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| 1 | import seaborn as sns | |
| 2 | import pandas as pd | |
| 3 | import numpy as np | |
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | dom = range(0,11) | |
| 8 | H = 8 | |
| 9 | ||
| 10 | ## Noiseless paths | |
| 11 | # Upward exponential --> 'Real' increase | |
| 12 | f1 = lambda x : 10 + np.exp(0.33*x) / 3 | |
| 13 | y1 = [f1(x) for x in dom] | |
| 14 | ||
| 15 | # Downward exponential --> 'Real' decrease | |
| 16 | f2 = lambda x : 10 - np.exp(0.33*x) / 3 | |
| 17 | y2 = [f2(x) for x in dom] | |
| 18 | ||
| 19 | # Upward exponential --> 'Fake' increase | |
| 20 | f3 = lambda x : 10 + (-(x-5)**2 + 5**2) / 9 | |
| 21 | y3 = [f3(x) for x in dom] | |
| 22 | ||
| 23 | # Downward exponential --> 'Fake' increase | |
| 24 | f4 = lambda x : 10 - (-(x-5)**2 + 5**2) / 9 | |
| 25 | y4 = [f4(x) for x in dom] | |
| 26 | ||
| 27 | ||
| 28 | ## Noisy Paths | |
| 29 | sigma = 0.75 | |
| 30 | y1_ = [f1(x) + np.random.randn()*sigma for x in dom] | |
| 31 | y2_ = [f2(x) + np.random.randn()*sigma for x in dom] | |
| 32 | y3_ = [f3(x) + np.random.randn()*sigma for x in dom] | |
| 33 | y4_ = [f4(x) + np.random.randn()*sigma for x in dom] | |
| 34 | ||
| 35 | ||
| 36 | # Plots | |
| 37 | fig, (ax1,ax2) = plt.subplots(1,2, figsize=(14,5)) | |
| 38 | colors = ['g', 'r', 'orange', 'lightgreen'] | |
| 39 | ||
| 40 | ax1.set_title("Noiseless")
| |
| 41 | ax1.axhline(10, color='k'); | |
| 42 | ax1.axvline( H, color='k',linestyle=':'); | |
| 43 | ax1.plot(dom,y1, marker='o', color=colors[0], label='Real Increase'); | |
| 44 | ax1.plot(dom,y3, marker='o', color=colors[2], label='Fake Increase'); | |
| 45 | ax1.plot(dom,y2, marker='o', color=colors[1], label='Real Decrease'); | |
| 46 | ax1.plot(dom,y4, marker='o', color=colors[3], label='Fake Decrease'); | |
| 47 | ax1.legend(frameon=True); | |
| 48 | ||
| 49 | ax2.set_title("Noisy")
| |
| 50 | ax2.axhline(10, color='k'); | |
| 51 | ax2.axvline( 8, color='k',linestyle=':'); | |
| 52 | ax2.plot(dom,y1_, marker='o', color=colors[0], label='Real Increase'); | |
| 53 | ax2.plot(dom,y3_, marker='o', color=colors[2], label='Fake Increase'); | |
| 54 | ax2.plot(dom,y2_, marker='o', color=colors[1], label='Real Decrease'); | |
| 55 | ax2.plot(dom,y4_, marker='o', color=colors[3], label='Fake Decrease'); | |
| 56 | ax2.legend(frameon=True); | |
| 57 | ||
| 58 | plt.tight_layout(); | |
| 59 | plt.savefig("noiseless_and_noisy.png");
| |
| 60 | ||
| 61 | ||
| 62 | # Simulated noisy data | |
| 63 | N = 100 | |
| 64 | y = [] | |
| 65 | for i in range(N): | |
| 66 | - | y1 = [f1(x) + np.random.randn()*sig for x in dom] + [100]; y.append(y1) |
| 66 | + | y1 = [f1(x) + np.random.randn()*sigma for x in dom] + [100]; y.append(y1) |
| 67 | - | y2 = [f2(x) + np.random.randn()*sig for x in dom] + [200]; y.append(y2) |
| 67 | + | y2 = [f2(x) + np.random.randn()*sigma for x in dom] + [200]; y.append(y2) |
| 68 | - | y3 = [f3(x) + np.random.randn()*sig for x in dom] + [300]; y.append(y3) |
| 68 | + | y3 = [f3(x) + np.random.randn()*sigma for x in dom] + [300]; y.append(y3) |
| 69 | - | y4 = [f4(x) + np.random.randn()*sig for x in dom] + [400]; y.append(y4) |
| 69 | + | y4 = [f4(x) + np.random.randn()*sigma for x in dom] + [400]; y.append(y4) |
| 70 | ||
| 71 | ds = pd.DataFrame(y) / 100 | |
