082\u3001\u79c1\u305f\u3061\u306f\u30c1\u30e3\u30cd\u30eb\u5bb9\u91cf\u3068\u3044\u3046\u4e0a\u9650\uff08upper bound\uff09\u306b\u9054\u3059\u308b\u307e\u3067\u3042\u3089\u3086\u308b\u60c5\u5831\u3092\u5fa9\u5143\u3067\u304d\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u3053\u3053\u3067\u3044\u3046\u30c1\u30e3\u30cd\u30eb\u5bb9\u91cf\u306f\u3001\u3053\u306e\u30a2\u30ca\u30ed\u30b8\u30fc\u3067\u306f\u300c\u81ea\u7136\u304c\u6301\u3064\u60c5\u5831\u91cf\u306e\u4e0a\u9650\uff08\uff1d\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\uff09\u300d\u3068\u540c\u7b49\u306b\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u5b9a\u7406\u306f\u3001\u4eca\u65e5\u306e\u79c1\u305f\u3061\u304b\u3089\u898b\u308b\u3068\u3042\u308b\u610f\u5473\u81ea\u660e\uff08self-evident\uff09\u3067\u3001\u8ad6\u7406\u7684\u771f\u7406\uff08\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\uff09\u306e\u3088\u3046\u306b\u611f\u3058\u3089\u308c\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u81ea\u7136\u754c\u304c\u78ba\u7387\u7684\u3067\u3001\u3082\u3057\u79c1\u305f\u3061\u304c\u81ea\u7136\u754c\u3092\u5b8c\u74a7\u306b\u8a18\u8ff0\uff08\u30e2\u30c7\u30eb\u5316\uff09\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u3057\u305f\u3089\u3001\u79c1\u305f\u3061\u306e\u30e2\u30c7\u30eb\u306e\u6301\u3064\u4e0d\u78ba\u5b9f\u3055\u306f\u81ea\u7136\u754c\u306e\u6301\u3064\u78ba\u7387\uff08\u4e0b\u9650\uff09\u306b\u53ce\u675f\u3059\u308b\u3001\u306a\u3069\u3068\u3044\u3046\u306e\u306f\u5f53\u7136\u306e\u3088\u3046\u306b\u611f\u3058\u3089\u308c\u308b\u3002\u540c\u69d8\u306b\u901a\u4fe1\u304c\u5b8c\u74a7\u3067\u3042\u308c\u3070\u3001\u901a\u4fe1\u306f\u30c1\u30e3\u30cd\u30eb\u306e\u4e0a\u9650\u306b\u53ce\u675f\u3059\u308b\u3001\u3068\u3044\u3046\u306e\u3082\u5f53\u305f\u308a\u524d\u3068\u8a00\u3048\u3070\u5f53\u305f\u308a\u524d\u306e\u3088\u3046\u306b\u611f\u3058\u308b\u3002<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u30b7\u30e3\u30ce\u30f3\u304c\u5049\u5927\u3060\u3063\u305f\u306e\u306f\u3001\u305d\u3046\u3057\u305f\u9650\u754c\u306b\u201c\u7406\u8ad6\u4e0a\u201d\u5230\u9054\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u3001\u78ba\u7387\u7684\u5b58\u5728\u8a3c\u660e\uff08probabilistic existence proof\uff09\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u793a\u3057\u305f\u3053\u3068\u306b\u3042\u308b\u3002\u3064\u307e\u308a\u5f7c\u304c\u5049\u5927\u3060\u3063\u305f\u306e\u306f\u5177\u4f53\u7684\u306a\u30b3\u30fc\u30c9\u3092\u793a\u3059\u3053\u3068\u306a\u304f\u3001\u5de7\u5999\u306b\u8a2d\u8a08\u3055\u308c\u305f\u7b26\u53f7\u306b\u3088\u3063\u3066\u305d\u306e\u9650\u754c\u304c\u9054\u6210\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u3053\u3068\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u305d\u306e\u8a3c\u660e\u306e\u969b\u306b\u306ftypicality\uff08\u5178\u578b\u6027\uff09\u3001i.i.d.