DEEP LEARNING: AI-Anesth 2 – Science To Medicine

Multilayer Perceptron Networkの構築
MLPClassSaturnをもう少し詳しく解析してみる。

まず、Neural Networkの構造を描いてみる。２個のInputニューロンと2個のOutputニューロン、間に20個の隠れ層Neuronという構造である。

2個のInputニューロンから20個の隠れ層ニューロンへの重みw1, w2が20個x2=40個、隠れ層ニューロンのバイアス値b1-20がそれぞれニューロンごとで合計20個、ここまでで合計60個のパラメータ。次に隠れ層20個から2個のOutputニューロンへの重みw3が20個x2=40個と、Output層のバイアス値b2がそれぞれのOutputニューロン(b21, b22)にあり、合計2個で、隠れ層からOutput層には合計42個のパラメータ。全部合わせて総計102個の重み係数＋バイアスパラメータとなる。
MultiLayerNetworkクラスのインスタンスであるmodelに、params()関数を与えると102個のパラメータが単純な横一列の配列で戻される。paramTable()関数を使えば、グループごと[w1：20個、w2:20個、b1-20:20個、w3:20個、b21, b22]にまとめられて戻される。
以下のようにコードを修正するとコンソールにパラメータ中間値が出力され、パラメータ変化を分析できる。

MultiLayerNetwork model = new MultiLayerNetwork(conf);
        model.init();
        System.out.println(model.paramTable()); //パラメータ初期値（テーブル）
        System.out.println(model.params()); //パラメータ初期値
        //model.setListeners(new ScoreIterationListener(1));    //Print score every 10 parameter updates

        for ( int n = 0; n < nEpochs; n++) {
            model.fit( trainIter );
            System.out.println(model.params()); //エポックごとのパラメータ中間値 30段階
        }

        System.out.println(model.summary());
        System.out.println(model.paramTable());　 //パラメータ最終値（テーブル）

MultiLayerNetwork model = new MultiLayerNetwork(conf);

model.init();

System.out.println(model.paramTable()); //パラメータ初期値（テーブル）

System.out.println(model.params()); //パラメータ初期値

//model.setListeners(new ScoreIterationListener(1)); //Print score every 10 parameter updates

for ( int n = 0; n < nEpochs; n++) {

model.fit( trainIter );

System.out.println(model.params()); //エポックごとのパラメータ中間値 30段階

}

System.out.println(model.summary());

