\ub525\ub7ec\ub2dd\uc758 \ubc1c\uc804\uc73c\ub85c \uc778\ud574 \ub9ce\uc740 \ubd84\uc57c\uc5d0\uc11c \uc778\uacf5\uc9c0\ub2a5\uc758 \uc0ac\uc6a9\uc774 \uc99d\uac00\ud558\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \ud30c\uc774\ud1a0\uce58(PyTorch)\ub97c \uc774\uc6a9\ud55c \uc790\uae30 \ud68c\uadc0(AR, AutoRegressive) \ubaa8\ub378\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc124\uba85\ud569\ub2c8\ub2e4. \uc790\uae30 \ud68c\uadc0 \ubaa8\ub378\uc740 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\uc758 \uc608\uce21\uc5d0 \ub110\ub9ac \uc0ac\uc6a9\ub418\ub294 \ud1b5\uacc4\uc801 \ubaa8\ub378\uc785\ub2c8\ub2e4. \uc774 \uac15\uc88c\ub97c \ud1b5\ud574 AR \ubaa8\ub378\uc758 \uac1c\ub150, \ud30c\uc774\ud1a0\uce58\ub97c \ud65c\uc6a9\ud55c \uad6c\ud604 \ubc0f \uad00\ub828 \uc608\uc81c \ucf54\ub4dc\ub97c \ub2e4\ub8f0 \uac83\uc785\ub2c8\ub2e4.<\/p>\n
\uc790\uae30 \ud68c\uadc0(AR) \ubaa8\ub378\uc740 \uacfc\uac70\uc758 \uac12\ub4e4\uc744 \uc0ac\uc6a9\ud558\uc5ec \ud604\uc7ac \uac12\uc744 \uc608\uce21\ud558\ub294 \ud1b5\uacc4\uc801 \ubaa8\ub378\uc785\ub2c8\ub2e4. \uc790\uae30 \ud68c\uadc0 \ubaa8\ub378\uc758 \uae30\ubcf8 \uac00\uc815\uc740 \ud604\uc7ac \uc2dc\uc810\uc758 \uac12\uc774 \uc774\uc804 \uc2dc\uc810\uc758 \uac12\uc758 \uc120\ud615 \uc870\ud569\uc73c\ub85c \ud45c\ud604\ub420 \uc218 \uc788\ub2e4\ub294 \uac83\uc785\ub2c8\ub2e4. \uc774\ub97c \uc218\uc2dd\uc73c\ub85c \ub098\ud0c0\ub0b4\uba74 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
X(t) = c + \u03d5\u2081X(t-1) + \u03d5\u2082X(t-2) + ... + \u03d5\u2096X(t-k) + \u03b5(t)<\/code><\/pre>\n\uc5ec\uae30\uc11c:<\/p>\n
\nX(t)<\/code>: \uc2dc\uc810 t<\/code>\uc758 \uac12<\/li>\nc<\/code>: \uc0c1\uc218\ud56d<\/li>\n\u03d5<\/code>: \uc790\uae30 \ud68c\uadc0 \uacc4\uc218<\/li>\nk<\/code>: \uc0ac\uc6a9\ub41c \uacfc\uac70 \uc2dc\uc810\uc758 \uc218 (\uc8fc\ubb38\ucc28\uc218)<\/li>\n\u03b5(t)<\/code>: \ubc31\uc0c9 \uc7a1\uc74c (\uc608\uce21 \uc624\ucc28)<\/li>\n<\/ul>\nAR \ubaa8\ub378\uc740 \ud2b9\ud788 \uae08\uc735 \ub370\uc774\ud130, \uae30\ud6c4 \ub370\uc774\ud130, \uc2e0\ud638 \ucc98\ub9ac \ub4f1\uc5d0\uc11c \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ub525\ub7ec\ub2dd\uacfc \uacb0\ud569\ud558\uba74 \ub370\uc774\ud130\uc758 \ubcf5\uc7a1\ud55c \ud328\ud134\uc744 \ubaa8\ub378\ub9c1\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
2. \ub525\ub7ec\ub2dd\uc5d0\uc11c\uc758 AR \ubaa8\ub378<\/h2>\n