\u6027\u3001\u305d\u3057\u3066LLN\uff08\u5927\u6570\u306e\u6cd5\u5247\uff09\u304c\u4f7f\u308f\u308c\u305f\u3002i.i.d.\u306a\u524d\u63d0\u306e\u3082\u3068\u3067\u3001\u9577\u3055\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u3068\u304d\u306b\u306f\u5178\u578b\u7684\u306a\u30d1\u30bf\u30fc\u30f3\u304c\u652f\u914d\u7684\u306b\u306a\u308b\u3002\u4eca\u65e5\u306e\u8996\u70b9\u304b\u3089\u3053\u308c\u3092\u898b\u308b\u3068\u3001\u3053\u308c\u3082\u307e\u305f\u3001\u3042\u308b\u610f\u5473\u3067\u306f\u81ea\u660e\u306a\u6027\u8cea\u306e\u3088\u3046\u306b\u601d\u3048\u308b\u3002\u30cb\u30e5\u30fc\u30c8\u30f3\u304c\u8a00\u3063\u305f\u3088\u3046\u306b\u3001\u79c1\u305f\u3061\u306f\u5de8\u4eba\u306e\u80a9\u306e\u4e0a\u306b\u7acb\u3063\u3066\u3044\u308b\uff08standing on the shoulders of giants\uff09\u3002\u5178\u578b\u7684\uff08typical\uff09\u306a\u5217\uff08sequence\uff09\u3068\u306f\u300c\u671f\u5f85\u3055\u308c\u308b\u901a\u308a\u306e\u3075\u308b\u307e\u3044\u300d\u3092\u3059\u308b\u5217\u306e\u3053\u3068\u3060\u3002<\/p>\n\n\n\n<p>\u305f\u3068\u3048\u3070\u3001\u60c5\u5831\u6e90\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5024\u3092\u51fa\u529b\u3059\u308b\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0 \u3092\u51fa\u3059\u78ba\u7387\u304c 0.6<\/li>\n\n\n\n<li>1 \u3092\u51fa\u3059\u78ba\u7387\u304c 0.4<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u3068\u304d\u3001\u6b21\u306e\u3088\u3046\u306a\u9577\u3044\u30d3\u30c3\u30c8\u5217\u3092\u751f\u6210\u3059\u308b\u3068\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>x\u207f = 010100010010110010\u2026<\/p>\n\n\n\n<p>\u3053\u306e\u5217\u304c\u5178\u578b\u7684\u3067\u3042\u308b\u3068\u306f\u3001\u51fa\u3066\u304f\u308b 0 \u306e\u5272\u5408\u304c\u304a\u304a\u3088\u305d 60%\u30011 \u306e\u5272\u5408\u304c\u304a\u304a\u3088\u305d 40% \u3067\u3042\u308a\u3001\u3064\u307e\u308a\u5b9f\u969b\u306e\u51fa\u73fe\u983b\u5ea6\uff08\u7d4c\u9a13\u7684\u5206\u5e03\uff09\u304c\u60c5\u5831\u6e90\u306e\u78ba\u7387\u3068\u3088\u304f\u4e00\u81f4\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3002\u5404\u78ba\u7387\u304ci.i.d.\u3001\u3064\u307e\u308a\u72ec\u7acb\u3067\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u5168\u304f\u540c\u3058\u78ba\u7387\u5206\u5e03\u306b\u5f93\u3063\u3066\u304a\u308a\u3001\u30b7\u30fc\u30af\u30a8\u30f3\u30b9\u306e\u9577\u3055\u304c\u6975\u9650\u306b\u9054\u3059\u308b\u306a\u3089\u3070\uff08LLN\uff09\u3001\u5f53\u7136\u30b7\u30fc\u30af\u30a8\u30f3\u30b9\u306f\u5178\u578b\u6027\u306b\u8fbf\u308a\u7740\u304f\u3002\u3053\u308c\u306f\u6f38\u8fd1\u7b49\u5206\u5272\u6027\uff08Asymptotic Equipartition Property, 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set\uff09\u3060\u3051\u3060\u3002\u3053\u308c\u306b\u3088\u3063\u3066\u5f7c\u306f\uff12\u3064\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u305f\u3002<\/p>\n\n\n\n<p><a