System.out.println(model.paramTable());　 //パラメータ最終値（テーブル）

上記のコンソール出力は以下の通り：

o.n.l.f.Nd4jBackend - Loaded [CpuBackend] backend
o.n.n.NativeOpsHolder - Number of threads used for NativeOps: 2
o.n.n.Nd4jBlas - Number of threads used for BLAS: 2
o.n.l.a.o.e.DefaultOpExecutioner - Backend used: [CPU]; OS: [Mac OS X]
o.n.l.a.o.e.DefaultOpExecutioner - Cores: [4]; Memory: [3.6GB];
o.n.l.a.o.e.DefaultOpExecutioner - Blas vendor: [MKL]
o.d.n.m.MultiLayerNetwork - Starting MultiLayerNetwork with WorkspaceModes set to [training: ENABLED; inference: ENABLED], cacheMode set to [NONE]
{0_W=[[    0.6075,   -0.3462,   -0.3778,    0.2016,   -0.3619,    0.0079,   -0.1621,   -0.0570,   -0.1800,    0.2769,    0.3980,   -0.1610,   -0.4054,    0.3921,   -0.4874,    0.0676,    0.5184,   -0.3940,    0.1001,   -0.0699], 
 [   -0.2595,    0.1405,    0.2820,    0.3897,   -0.9650,    0.0377,    0.0548,   -0.3151,    0.2252,    0.0146,    0.6966,   -0.3013,   -0.2327,    0.2102,    0.0408,   -0.1887,   -0.0686,    0.1658,    0.1481,    0.4032]], 0_b=[[         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0]], 1_W=[[    0.2367,   -0.3284], 
 [   -0.5487,    0.2360], 
 [    0.6404,    0.0237], 
 [   -0.1906,   -0.4099], 
 [   -0.0716,    0.2596], 
 [   -0.2307,   -0.2039], 
 [   -0.3095,    0.0487], 
 [    0.3670,   -0.4921], 
 [   -0.2990,   -0.0390], 
 [   -0.0005,    0.3827], 
 [   -0.1261,    0.6093], 
 [    0.3013,   -0.2682], 
 [    0.2553,   -0.0227], 
 [   -0.0464,    0.1790], 
 [    0.1783,   -0.3751], 
 [    0.4470,   -0.7521], 
 [   -0.0244,   -0.1032], 
 [   -0.3861,   -0.2370], 
 [    0.1981,    0.0719], 
 [    0.0737,    0.0921]], 1_b=[[         0,         0]]}
[[    0.6075,   -0.2595,   -0.3462,    0.1405,   -0.3778,    0.2820,    0.2016,    0.3897,   -0.3619,   -0.9650,    0.0079,    0.0377,   -0.1621,    0.0548,   -0.0570,   -0.3151,   -0.1800,    0.2252,    0.2769,    0.0146,    0.3980,    0.6966,   -0.1610,   -0.3013,   -0.4054,   -0.2327,    0.3921,    0.2102,   -0.4874,    0.0408,    0.0676,   -0.1887,    0.5184,   -0.0686,   -0.3940,    0.1658,    0.1001,    0.1481,   -0.0699,    0.4032,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,         0,    0.2367,   -0.5487,    0.6404,   -0.1906,   -0.0716,   -0.2307,   -0.3095,    0.3670,   -0.2990,   -0.0005,   -0.1261,    0.3013,    0.2553,   -0.0464,    0.1783,    0.4470,   -0.0244,   -0.3861,    0.1981,    0.0737,   -0.3284,    0.2360,    0.0237,   -0.4099,    0.2596,   -0.2039,    0.0487,   -0.4921,   -0.0390,    0.3827,    0.6093,   -0.2682,   -0.0227,    0.1790,   -0.3751,   -0.7521,   -0.1032,   -0.2370,    0.0719,    0.0921,         0,         0]]
[[    0.5585,   -0.1634,   -0.4435,    0.1016,   -0.3025,    0.3131,    0.1956,    0.4011,   -0.3673,   -1.0402,    0.0070,    0.0369,   -0.2070,    0.0362,   -0.0639,   -0.1426,   -0.2124,    0.2114,    0.3158,   -0.0423,    0.4215,    0.6576,   -0.1263,   -0.2008,   -0.3742,   -0.1986,    0.4119,    0.1860,   -0.4167,    0.0856,    0.0159,    0.0730,    0.5127,   -0.0604,   -0.4135,    0.1573,    0.0946,    0.1559,   -0.0713,    0.4027,    0.0003,   -0.0125,    0.0084,    0.0065,    0.0016,   -0.0007,   -0.0050,   -0.0120,   -0.0046,   -0.0045,   -0.0198,   -0.0076,   -0.0020,   -0.0046,    0.0033,   -0.0134,   -0.0002,   -0.0032,    0.0035,   -0.0005,    0.1372,   -0.5856,    0.6097,   -0.1762,   -0.2716,   -0.2293,   -0.3273,    0.3071,   -0.3101,   -0.0282,   -0.1023,    0.2388,    0.1785,   -0.0590,    0.1192,    0.4130,   -0.0858,   -0.4265,    0.2029,    0.0790,   -0.2289,    0.2730,    0.0543,   -0.4244,    0.4597,   -0.2053,    0.0665,   -0.4322,   -0.0278,    0.4103,    0.5855,   -0.2057,    0.0541,    0.1916,   -0.3160,   -0.7180,   -0.0418,   -0.1965,    0.0670,    0.0867,    0.0171,   -0.0171]]