| 72 | ds.rename({11:'c'}, axis=1, inplace=True)
| |
| 73 | ds['y'] = ds[10] - ds[7] | |
| 74 | ||
| 75 | ||
| 76 | # Train, validation and test | |
| 77 | N = len(ds) | |
| 78 | N1 = int(N * 0.6) | |
| 79 | N2 = int(N * 0.8) | |
| 80 | ||
| 81 | train = ds.iloc[:N1] | |
| 82 | vali = ds.iloc[N1:N2] | |
| 83 | test = ds.iloc[N2:] | |
| 84 | ||
| 85 | lags = np.arange(0,11) | |
| 86 | ||
| 87 | # For Random Forest | |
| 88 | train_X_RF = train[lags[:H]].values | |
| 89 | train_y_RF = train['y'].values | |
| 90 | vali_X_RF = vali [lags[:H]].values | |
| 91 | vali_y_RF = vali ['y'].values | |
| 92 | test_X_RF = test [lags[:H]].values | |
| 93 | test_y_RF = test ['y'].values | |
| 94 | ||
| 95 | # For LSTM | |
| 96 | train_X_LS = train[lags[:H]].values.reshape(len(train), H, 1) | |
| 97 | train_y_LS = train[['y']].values | |
| 98 | vali_X_LS = vali [lags[:H]].values.reshape(len(vali ), H, 1) | |
| 99 | vali_y_LS = vali [['y']].values | |
| 100 | test_X_LS = test [lags[:H]].values.reshape(len(test ), H, 1) | |
| 101 | test_y_LS = test [['y']].values | |
| 102 | ||
| 103 | # Copy the test set (predictions will be added here) | |
| 104 | te = ds.iloc[N2:].copy() | |
| 105 | ||
| 106 | ||
| 107 | # Train the Random Forest Model | |
| 108 | RF = RandomForestRegressor(random_state=0, n_estimators=20) | |
| 109 | RF.fit(train_X_RF, train_y_RF); | |
| 110 | ||
| 111 | # Out-of-sample Prediction (Random Forest) | |
| 112 | te['RF'] = RF.predict(test_X_RF) | |
| 113 | ||
| 114 | # Train the LSTM Model | |
| 115 | model = Sequential() | |
| 116 | model.add(LSTM((1), batch_input_shape=(None, H, 1), return_sequences=True)) | |
| 117 | model.add(LSTM((1), return_sequences=False)) | |
| 118 | model.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy']) | |
| 119 | history = model.fit(train_X_LS, train_y_LS, epochs=100, validation_data=(vali_X_LS, vali_y_LS), verbose=0) | |
| 120 | ||
| 121 | # Out-of-sample Prediction (LSTM) | |
| 122 | te['LSTM'] = model.predict(test_X_LS) | |
| 123 | ||
| 124 | ||
| 125 | # Plot Results | |
| 126 | fig, (ax1,ax2) = plt.subplots(1,2, figsize=(15,5), sharey=True) | |
| 127 | ||
| 128 | ax1.set_title("Random Forest")
| |
| 129 | (te[te['c']==1]*100).plot.scatter('RF', 'y', ax=ax1, color=colors[0], s=50, alpha=0.75);
| |
| 130 | (te[te['c']==2]*100).plot.scatter('RF', 'y', ax=ax1, color=colors[1], s=50, alpha=0.75);
| |
| 131 | (te[te['c']==3]*100).plot.scatter('RF', 'y', ax=ax1, color=colors[2], s=50, alpha=0.75);
| |
| 132 | (te[te['c']==4]*100).plot.scatter('RF', 'y', ax=ax1, color=colors[3], s=50, alpha=0.75);
| |
| 133 | ax1.xaxis.set_label_text("Prediction");
| |
| 134 | ax1.yaxis.set_label_text("Target");
| |
| 135 | ||
| 136 | ax2.set_title("LSTM")
| |
| 137 | (te[te['c']==1]*100).plot.scatter('LSTM', 'y', ax=ax2, color=colors[0], s=50, alpha=0.75);
| |
| 138 | (te[te['c']==2]*100).plot.scatter('LSTM', 'y', ax=ax2, color=colors[1], s=50, alpha=0.75);
| |
| 139 | (te[te['c']==3]*100).plot.scatter('LSTM', 'y', ax=ax2, color=colors[2], s=50, alpha=0.75);
| |
| 140 | (te[te['c']==4]*100).plot.scatter('LSTM', 'y', ax=ax2, color=colors[3], s=50, alpha=0.75);
| |
| 141 | ax2.xaxis.set_label_text("Prediction");
| |
| 142 | ax2.yaxis.set_label_text("Target");
| |
| 143 | ||
| 144 | plt.tight_layout(); | |
| 145 | ||
| 146 | plt.savefig("experimental_results.png"); |