href=\"https:\/\/naomaeda.jp\/?p=1001\">ELBO\u306b\u3057\u3066\u3082MCMC\u306b\u3057\u3066\u3082AIC\u306b\u3057\u3066\u3082<\/a>\u3001\u305d\u3057\u3066\u30b7\u30e3\u30ce\u30f3\u306b\u3057\u3066\u3082\u3001\u6570\u5b66\u8005\u3068\u3044\u3046\u306e\u306f\u672c\u5f53\u306b\u30af\u30ec\u30d0\u30fc\u3060\u3068\u601d\u3046\u3002<\/p>\n\n\n\n<p>\u56e0\u307f\u306b\u3053\u306e\u30b7\u30e3\u30ce\u30f3\u306e\u60c5\u5831\u7406\u8ad6\u306f\u78ba\u7387\u7406\u8ad6\u306e\u5ef6\u9577\u3067\u3042\u308a\u3001\u540c\u3058\u304f\u78ba\u7387\u7406\u8ad6\u306e\u5ef6\u9577\u3067\u3042\u308b\u30d9\u30a4\u30ba\u7d71\u8a08\u5b66\u3068\u76f8\u6027\u304c\u826f\u3044\u3002\u60c5\u5831\u7406\u8ad6\u3068\u30d9\u30a4\u30ba\u7d71\u8a08\u304c\u78ba\u7387\u7406\u8ad6\u306e\u5ef6\u9577\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u305d\u308c\u3089\u306f\u516c\u7406\u7cfb\u304b\u3089\u59cb\u307e\u308b\u6570\u5b66\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3002<a href=\"https:\/\/naomaeda.jp\/?p=601\">\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u3001\u30cd\u30a4\u30de\u30f3\u3001\u30d4\u30a2\u30bd\u30f3\u3089\u306e\u3044\u308f\u3086\u308b\u983b\u5ea6\u4e3b\u7fa9\u7d71\u8a08<\/a>\u3084\u5c24\u5ea6\u4e3b\u7fa9\u306f\u5c24\u5ea6\u306b\u57fa\u3065\u3044\u305f\u9053\u5177\u7684\u306a\u5b58\u5728\u3067\u3042\u308a\u3001\u516c\u7406\u304b\u3089\u5c0e\u304b\u308c\u308b\u6570\u5b66\u3068\u306f\u7570\u306a\u308b\uff08\u5c24\u5ea6\u306f\u78ba\u7387\u306e\u516c\u7406\u3092\u6e80\u305f\u3055\u306a\u3044\u3002\u3055\u3089\u306b\u3044\u3046\u306a\u3089\u3001\u983b\u5ea6\u4e3b\u7fa9\u3082\u5c24\u5ea6\u4e3b\u7fa9\u3082\u8907\u5408\u4eee\u8aac\u3092\u6271\u3048\u306a\u3044\u304c\u3001\u30d9\u30a4\u30ba\u306f\u81ea\u7136\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u3057\u3066\u3055\u3089\u306b\u3044\u3046\u306a\u3089\u3070\u5c24\u5ea6\u4e3b\u7fa9\u306f\u4e00\u4f53\u5168\u4f53\u4f55\u304c\u3057\u305f\u3044\u306e\u304b\u304c\u5168\u304f\u308f\u304b\u3089\u306a\u3044\u307b\u3069\u306b\u610f\u5473\u304c\u4e0d\u660e\u3060\uff09\u3002<a href=\"https:\/\/naomaeda.jp\/?p=1001\">AIC<\/a>\u306f\u983b\u5ea6\u4e3b\u7fa9\u304b\u3089\u59cb\u307e\u3063\u3066\u3044\u308b\u304c\u3001\u60c5\u5831\u7406\u8ad6\u7684\u7d44\u307f\u7acb\u3066\u65b9\u304c\u3055\u308c\u3066\u3044\u308b\u304b\u3089AIC\u306f\u60c5\u5831\u7406\u8ad6\u3084\u30d9\u30a4\u30ba\u3068\u983b\u5ea6\u4e3b\u7fa9\u306e\u6a4b\u6e21\u3057\u3092\u3059\u308b\u3088\u3046\u306a\u5b58\u5728\u3060\u308d\u3046\u3002<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u308c\u3082\u307e\u3060\u7de8\u96c6\u4e2d\uff08\u5b8c\u5168\u306b\u8da3\u5473\u306e\u9818\u57df\uff09 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[&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":735,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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