[[    0.5480,   -0.1280,   -0.4503,    0.1206,   -0.2847,    0.3191,    0.2012,    0.4087,   -0.3388,   -1.0269,    0.0054,    0.0364,   -0.2097,    0.0470,   -0.1000,   -0.1196,   -0.2189,    0.2096,    0.3176,   -0.0660,    0.4139,    0.6291,   -0.1303,   -0.1893,   -0.3676,   -0.1931,    0.4127,    0.1727,   -0.4066,    0.0820,    0.0157,    0.1879,    0.5085,   -0.0564,   -0.4135,    0.1619,    0.0965,    0.1609,   -0.0718,    0.4022,    0.0143,   -0.0528,    0.0337,    0.0196,   -0.0293,   -0.0019,   -0.0234,    0.0128,   -0.0164,   -0.0234,   -0.0531,    0.0076,    0.0026,   -0.0162,    0.0240,    0.0195,   -0.0022,   -0.0141,    0.0105,   -0.0008,    0.1141,   -0.5892,    0.6010,   -0.1584,   -0.2723,   -0.2281,   -0.3287,    0.2942,   -0.3127,   -0.0291,   -0.0709,    0.2316,    0.1747,   -0.0495,    0.1089,    0.3985,   -0.0949,   -0.4336,    0.2101,    0.0832,   -0.2058,    0.2765,    0.0631,   -0.4421,    0.4603,   -0.2064,    0.0679,   -0.4193,   -0.0252,    0.4113,    0.5541,   -0.1985,    0.0579,    0.1821,   -0.3057,   -0.7035,   -0.0327,   -0.1895,    0.0599,    0.0825,    0.1066,   -0.1066]]
[[    0.5485,   -0.1280,   -0.4377,    0.1865,   -0.2852,    0.2886,    0.2074,    0.3995,   -0.3093,   -0.9788,    0.0041,    0.0372,   -0.2038,    0.0773,   -0.1231,   -0.1596,   -0.2166,    0.2276,    0.3121,   -0.0589,    0.4041,    0.6440,   -0.1382,   -0.2143,   -0.3677,   -0.1987,    0.4100,    0.1770,   -0.4106,    0.0513,    0.0463,    0.1759,    0.5061,   -0.0530,   -0.4095,    0.1794,    0.0993,    0.1564,   -0.0720,    0.4022,    0.0304,   -0.0925,    0.0589,    0.0326,   -0.0677,   -0.0029,   -0.0420,    0.0523,   -0.0277,   -0.0431,   -0.0808,    0.0312,    0.0090,   -0.0272,    0.0471,    0.0632,   -0.0049,   -0.0257,    0.0174,   -0.0011,    0.1187,   -0.5931,    0.5834,   -0.1656,   -0.2026,   -0.2294,   -0.3298,    0.3004,   -0.3242,   -0.0235,   -0.0816,    0.2444,    0.1927,   -0.0483,    0.1083,    0.3859,   -0.0891,   -0.4406,    0.2076,    0.0643,   -0.2104,    0.2804,    0.0807,   -0.4349,    0.3906,   -0.2052,    0.0690,   -0.4255,   -0.0137,    0.4056,    0.5647,   -0.2113,    0.0400,    0.1809,   -0.3050,   -0.6910,   -0.0384,   -0.1825,    0.0623,    0.1014,    0.2065,   -0.2065]]
[[    0.5424,   -0.1270,   -0.4375,    0.2047,   -0.2849,    0.2771,    0.2042,    0.3982,   -0.2935,   -0.9620,    0.0035,    0.0376,   -0.2035,    0.0863,   -0.1281,   -0.1749,   -0.2159,    0.2346,    0.3184,   -0.0579,    0.4135,    0.6439,   -0.1395,   -0.2239,   -0.3672,   -0.2003,    0.4134,    0.1776,   -0.4109,    0.0409,    0.0534,    0.1720,    0.5063,   -0.0522,   -0.4095,    0.1836,    0.0972,    0.1560,   -0.0723,    0.4021,    0.0443,   -0.1281,    0.0824,    0.0454,   -0.0945,   -0.0038,   -0.0581,    0.0879,   -0.0389,   -0.0583,   -0.1076,    0.0518,    0.0153,   -0.0368,    0.0683,    0.1159,   -0.0070,   -0.0367,    0.0243,   -0.0021,    0.1102,   -0.5975,    0.5782,   -0.1682,   -0.1786,   -0.2299,   -0.3316,    0.3037,   -0.3294,   -0.0285,   -0.0906,    0.2496,    0.1980,   -0.0556,    0.1084,    0.3838,   -0.0970,   -0.4445,    0.2065,    0.0570,   -0.2019,    0.2849,    0.0859,   -0.4323,    0.3666,   -0.2047,    0.0708,   -0.4288,   -0.0086,    0.4107,    0.5737,   -0.2166,    0.0346,    0.1883,   -0.3052,   -0.6888,   -0.0306,   -0.1786,    0.0634,    0.1087,    0.2942,   -0.2942]]
[[    0.5352,   -0.1210,   -0.4555,    0.1933,   -0.2778,    0.2773,    0.1991,    0.4009,   -0.2911,   -0.9725,    0.0030,    0.0376,   -0.2114,    0.0820,   -0.1177,   -0.1598,   -0.2195,    0.2347,    0.3281,   -0.0643,    0.4276,    0.6354,   -0.1320,   -0.2153,   -0.3641,   -0.1964,    0.4183,    0.1756,   -0.4030,    0.0465,    0.0535,    0.1752,    0.5074,   -0.0531,   -0.4150,    0.1792,    0.0943,    0.1576,   -0.0728,    0.4018,    0.0559,   -0.1571,    0.1031,    0.0577,   -0.1122,   -0.0048,   -0.0711,    0.1179,   -0.0491,   -0.0706,   -0.1330,    0.0682,    0.0207,   -0.0456,    0.0860,    0.1716,   -0.0092,   -0.0464,    0.0309,   -0.0037,    0.0971,   -0.6064,    0.5769,   -0.1661,   -0.2021,   -0.2300,   -0.3358,    0.3000,   -0.3330,   -0.0375,   -0.0949,    0.2444,    0.1881,   -0.0636,    0.1032,    0.3879,   -0.1089,   -0.4511,    0.2073,    0.0555,   -0.1888,    0.2937,    0.0872,   -0.4344,    0.3901,   -0.2046,    0.0750,   -0.4251,   -0.0050,    0.4197,    0.5780,   -0.2114,    0.0445,    0.1962,   -0.3000,   -0.6930,   -0.0186,   -0.1720,    0.0626,    0.1102,    0.3683,   -0.3683]]
