Hyperparameters, Bias, and Variance
Hyperparameters control the bias-variance tradeoff, which is crucial for building models that generalize to new data. For example, tree depth in decision trees and regularization strength in linear models directly affect model complexity. Increasing complexity—by allowing deeper trees or using less regularization—reduces bias (error from incorrect assumptions) but raises variance (error from sensitivity to training data). Limiting complexity—by using shallower trees or stronger regularization—raises bias but lowers variance, making the model less sensitive to noise but possibly less accurate on the training set. Tuning these hyperparameters helps you find the right balance for optimal model performance.
Bias is error from erroneous assumptions. Variance is error from sensitivity to small fluctuations in the training set.
12345678910111213141516171819202122import numpy as np import matplotlib.pyplot as plt # Simulate model complexity from low (simple model) to high (complex model) complexity = np.linspace(1, 10, 100) # Bias decreases as complexity increases bias = (10 - complexity) ** 2 / 20 # Variance increases as complexity increases variance = (complexity - 1) ** 2 / 20 # Total error is sum of bias and variance total_error = bias + variance plt.figure(figsize=(8, 5)) plt.plot(complexity, bias, label="Bias^2", color="blue") plt.plot(complexity, variance, label="Variance", color="red") plt.plot(complexity, total_error, label="Total Error", color="green", linestyle="--") plt.xlabel("Model Complexity") plt.ylabel("Error") plt.title("Bias-Variance Tradeoff Curve") plt.legend() plt.tight_layout() plt.show()
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Hyperparameters control the bias-variance tradeoff, which is crucial for building models that generalize to new data. For example, tree depth in decision trees and regularization strength in linear models directly affect model complexity. Increasing complexity—by allowing deeper trees or using less regularization—reduces bias (error from incorrect assumptions) but raises variance (error from sensitivity to training data). Limiting complexity—by using shallower trees or stronger regularization—raises bias but lowers variance, making the model less sensitive to noise but possibly less accurate on the training set. Tuning these hyperparameters helps you find the right balance for optimal model performance.
Bias is error from erroneous assumptions. Variance is error from sensitivity to small fluctuations in the training set.
12345678910111213141516171819202122import numpy as np import matplotlib.pyplot as plt # Simulate model complexity from low (simple model) to high (complex model) complexity = np.linspace(1, 10, 100) # Bias decreases as complexity increases bias = (10 - complexity) ** 2 / 20 # Variance increases as complexity increases variance = (complexity - 1) ** 2 / 20 # Total error is sum of bias and variance total_error = bias + variance plt.figure(figsize=(8, 5)) plt.plot(complexity, bias, label="Bias^2", color="blue") plt.plot(complexity, variance, label="Variance", color="red") plt.plot(complexity, total_error, label="Total Error", color="green", linestyle="--") plt.xlabel("Model Complexity") plt.ylabel("Error") plt.title("Bias-Variance Tradeoff Curve") plt.legend() plt.tight_layout() plt.show()
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