\ub525\ub7ec\ub2dd\uc5d0\uc11c\ub294 AR \ubaa8\ub378\uc744 \uc2e0\uacbd\ub9dd \uc544\ud0a4\ud14d\ucc98\ub85c \ud655\uc7a5\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc21c\ud658 \uc2e0\uacbd\ub9dd(RNN), \uc7a5\ub2e8\uae30 \uba54\ubaa8\ub9ac \ub124\ud2b8\uc6cc\ud06c(LSTM), \ub610\ub294 \uac8c\uc774\ud2b8 \uc21c\ud658 \uc720\ub2db(GRU)\uc744 \uc0ac\uc6a9\ud558\uc5ec AR \ubaa8\ub378\uc758 \uc131\ub2a5\uc744 \ud5a5\uc0c1\uc2dc\ud0ac \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc2e0\uacbd\ub9dd\uc740 \ube44\uc120\ud615\uc131\uc744 \uc591\uc9c8\uc758 \uc608\uce21\uc744 \ud1b5\ud574 \uc0ac\uc6a9\ud558\uace0, \ub9ce\uc740 \uc591\uc758 \ub370\uc774\ud130\uc5d0\uc11c \ud6c8\ub828\ub418\uc5b4 \ub354 \ud6a8\uacfc\uc801\uc73c\ub85c \ud328\ud134\uc744 \ud559\uc2b5\ud558\uac8c \ub429\ub2c8\ub2e4.<\/p>\n
3. \ud30c\uc774\ud1a0\uce58(PyTorch) \uc18c\uac1c<\/h2>\n
\ud30c\uc774\ud1a0\uce58\ub294 Facebook\uc5d0\uc11c \uac1c\ubc1c\ud55c \uc624\ud508\uc18c\uc2a4 \uba38\uc2e0\ub7ec\ub2dd \ub77c\uc774\ube0c\ub7ec\ub9ac\uc785\ub2c8\ub2e4. \ud30c\uc774\uc36c\uacfc C++\uc5d0\uc11c \uc0ac\uc6a9\ud560 \uc218 \uc788\uc73c\uba70, \uc9c1\uad00\uc801\uc778 \uc778\ud130\ud398\uc774\uc2a4\uc640 \ub3d9\uc801 \uacc4\uc0b0 \uadf8\ub798\ud504 \ub355\ubd84\uc5d0 \uc5f0\uad6c\uc790\uc640 \uac1c\ubc1c\uc790\uc5d0\uac8c \uc778\uae30\uac00 \ub9ce\uc2b5\ub2c8\ub2e4. \ud30c\uc774\ud1a0\uce58\ub294 \ud150\uc11c \uc5f0\uc0b0, \uc790\ub3d9 \ubbf8\ubd84, \ub2e4\uc591\ud55c \ucd5c\uc801\ud654 \uc54c\uace0\ub9ac\uc998\uc744 \uc9c0\uc6d0\ud558\uba70, \ub525\ub7ec\ub2dd \ubaa8\ub378\uc744 \uc27d\uac8c \uad6c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
4. \ud30c\uc774\ud1a0\uce58\ub85c AR \ubaa8\ub378 \uad6c\ud604\ud558\uae30<\/h2>\n
\uc774\uc81c \ud30c\uc774\ud1a0\uce58\ub97c \uc0ac\uc6a9\ud558\uc5ec AR \ubaa8\ub378\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
4.1 \ub370\uc774\ud130 \uc900\ube44<\/h3>\n
AR \ubaa8\ub378\uc744 \uad6c\ud604\ud558\uae30 \uc704\ud574 \uba3c\uc800 \ub370\uc774\ud130\ub97c \uc900\ube44\ud574\uc57c \ud569\ub2c8\ub2e4. \uac04\ub2e8\ud55c \uc608\ub85c, \uc778\uacf5\uc9c0\ub2a5 \ubaa8\ub378\uc758 \uc785\ub825 \ub370\uc774\ud130\ub85c \uc0ac\uc6a9\ud560 \uc218\uce58 \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