[[    0.5316,   -0.1191,   -0.4635,    0.1903,   -0.2763,    0.2733,    0.1955,    0.4016,   -0.2857,   -0.9770,    0.0027,    0.0377,   -0.2149,    0.0811,   -0.1127,   -0.1535,   -0.2198,    0.2378,    0.3335,   -0.0649,    0.4372,    0.6326,   -0.1280,   -0.2133,   -0.3629,   -0.1948,    0.4208,    0.1764,   -0.3998,    0.0490,    0.0572,    0.1668,    0.5080,   -0.0533,   -0.4175,    0.1775,    0.0924,    0.1580,   -0.0732,    0.4021,    0.0665,   -0.1830,    0.1218,    0.0690,   -0.1293,   -0.0056,   -0.0827,    0.1489,   -0.0584,   -0.0821,   -0.1558,    0.0844,    0.0258,   -0.0541,    0.1025,    0.2257,   -0.0119,   -0.0554,    0.0372,   -0.0053,    0.0920,   -0.6133,    0.5771,   -0.1654,   -0.2116,   -0.2303,   -0.3390,    0.3018,   -0.3366,   -0.0430,   -0.1023,    0.2443,    0.1847,   -0.0697,    0.1033,    0.3938,   -0.1150,   -0.4551,    0.2077,    0.0520,   -0.1837,    0.3007,    0.0870,   -0.4351,    0.3996,   -0.2043,    0.0782,   -0.4269,   -0.0014,    0.4252,    0.5855,   -0.2112,    0.0480,    0.2024,   -0.3000,   -0.6988,   -0.0126,   -0.1680,    0.0623,    0.1137,    0.4373,   -0.4373]]
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[[    0.5063,   -0.1055,   -0.5816,    0.2142,   -0.2511,    0.1754,    0.1840,    0.3978,   -0.1251,   -1.0607,   -0.0037,    0.0411,   -0.2676,    0.0963,   -0.0161,   -0.0185,   -0.2423,    0.3059,    0.3818,   -0.1090,    0.5199,    0.6179,   -0.1063,   -0.1766,   -0.3516,   -0.1894,    0.4528,    0.1873,   -0.3522,    0.0635,    0.0171,    0.0302,    0.5219,   -0.0615,   -0.4542,    0.1864,    0.0808,    0.1582,   -0.0923,    0.4147,    0.1490,   -0.4052,    0.2825,    0.1827,   -0.2837,   -0.0133,   -0.1836,    0.5571,   -0.1399,   -0.1993,   -0.3624,    0.2430,    0.0601,   -0.1444,    0.2560,    0.9427,   -0.0525,   -0.1409,    0.1004,   -0.0307,    0.0681,   -0.7375,    0.5805,   -0.1318,   -0.3265,   -0.2367,   -0.3957,    0.4370,   -0.4133,   -0.1117,   -0.2058,    0.2745,    0.1509,   -0.1423,    0.1241,    0.6710,   -0.1733,   -0.5273,    0.2271,   -0.0098,   -0.1598,    0.4249,    0.0836,   -0.4687,    0.5145,   -0.1979,    0.1349,   -0.5621,    0.0753,    0.4939,    0.6889,   -0.2415,    0.0817,    0.2749,   -0.3209,   -0.9760,    0.0458,   -0.0958,    0.0429,    0.1755,    1.0242,   -1.0242]]
[[    0.5057,   -0.1060,   -0.5848,    0.2145,   -0.2507,    0.1726,    0.1834,    0.3972,   -0.1206,   -1.0637,   -0.0038,    0.0413,   -0.2691,    0.0964,   -0.0156,   -0.0184,   -0.2432,    0.3079,    0.3828,   -0.1099,    0.5226,    0.6194,   -0.1052,   -0.1745,   -0.3513,   -0.1892,    0.4540,    0.1887,   -0.3509,    0.0639,    0.0179,    0.0304,    0.5224,   -0.0612,   -0.4553,    0.1864,    0.0803,    0.1579,   -0.0928,    0.4153,    0.1503,   -0.4095,    0.2855,    0.1850,   -0.2868,   -0.0134,   -0.1855,    0.5674,   -0.1415,   -0.2019,   -0.3665,    0.2466,    0.0605,   -0.1464,    0.2588,    0.9598,   -0.0536,   -0.1426,    0.1017,   -0.0315,    0.0679,   -0.7407,    0.5809,   -0.1316,   -0.3307,   -0.2369,   -0.3972,    0.4427,   -0.4154,   -0.1134,   -0.2100,    0.2753,    0.1495,   -0.1448,    0.1247,    0.6807,   -0.1747,   -0.5290,    0.2273,   -0.0117,   -0.1596,    0.4280,    0.0832,   -0.4689,    0.5187,   -0.1977,    0.1364,   -0.5678,    0.0775,    0.4955,    0.6932,   -0.2422,    0.0832,    0.2775,   -0.3215,   -0.9858,    0.0472,   -0.0940,    0.0426,    0.1775,    1.0347,   -1.0347]]
[[    0.5051,   -0.1064,   -0.5878,    0.2147,   -0.2506,    0.1694,    0.1828,    0.3966,   -0.1159,   -1.0667,   -0.0039,    0.0414,   -0.2705,    0.0965,   -0.0151,   -0.0183,   -0.2440,    0.3099,    0.3838,   -0.1108,    0.5253,    0.6209,   -0.1041,   -0.1726,   -0.3511,   -0.1890,    0.4551,    0.1900,   -0.3496,    0.0644,    0.0187,    0.0306,    0.5229,   -0.0608,   -0.4564,    0.1865,    0.0799,    0.1576,   -0.0933,    0.4160,    0.1516,   -0.4136,    0.2882,    0.1872,   -0.2897,   -0.0136,   -0.1874,    0.5774,   -0.1431,   -0.2045,   -0.3704,    0.2499,    0.0608,   -0.1484,    0.2614,    0.9763,   -0.0547,   -0.1443,    0.1029,   -0.0322,    0.0677,   -0.7437,    0.5813,   -0.1314,   -0.3347,   -0.2371,   -0.3985,    0.4483,   -0.4175,   -0.1150,   -0.2141,    0.2760,    0.1480,   -0.1473,    0.1253,    0.6902,   -0.1761,   -0.5307,    0.2276,   -0.0136,   -0.1594,    0.4310,    0.0827,   -0.4691,    0.5227,   -0.1974,    0.1377,   -0.5734,    0.0795,    0.4972,    0.6973,   -0.2429,    0.0846,    0.2800,   -0.3221,   -0.9952,    0.0485,   -0.0923,    0.0424,    0.1793,    1.0446,   -1.0446]]

