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James-Stein Estimation
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| import numpy as np | |
| def run_trial(): | |
| # Hidden Variables | |
| a = np.random.rand() | |
| b = np.random.rand() | |
| c = np.random.rand() | |
| # Create 3 variables sampled from normal distributions | |
| var1 = np.random.normal(loc=a, scale=1) | |
| var2 = np.random.normal(loc=b, scale=1) | |
| var3 = np.random.normal(loc=c, scale=1) | |
| # Naive Estimation | |
| err1 = (a - var1) ** 2 | |
| err2 = (b - var2) ** 2 | |
| err3 = (c - var3) ** 2 | |
| ne_mse = np.mean([err1,err2,err3]) | |
| # James-Stein Estimation | |
| norm_sq = var1**2 + var2**2 + var3**2 | |
| shrinkage = max(0, 1 - (1 / norm_sq)) | |
| jse1 = (a - var1 * shrinkage) ** 2 | |
| jse2 = (b - var2 * shrinkage) ** 2 | |
| jse3 = (c - var3 * shrinkage) ** 2 | |
| jse_mse = np.mean([jse1,jse2,jse3]) | |
| return ne_mse, jse_mse | |
| def run_experiment(trial_count): | |
| ne_errors = [] | |
| jse_errors = [] | |
| for i in range(trial_count): | |
| ne_err, jse_err = run_trial() | |
| ne_errors.append(ne_err) | |
| jse_errors.append(jse_err) | |
| mean_ne_err = np.mean(ne_errors) | |
| mean_jse_err = np.mean(jse_errors) | |
| print(f"Naive Est. MSE: {mean_ne_err}") | |
| print(f"James-Stein Est. MSE: {mean_jse_err}") | |
| jse_win = (mean_ne_err > mean_jse_err) | |
| if jse_win: | |
| print("Winner: James-Stein Estimate") | |
| else: | |
| print("Winner: Naive Estimation") | |
| return jse_win | |
| experiment_count = 5 | |
| trial_count = 1000 | |
| jse_wins = 0 | |
| for i in range(experiment_count): | |
| print(f"Experiment {i+1}") | |
| if run_experiment(trial_count): | |
| jse_wins += 1 | |
| print("----------------------------") | |
| print(f"James-Stein Estimation winrate = {round(jse_wins/experiment_count*100)}%") | |
| # Experiment 1 | |
| # Naive Est. MSE: 0.9792049390277211 | |
| # James-Stein Est. MSE: 0.6422371792832063 | |
| # Winner: James-Stein Estimate | |
| # ---------------------------- | |
| # Experiment 2 | |
| # Naive Est. MSE: 0.9729797681574638 | |
| # James-Stein Est. MSE: 0.6441794373594659 | |
| # Winner: James-Stein Estimate | |
| # ---------------------------- | |
| # Experiment 3 | |
| # Naive Est. MSE: 1.02369053560002 | |
| # James-Stein Est. MSE: 0.6752645156636279 | |
| # Winner: James-Stein Estimate | |
| # ---------------------------- | |
| # Experiment 4 | |
| # Naive Est. MSE: 1.0137424522022978 | |
| # James-Stein Est. MSE: 0.6696755267702634 | |
| # Winner: James-Stein Estimate | |
| # ---------------------------- | |
| # Experiment 5 | |
| # Naive Est. MSE: 0.9881777449461806 | |
| # James-Stein Est. MSE: 0.6501366130770861 | |
| # Winner: James-Stein Estimate | |
| # ---------------------------- | |
| # James-Stein Estimation winrate = 100% |
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