import numpy as np\nimport pandas as pd\n\n# \uc608\uc2dc \ub370\uc774\ud130 \uc0dd\uc131\nnp.random.seed(42) # \ub79c\ub364 \uc2dc\ub4dc \uace0\uc815\nn = 1000 # \ub370\uc774\ud130 \ud3ec\uc778\ud2b8 \uc218\ndata = np.zeros(n)\n\n# AR(1) \ud504\ub85c\uc138\uc2a4 \uc0dd\uc131\nfor t in range(1, n):\n data[t] = 0.5 * data[t-1] + np.random.normal(scale=0.1)\n\n# \ub370\uc774\ud130\ud504\ub808\uc784\uc73c\ub85c \ubcc0\ud658\ndf = pd.DataFrame(data, columns=['Value'])\ndf.head()<\/code><\/pre>\n4.2 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130 \uc804\ucc98\ub9ac<\/h3>\n
\uc0dd\uc131\ub41c \ub370\uc774\ud130\ub97c \uc0ac\uc6a9\ud558\uae30 \uc704\ud574 \uc785\ub825 \uc2dc\ud000\uc2a4\uc640 \ud0c0\uac9f \uac12\uc744 \uc0dd\uc131\ud569\ub2c8\ub2e4. \uacfc\uac70 k<\/code>\uac1c\uc758 \uac12\uc744 \uae30\ubc18\uc73c\ub85c \ud604\uc7ac \uac12\uc744 \uc608\uce21\ud558\ub294 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud560 \uac83\uc785\ub2c8\ub2e4.<\/p>\ndef create_dataset(data, k=1):\n X, y = [], []\n for i in range(len(data)-k):\n X.append(data[i:(i+k)])\n y.append(data[i+k])\n return np.array(X), np.array(y)\n\n# \ub370\uc774\ud130\uc14b \uc0dd\uc131\nk = 5 # \uc2dc\ud000\uc2a4 \uae38\uc774\nX, y = create_dataset(df['Value'].values, k)\nX.shape, y.shape<\/code><\/pre>\n4.3 \ub370\uc774\ud130\uc14b\uc744 \ud30c\uc774\ud1a0\uce58 \ud150\uc11c\ub85c \ubcc0\ud658<\/h3>\n
\uc0dd\uc131\ud55c \uc785\ub825 \ub370\uc774\ud130\uc640 \ud0c0\uac9f \uac12\uc744 \ud30c\uc774\ud1a0\uce58 \ud150\uc11c\ub85c \ubcc0\ud658\ud569\ub2c8\ub2e4.<\/p>\n
import torch\nfrom torch.utils.data import Dataset, DataLoader\n\nclass TimeSeriesDataset(Dataset):\n def __init__(self, X, y):\n self.X = torch.FloatTensor(X)\n self.y = torch.FloatTensor(y)\n \n def __len__(self):\n return len(self.y)\n \n def __getitem__(self, index):\n return self.X[index], self.y[index]\n\n# \ub370\uc774\ud130\uc14b \ubc0f \ub370\uc774\ud130\ub85c\ub354 \uc0dd\uc131\ndataset = TimeSeriesDataset(X, y)\ndataloader = DataLoader(dataset, batch_size=32, shuffle=True)<\/code><\/pre>\n4.4 AR \ubaa8\ub378 \uc815\uc758<\/h3>\n
\uc774\uc81c \uc2e0\uacbd\ub9dd \ubaa8\ub378\uc744 \uc815\uc758\ud558\uaca0\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uc740 \uac04\ub2e8\ud55c LSTM \ubaa8\ub378\uc758 \uc608\uc785\ub2c8\ub2e4.<\/p>\n
import torch.nn as nn\n\nclass ARModel(nn.Module):\n def __init__(self, input_size, hidden_size, output_size):\n super(ARModel, self).