==========================================================================================================================================================================================================================================================
LayerName (LayerType)                   nIn,nOut  TotalParams ParamsShape                             
==========================================================================================================================================================================================================================================================
layer0 (DenseLayer)                     2,20        60        W:{2,20}, b:{1,20}                      
layer1 (OutputLayer)                    20,2        42        W:{20,2}, b:{1,2}                       
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
            Total Parameters:  102
        Trainable Parameters:  102
           Frozen Parameters:  0
==========================================================================================================================================================================================================================================================

{0_W=[[    0.5051,   -0.5878,   -0.2506,    0.1828,   -0.1159,   -0.0039,   -0.2705,   -0.0151,   -0.2440,    0.3838,    0.5253,   -0.1041,   -0.3511,    0.4551,   -0.3496,    0.0187,    0.5229,   -0.4564,    0.0799,   -0.0933], 
 [   -0.1064,    0.2147,    0.1694,    0.3966,   -1.0667,    0.0414,    0.0965,   -0.0183,    0.3099,   -0.1108,    0.6209,   -0.1726,   -0.1890,    0.1900,    0.0644,    0.0306,   -0.0608,    0.1865,    0.1576,    0.4160]], 0_b=[[    0.1516,   -0.4136,    0.2882,    0.1872,   -0.2897,   -0.0136,   -0.1874,    0.5774,   -0.1431,   -0.2045,   -0.3704,    0.2499,    0.0608,   -0.1484,    0.2614,    0.9763,   -0.0547,   -0.1443,    0.1029,   -0.0322]], 1_W=[[    0.0677,   -0.1594], 
 [   -0.7437,    0.4310], 
 [    0.5813,    0.0827], 
 [   -0.1314,   -0.4691], 
 [   -0.3347,    0.5227], 
 [   -0.2371,   -0.1974], 
 [   -0.3985,    0.1377], 
 [    0.4483,   -0.5734], 
 [   -0.4175,    0.0795], 
 [   -0.1150,    0.4972], 
 [   -0.2141,    0.6973], 
 [    0.2760,   -0.2429], 
 [    0.1480,    0.0846], 
 [   -0.1473,    0.2800], 
 [    0.1253,   -0.3221], 
 [    0.6902,   -0.9952], 
 [   -0.1761,    0.0485], 
 [   -0.5307,   -0.0923], 
 [    0.2276,    0.0424], 
 [   -0.0136,    0.1793]], 1_b=[[    1.0446,   -1.0446]]}
Evaluate model....


========================Evaluation Metrics========================
 # of classes:    2
 Accuracy:        1.0000
 Precision:       1.0000
 Recall:          1.0000
 F1 Score:        1.0000
Precision, recall & F1: reported for positive class (class 1 - "1") only


=========================Confusion Matrix=========================
  0  1
-------
 48  0 | 0 = 0
  0 52 | 1 = 1

Confusion matrix format: Actual (rowClass) predicted as (columnClass) N times
==================================================================
****************Example finished********************

100

101

102

103

104

105

106

107

108

109

110

111

112

113

o.n.l.f.Nd4jBackend - Loaded [CpuBackend] backend

o.n.n.NativeOpsHolder - Number of threads used for NativeOps: 2

o.n.n.Nd4jBlas - Number of threads used for BLAS: 2

o.n.l.a.o.e.DefaultOpExecutioner - Backend used: [CPU]; OS: [Mac OS X]

o.n.l.a.o.e.DefaultOpExecutioner - Cores: [4]; Memory: [3.6GB];

o.n.l.a.o.e.DefaultOpExecutioner - Blas vendor: [MKL]

o.d.n.m.MultiLayerNetwork - Starting MultiLayerNetwork with WorkspaceModes set to [training: ENABLED; inference: ENABLED], cacheMode set to [NONE]

{0_W=[[ 0.6075, -0.3462, -0.3778, 0.2016, -0.3619, 0.0079, -0.1621, -0.0570, -0.1800, 0.2769, 0.3980, -0.1610, -0.4054, 0.3921, -0.4874, 0.0676, 0.5184, -0.3940, 0.1001, -0.0699],

[ -0.2595, 0.1405, 0.2820, 0.3897, -0.9650, 0.0377, 0.0548, -0.3151, 0.2252, 0.0146, 0.6966, -0.3013, -0.2327, 0.2102, 0.0408, -0.1887, -0.0686, 0.1658, 0.1481, 0.4032]], 0_b=[[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 1_W=[[ 0.2367, -0.3284],

