時間序列(單變數/多變數+多個步預測)
阿新 • • 發佈:2018-12-24
''' 用之前時間預測往後不止是一步,而是多步 ''' from numpy import array # split a univariate sequence into samples def split_sequence(sequence, n_steps_in, n_steps_out): X, y = list(), list() for i in range(len(sequence)): # find the end of this pattern end_ix = i + n_steps_in out_end_ix = end_ix + n_steps_out # check if we are beyond the sequence if out_end_ix > len(sequence): break # gather input and output parts of the pattern seq_x, seq_y = sequence[i:end_ix], sequence[end_ix:out_end_ix] X.append(seq_x) y.append(seq_y) return array(X), array(y) raw_seq = [10, 20, 30, 40, 50, 60, 70, 80, 90] # 也就是用之前的三步,預測之後的2步 n_steps_in, n_steps_out = 3, 2 X, y = split_sequence(raw_seq, n_steps_in, n_steps_out) for i in range(len(X)): print(X[i], y[i]) ''' [10 20 30] [40 50] [20 30 40] [50 60] [30 40 50] [60 70] [40 50 60] [70 80] [50 60 70] [80 90] ''' # reshape from [samples, timesteps] into [samples, timesteps, features] n_features = 1 X = X.reshape((X.shape[0], X.shape[1], n_features)) # define model model = Sequential() model.add(LSTM(100, activation='relu', return_sequences=True, input_shape=(n_steps_in, n_features))) model.add(LSTM(100, activation='relu')) # 和之前單個步不同點在於 這一層的神經元=n_steps_out model.add(Dense(n_steps_out)) model.compile(optimizer='adam', loss='mse') model.fit(X, y, epochs=50, verbose=0) # demonstrate prediction x_input = array([70, 80, 90]) x_input = x_input.reshape((1, n_steps_in, n_features)) yhat = model.predict(x_input, verbose=0) print(yhat) # [[107.168686 118.79841 ]] ###################################################Encoder-Decoder Model ''' 這個模型主要是基於輸入序列和輸出序列長度不一樣,比如機器翻譯 當然一樣也可以 1.model.add(LSTM(100, activation='relu', input_shape=(n_steps_in, n_features))) 首先encoderLSTM接受了(None,n_steps_in,n_features) 輸出了(None,100)為什麼100呢,因為return_sequences=FALSE,只輸出最後一個ht 2.model.add(RepeatVector(n_steps_out)) 第二步重複變成3D(None,n_steps_out,100) 看出來優點了嗎!即使設定return_sequences=TRUE,變成3D的形式 但是!你只能會使xt和yt一一對應,沒法實現不對等 3.model.add(LSTM(100, activation='relu', return_sequences=True)) 第三步解碼 4.model.add(TimeDistributed(Dense(1))) TimeDistributed 接受一個3D的輸入,相當於獨立對每個時間步操作(可以減少引數學習量) model = Sequential() model.add(TimeDistributed(Dense(8), input_shape=(10, 16))) # 現在 model.output_shape == (None, 10, 8) 這裡一定要保證LSTM上層的return_sequence=TRUE , TimeDistributed(Dense(1))是1代表最後輸出=(none,return_sequence長度,1) ''' from numpy import array from keras.models import Sequential from keras.layers import LSTM from keras.layers import Dense from keras.layers import RepeatVector from keras.layers import TimeDistributed # split a univariate sequence into samples def split_sequence(sequence, n_steps_in, n_steps_out): X, y = list(), list() for i in range(len(sequence)): # find the end of this pattern end_ix = i + n_steps_in out_end_ix = end_ix + n_steps_out # check if we are beyond the sequence if out_end_ix > len(sequence): break # gather input and output parts of the pattern seq_x, seq_y = sequence[i:end_ix], sequence[end_ix:out_end_ix] X.append(seq_x) y.append(seq_y) return array(X), array(y) # define input sequence raw_seq = [10, 20, 30, 40, 50, 60, 70, 80, 90] # choose a number of time steps n_steps_in, n_steps_out = 3, 2 # split into samples X, y = split_sequence(raw_seq, n_steps_in, n_steps_out) # reshape from [samples, timesteps] into [samples, timesteps, features] n_features = 1 X = X.reshape((X.shape[0], X.shape[1], n_features)) y = y.reshape((y.shape[0], y.shape[1], n_features)) # define model model = Sequential() model.add(LSTM(100, activation='relu', input_shape=(n_steps_in, n_features))) model.add(RepeatVector(n_steps_out)) model.add(LSTM(100, activation='relu', return_sequences=True)) model.add(TimeDistributed(Dense(1))) model.compile(optimizer='adam', loss='mse') # fit model model.fit(X, y, epochs=100, verbose=0) # demonstrate prediction x_input = array([70, 80, 90]) x_input = x_input.reshape((1, n_steps_in, n_features)) yhat = model.predict(x_input, verbose=0) print(yhat) #######################################多變數,多步驟預測 from numpy import array from numpy import hstack from keras.models import Sequential from keras.layers import LSTM from keras.layers import Dense # split a multivariate sequence into samples def