__init__()\n self.lstm = nn.LSTM(input_size, hidden_size, batch_first=True)\n self.fc = nn.Linear(hidden_size, output_size)\n \n def forward(self, x):\n out, _ = self.lstm(x.unsqueeze(-1)) # LSTM\uc5d0\ub294 3D \ud150\uc11c\uac00 \ud544\uc694\n out = self.fc(out[:, -1, :]) # \ub9c8\uc9c0\ub9c9 \ud0c0\uc784 \uc2a4\ud15d\uc758 \ucd9c\ub825 \uc0ac\uc6a9\n return out\n\n# \ubaa8\ub378 \ucd08\uae30\ud654\ninput_size = 1 # \uc785\ub825 \ud06c\uae30\nhidden_size = 64 # \uc228\uc740 \uce35 \ud06c\uae30\noutput_size = 1 # \ucd9c\ub825 \ud06c\uae30\nmodel = ARModel(input_size, hidden_size, output_size)<\/code><\/pre>\n4.5 \ubaa8\ub378 \ud559\uc2b5\ud558\uae30<\/h3>\n
\ubaa8\ub378\uc744 \ud559\uc2b5\ud558\uae30 \uc704\ud574 \uc190\uc2e4 \ud568\uc218\uc640 \uc635\ud2f0\ub9c8\uc774\uc800\ub97c \uc124\uc815\ud569\ub2c8\ub2e4. Mean Squared Error(MSE)\ub97c \uc190\uc2e4 \ud568\uc218\ub85c \uc0ac\uc6a9\ud558\uace0, Adam \uc635\ud2f0\ub9c8\uc774\uc800\ub97c \uc0ac\uc6a9\ud560 \uac83\uc785\ub2c8\ub2e4.<\/p>\n
import torch.optim as optim\n\ncriterion = nn.MSELoss()\noptimizer = optim.Adam(model.parameters(), lr=0.001)\n\n# \ubaa8\ub378 \ud6c8\ub828\nnum_epochs = 100\nfor epoch in range(num_epochs):\n for inputs, labels in dataloader:\n model.train()\n optimizer.zero_grad()\n outputs = model(inputs)\n loss = criterion(outputs, labels.view(-1, 1)) # \uc815\ub2f5 \ud06c\uae30\uc5d0 \ub9de\ucdb0 \uc8fc\uc758\n loss.backward()\n optimizer.step()\n \n if (epoch+1) % 10 == 0:\n print(f'Epoch [{epoch+1}\/{num_epochs}], Loss: {loss.item():.4f}')<\/code><\/pre>\n4.6 \uc608\uce21\ud558\uae30<\/h3>\n
\ubaa8\ub378\uc774 \ud6c8\ub828\ub41c \ud6c4 \uc608\uce21\uc744 \uc218\ud589\ud569\ub2c8\ub2e4.<\/p>\n
<\/code#><\/pre>\n5. \uacb0\ub860<\/h2>\n
\ud30c\uc774\ud1a0\uce58\ub97c \uc774\uc6a9\ud558\uc5ec \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\uc758 \uc790\uae30 \ud68c\uadc0 \ubaa8\ub378\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc744 \uc790\uc138\ud788 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4. AR \ubaa8\ub378\uc740 \ub370\uc774\ud130\uc758 \uacfc\uac70 \uac12\ub4e4\uc744 \uae30\ubc18\uc73c\ub85c \ud604\uc7ac \uac12\uc744 \uc608\uce21\ud558\ub294 \uac15\ub825\ud55c \ub3c4\uad6c\uc785\ub2c8\ub2e4. \uc6b0\ub9ac\ub294 LSTM\uc744 \ud65c\uc6a9\ud558\uc5ec AR \ubaa8\ub378\uc744 \ub354 \ubcf5\uc7a1\ud558\uace0 \uc608\uce21 \uc815\ud655\ub3c4\ub97c \ub192\uc77c \uc218 \uc788\ub294 \ubc29\ubc95\uc744 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4. \uc774\ub7ec\ud55c \ubaa8\ub378\uc740 \uae08\uc735, \uae30\ud6c4, \ud5ec\uc2a4\ucf00\uc5b4 \ub4f1 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ud65c\uc6a9\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
6. \ucc38\uace0\ubb38\ud5cc<\/h2>\n