[ -0.5487, 0.2360],

[ 0.6404, 0.0237],

[ -0.1906, -0.4099],

[ -0.0716, 0.2596],

[ -0.2307, -0.2039],

[ -0.3095, 0.0487],

[ 0.3670, -0.4921],

[ -0.2990, -0.0390],

[ -0.0005, 0.3827],

[ -0.1261, 0.6093],

[ 0.3013, -0.2682],

[ 0.2553, -0.0227],

[ -0.0464, 0.1790],

[ 0.1783, -0.3751],

[ 0.4470, -0.7521],

[ -0.0244, -0.1032],

[ -0.3861, -0.2370],

[ 0.1981, 0.0719],

[ 0.0737, 0.0921]], 1_b=[[ 0, 0]]}

[[ 0.6075, -0.2595, -0.3462, 0.1405, -0.3778, 0.2820, 0.2016, 0.3897, -0.3619, -0.9650, 0.0079, 0.0377, -0.1621, 0.0548, -0.0570, -0.3151, -0.1800, 0.2252, 0.2769, 0.0146, 0.3980, 0.6966, -0.1610, -0.3013, -0.4054, -0.2327, 0.3921, 0.2102, -0.4874, 0.0408, 0.0676, -0.1887, 0.5184, -0.0686, -0.3940, 0.1658, 0.1001, 0.1481, -0.0699, 0.4032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2367, -0.5487, 0.6404, -0.1906, -0.0716, -0.2307, -0.3095, 0.3670, -0.2990, -0.0005, -0.1261, 0.3013, 0.2553, -0.0464, 0.1783, 0.4470, -0.0244, -0.3861, 0.1981, 0.0737, -0.3284, 0.2360, 0.0237, -0.4099, 0.2596, -0.2039, 0.0487, -0.4921, -0.0390, 0.3827, 0.6093, -0.2682, -0.0227, 0.1790, -0.3751, -0.7521, -0.1032, -0.2370, 0.0719, 0.0921, 0, 0]]

[[ 0.5585, -0.1634, -0.4435, 0.1016, -0.3025, 0.3131, 0.1956, 0.4011, -0.3673, -1.0402, 0.0070, 0.0369, -0.2070, 0.0362, -0.0639, -0.1426, -0.2124, 0.2114, 0.3158, -0.0423, 0.4215, 0.6576, -0.1263, -0.2008, -0.3742, -0.1986, 0.4119, 0.1860, -0.4167, 0.0856, 0.0159, 0.0730, 0.5127, -0.0604, -0.4135, 0.1573, 0.0946, 0.1559, -0.0713, 0.4027, 0.0003, -0.0125, 0.0084, 0.0065, 0.0016, -0.0007, -0.0050, -0.0120, -0.0046, -0.0045, -0.0198, -0.0076, -0.0020, -0.0046, 0.0033, -0.0134, -0.0002, -0.0032, 0.0035, -0.0005, 0.1372, -0.5856, 0.6097, -0.1762, -0.2716, -0.2293, -0.3273, 0.3071, -0.3101, -0.0282, -0.1023, 0.2388, 0.1785, -0.0590, 0.1192, 0.4130, -0.0858, -0.4265, 0.2029, 0.0790, -0.2289, 0.2730, 0.0543, -0.4244, 0.4597, -0.2053, 0.0665, -0.4322, -0.0278, 0.4103, 0.5855, -0.2057, 0.0541, 0.1916, -0.3160, -0.7180, -0.0418, -0.1965, 0.0670, 0.0867, 0.0171, -0.0171]]

[[ 0.5480, -0.1280, -0.4503, 0.1206, -0.2847, 0.3191, 0.2012, 0.4087, -0.3388, -1.0269, 0.0054, 0.0364, -0.2097, 0.0470, -0.1000, -0.1196, -0.2189, 0.2096, 0.3176, -0.0660, 0.4139, 0.6291, -0.1303, -0.1893, -0.3676, -0.1931, 0.4127, 0.1727, -0.4066, 0.0820, 0.0157, 0.1879, 0.5085, -0.0564, -0.4135, 0.1619, 0.0965, 0.1609, -0.0718, 0.4022, 0.0143, -0.0528, 0.0337, 0.0196, -0.0293, -0.0019, -0.0234, 0.0128, -0.0164, -0.0234, -0.0531, 0.0076, 0.0026, -0.0162, 0.0240, 0.0195, -0.0022, -0.0141, 0.0105, -0.0008, 0.1141, -0.5892, 0.6010, -0.1584, -0.2723, -0.2281, -0.3287, 0.2942, -0.3127, -0.0291, -0.0709, 0.2316, 0.1747, -0.0495, 0.1089, 0.3985, -0.0949, -0.4336, 0.2101, 0.0832, -0.2058, 0.2765, 0.0631, -0.4421, 0.4603, -0.2064, 0.0679, -0.4193, -0.0252, 0.4113, 0.5541, -0.1985, 0.0579, 0.1821, -0.3057, -0.7035, -0.0327, -0.1895, 0.0599, 0.0825, 0.1066, -0.1066]]