split_sequences(sequences, n_steps_in, n_steps_out): X, y = list(), list() for i in range(len(sequences)): # find the end of this pattern end_ix = i + n_steps_in out_end_ix = end_ix + n_steps_out-1 # check if we are beyond the dataset if out_end_ix > len(sequences): break # gather input and output parts of the pattern seq_x, seq_y = sequences[i:end_ix, :-1], sequences[end_ix-1:out_end_ix, -1] X.append(seq_x) y.append(seq_y) return array(X), array(y) # define input sequence in_seq1 = array([10, 20, 30, 40, 50, 60, 70, 80, 90]) in_seq2 = array([15, 25, 35, 45, 55, 65, 75, 85, 95]) out_seq = array([in_seq1[i]+in_seq2[i] for i in range(len(in_seq1))]) # convert to [rows, columns] structure in_seq1 = in_seq1.reshape((len(in_seq1), 1)) in_seq2 = in_seq2.reshape((len(in_seq2), 1)) out_seq = out_seq.reshape((len(out_seq), 1)) # horizontally stack columns dataset = hstack((in_seq1, in_seq2, out_seq)) # choose a number of time steps n_steps_in, n_steps_out = 3, 2 # covert into input/output X, y = split_sequences(dataset, n_steps_in, n_steps_out) # the dataset knows the number of features, e.g. 2 n_features = X.shape[2] # define model model = Sequential() model.add(LSTM(100, activation='relu', return_sequences=True, input_shape=(n_steps_in, n_features))) model.add(LSTM(100, activation='relu')) model.add(Dense(n_steps_out)) model.compile(optimizer='adam', loss='mse') # fit model model.fit(X, y, epochs=200, verbose=0) # demonstrate prediction x_input = array([[70, 75], [80, 85], [90, 95]]) x_input = x_input.reshape((1, n_steps_in, n_features)) yhat = model.predict(x_input, verbose=0) print(yhat) ############################################################多變數,多對多 ''' [[10 15 25] [20 25 45] [30 35 65]] [[ 40 45 85] [ 50 55 105]]-----y(輸出為2*3維) [[20 25 45] [30 35 65] [40 45 85]] [[ 50 55 105] [ 60 65 125]]-----y [[ 30 35 65] [ 40 45 85] [ 50 55 105]] [[ 60 65 125] [ 70 75 145]] [[ 40 45 85] [ 50 55 105] [ 60 65 125]] [[ 70 75 145] [ 80 85 165]] [[ 50 55 105] [ 60 65 125] [ 70 75 145]] [[ 80 85 165] [ 90 95 185]] ''' from numpy import array from numpy import hstack from keras.models import Sequential from keras.layers import LSTM from keras.layers import Dense from keras.layers import RepeatVector from keras.layers import TimeDistributed # split a multivariate sequence into samples def split_sequences(sequences, n_steps_in, n_steps_out): X, y = list(), list() for i in range(len(sequences)): # find the end of this pattern end_ix = i + n_steps_in out_end_ix = end_ix + n_steps_out # check if we are beyond the dataset if out_end_ix > len(sequences): break # gather input and output parts of the pattern seq_x, seq_y = sequences[i:end_ix, :], sequences[end_ix:out_end_ix, :] X.append(seq_x) y.append(seq_y) return array(X), array(y) # define input sequence in_seq1 = array([10, 20, 30, 40, 50, 60, 70, 80, 90]) in_seq2 = array([15, 25, 35, 45, 55, 65, 75, 85, 95]) out_seq = array([in_seq1[i]+in_seq2[i] for i in range(len(in_seq1))]) # convert to [rows, columns] structure in_seq1 = in_seq1.reshape((len(in_seq1), 1)) in_seq2 = in_seq2.reshape((len(in_seq2), 1)) out_seq = out_seq.reshape((len(out_seq), 1)) # horizontally stack columns dataset = hstack((in_seq1, in_seq2, out_seq)) # choose a number of time steps n_steps_in, n_steps_out = 3, 2 # covert into input/output X, y = split_sequences(dataset, n_steps_in, n_steps_out) # the dataset knows the number of features, e.g. 2 n_features = X.shape[2] # define model model = Sequential() model.add(LSTM(200, activation='relu', input_shape=(n_steps_in, n_features))) model.add(RepeatVector(n_steps_out)) model.add(LSTM(200, activation='relu', return_sequences=True)) model.add(TimeDistributed(Dense(n_features))) ''' 這裡輸入3D為(樣本量,return_sequences數量(=n_steps_out),200) 輸出為(樣本量,return_sequences數量(=n_steps_out),n_features) 就是每個輸出是(3,2)維度的 ''' model.compile(optimizer='adam', loss='mse') # fit model model.fit(X, y, epochs=300, verbose=0) # demonstrate prediction x_input = array([[60, 65, 125], [70, 75, 145], [80, 85, 165]]) x_input = x_input.reshape((1, n_steps_in, n_features)) yhat = model.predict(x_input, verbose=0) print(yhat) ''' 總結:注意的點: 最大不同在DENSE的輸出層,其實在多步驟的時候什麼時候用n_featues,什麼時候用n_steps還是看y的格式鴨 '''