[[ 0.5485, -0.1280, -0.4377, 0.1865, -0.2852, 0.2886, 0.2074, 0.3995, -0.3093, -0.9788, 0.0041, 0.0372, -0.2038, 0.0773, -0.1231, -0.1596, -0.2166, 0.2276, 0.3121, -0.0589, 0.4041, 0.6440, -0.1382, -0.2143, -0.3677, -0.1987, 0.4100, 0.1770, -0.4106, 0.0513, 0.0463, 0.1759, 0.5061, -0.0530, -0.4095, 0.1794, 0.0993, 0.1564, -0.0720, 0.4022, 0.0304, -0.0925, 0.0589, 0.0326, -0.0677, -0.0029, -0.0420, 0.0523, -0.0277, -0.0431, -0.0808, 0.0312, 0.0090, -0.0272, 0.0471, 0.0632, -0.0049, -0.0257, 0.0174, -0.0011, 0.1187, -0.5931, 0.5834, -0.1656, -0.2026, -0.2294, -0.3298, 0.3004, -0.3242, -0.0235, -0.0816, 0.2444, 0.1927, -0.0483, 0.1083, 0.3859, -0.0891, -0.4406, 0.2076, 0.0643, -0.2104, 0.2804, 0.0807, -0.4349, 0.3906, -0.2052, 0.0690, -0.4255, -0.0137, 0.4056, 0.5647, -0.2113, 0.0400, 0.1809, -0.3050, -0.6910, -0.0384, -0.1825, 0.0623, 0.1014, 0.2065, -0.2065]]

[[ 0.5424, -0.1270, -0.4375, 0.2047, -0.2849, 0.2771, 0.2042, 0.3982, -0.2935, -0.9620, 0.0035, 0.0376, -0.2035, 0.0863, -0.1281, -0.1749, -0.2159, 0.2346, 0.3184, -0.0579, 0.4135, 0.6439, -0.1395, -0.2239, -0.3672, -0.2003, 0.4134, 0.1776, -0.4109, 0.0409, 0.0534, 0.1720, 0.5063, -0.0522, -0.4095, 0.1836, 0.0972, 0.1560, -0.0723, 0.4021, 0.0443, -0.1281, 0.0824, 0.0454, -0.0945, -0.0038, -0.0581, 0.0879, -0.0389, -0.0583, -0.1076, 0.0518, 0.0153, -0.0368, 0.0683, 0.1159, -0.0070, -0.0367, 0.0243, -0.0021, 0.1102, -0.5975, 0.5782, -0.1682, -0.1786, -0.2299, -0.3316, 0.3037, -0.3294, -0.0285, -0.0906, 0.2496, 0.1980, -0.0556, 0.1084, 0.3838, -0.0970, -0.4445, 0.2065, 0.0570, -0.2019, 0.2849, 0.0859, -0.4323, 0.3666, -0.2047, 0.0708, -0.4288, -0.0086, 0.4107, 0.5737, -0.2166, 0.0346, 0.1883, -0.3052, -0.6888, -0.0306, -0.1786, 0.0634, 0.1087, 0.2942, -0.2942]]

[[ 0.5352, -0.1210, -0.4555, 0.1933, -0.2778, 0.2773, 0.1991, 0.4009, -0.2911, -0.9725, 0.0030, 0.0376, -0.2114, 0.0820, -0.1177, -0.1598, -0.2195, 0.2347, 0.3281, -0.0643, 0.4276, 0.6354, -0.1320, -0.2153, -0.3641, -0.1964, 0.4183, 0.1756, -0.4030, 0.0465, 0.0535, 0.1752, 0.5074, -0.0531, -0.4150, 0.1792, 0.0943, 0.1576, -0.0728, 0.4018, 0.0559, -0.1571, 0.1031, 0.0577, -0.1122, -0.0048, -0.0711, 0.1179, -0.0491, -0.0706, -0.1330, 0.0682, 0.0207, -0.0456, 0.0860, 0.1716, -0.0092, -0.0464, 0.0309, -0.0037, 0.0971, -0.6064, 0.5769, -0.1661, -0.2021, -0.2300, -0.3358, 0.3000, -0.3330, -0.0375, -0.0949, 0.2444, 0.1881, -0.0636, 0.1032, 0.3879, -0.1089, -0.4511, 0.2073, 0.0555, -0.1888, 0.2937, 0.0872, -0.4344, 0.3901, -0.2046, 0.0750, -0.4251, -0.0050, 0.4197, 0.5780, -0.2114, 0.0445, 0.1962, -0.3000, -0.6930, -0.0186, -0.1720, 0.0626, 0.1102, 0.3683, -0.3683]]

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[[ 0.5051, -0.1064, -0.5878, 0.2147, -0.2506, 0.1694, 0.1828, 0.3966, -0.1159, -1.0667, -0.0039, 0.0414, -0.2705, 0.0965, -0.0151, -0.0183, -0.2440, 0.3099, 0.3838, -0.1108, 0.5253, 0.6209, -0.1041, -0.1726, -0.3511, -0.1890, 0.4551, 0.1900, -0.3496, 0.0644, 0.0187, 0.0306, 0.5229, -0.0608, -0.4564, 0.1865, 0.0799, 0.1576, -0.0933, 0.4160, 0.1516, -0.4136, 0.2882, 0.1872, -0.2897, -0.0136, -0.1874, 0.5774, -0.1431, -0.2045, -0.3704, 0.2499, 0.0608, -0.1484, 0.2614, 0.9763, -0.0547, -0.1443, 0.1029, -0.0322, 0.0677, -0.7437, 0.5813, -0.1314, -0.3347, -0.2371, -0.3985, 0.4483, -0.4175, -0.1150, -0.2141, 0.2760, 0.1480, -0.1473, 0.1253, 0.6902, -0.1761, -0.5307, 0.2276, -0.0136, -0.1594, 0.4310, 0.0827, -0.4691, 0.5227, -0.1974, 0.1377, -0.5734, 0.0795, 0.4972, 0.6973, -0.2429, 0.0846, 0.2800, -0.3221, -0.9952, 0.0485, -0.0923, 0.0424, 0.1793, 1.0446, -1.0446]]

==========================================================================================================================================================================================================================================================

LayerName (LayerType) nIn,nOut TotalParams ParamsShape

layer0 (DenseLayer) 2,20 60 W:{2,20}, b:{1,20}

layer1 (OutputLayer) 20,2 42 W:{20,2}, b:{1,2}

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Total Parameters: 102

Trainable Parameters: 102

Frozen Parameters: 0

{0_W=[[ 0.5051, -0.5878, -0.2506, 0.1828, -0.1159, -0.0039, -0.2705, -0.0151, -0.2440, 0.3838, 0.5253, -0.1041, -0.3511, 0.4551, -0.3496, 0.0187, 0.5229, -0.4564, 0.0799, -0.0933],

[ -0.1064, 0.2147, 0.1694, 0.3966, -1.0667, 0.0414, 0.0965, -0.0183, 0.3099, -0.1108, 0.6209, -0.1726, -0.1890, 0.1900, 0.0644, 0.0306, -0.0608, 0.1865, 0.1576, 0.4160]], 0_b=[[ 0.1516, -0.4136, 0.2882, 0.1872, -0.2897, -0.0136, -0.1874, 0.5774, -0.1431, -0.2045, -0.3704, 0.2499, 0.0608, -0.1484, 0.2614, 0.9763, -0.0547, -0.1443, 0.1029, -0.0322]], 1_W=[[ 0.0677, -0.1594],

[ -0.7437, 0.4310],

[ 0.5813, 0.0827],

[ -0.1314, -0.4691],

[ -0.3347, 0.5227],

[ -0.2371, -0.1974],

[ -0.3985, 0.1377],

[ 0.4483, -0.5734],

[ -0.4175, 0.0795],

[ -0.1150, 0.4972],

[ -0.2141, 0.6973],

[ 0.2760, -0.2429],

[ 0.1480, 0.0846],

[ -0.1473, 0.2800],

[ 0.1253, -0.3221],

[ 0.6902, -0.9952],

[ -0.1761, 0.0485],

[ -0.5307, -0.0923],

[ 0.2276, 0.0424],

[ -0.0136, 0.1793]], 1_b=[[ 1.0446, -1.0446]]}

Evaluate model....

========================Evaluation Metrics========================

# of classes: 2

Accuracy: 1.0000

Precision: 1.0000

Recall: 1.0000

F1 Score: 1.0000

Precision, recall & F1: reported for positive class (class 1 - "1") only

=========================Confusion Matrix=========================

0 1

-------

48 0 | 0 = 0

0 52 | 1 = 1

Confusion matrix format: Actual (rowClass) predicted as (columnClass) N times

==================================================================

****************Example finished********************

パラメータ初期値、中間値、最終値をエクセルに取り込んで、パラメータの変化をグラフにしてみると以下の通り：

このようにザビエルの初期値で選ばれた重み係数は、初期値からあまり変化していないが、バイアス値はゼロから始まり大きく変化していることがわかる。重みの初期値は、一般的にはガウス分布からランダムに生成したものを初期値とし、バイアス初期値はゼロとするのが通常のようだ。
重みの初期値はその後の学習に大きく影響する。
以下のようにconvolution層でもいろいろな方法がある。
http://arakan-pgm-ai.hatenablog.com/entry/2017/09/02/003000
ーーーーーーーーーーーーーーーーーーーーーーーー
Uniform：-1.0?1.0の一様乱数で初期化
UniformAffineGlorot：一様乱数にXavier Glorot提案の係数をかけて初期化
Normal：平均0.0、分散1.0であるガウス乱数で初期化
NormalAffineHeForward：ガウス乱数にKaiming He提案の係数をかけて初期化（Forward Case）
NormalAffineHeBackward：ガウス乱数にKaiming He提案の係数をかけて初期化（Backward Case）
NormalAffineGlorot：ガウス乱数にXavier Glorot提案の係数をかけて初期化（デフォルト）
Constant：全ての要素を一定値（1.0）で初期化
ーーーーーーーーーーーーーーーーーーーーーーーー
上記のうち、説明に「Xavier Glorot提案」と書かれている種類が「Xavierの初期値」と呼ばれるもの。「ザビエXavierの初期値」は層のノードの数によって、作用させる係数を変化させる。たとえば、前層から渡されるノード数がn個であるときには、標準偏差√nで割る。

Science To Medicine

Just My Daily Study Note by ts.anesth.kpum