🧠 Bias and variance are two factors that affect the error in classification or regression models.

📉 High bias results in significant error during both training and testing, while high variance leads to low error during training but significant error during testing.

⚖️ There should be a trade-off between bias and variance, with the model complexity neither too simple nor too complex.

🔑 Bias-variance tradeoff refers to finding a balance between high bias (underfitting) and high variance (overfitting) in a model.

📈 The objective is to minimize the combined effect of bias and variance on the test error by building a model that achieves a balance between the two.

🔎 The tradeoff can be visualized in classification and regression problems, where underfitting leads to misclassifications and significant errors, while overfitting leads to low training error but high testing error.

📝 The goal is to find a function that is as close as possible to the true function, f, and can be learned from the training data.

🔍 The bias is the average difference between the predictions of the learned function and the true underlying function over different training data sets.

💯 The variance is the average squared difference between the predictions of the learned function and its expected value.

📊 The variance measures the mean square deviation of F hat X from its expected value over different training datasets.

⚖️ The bias-variance tradeoff is a formula that decomposes the mean squared error into bias, variance, and irreducible error.

🔍 The mean squared error can be decomposed into the bias, variance, and irreducible error components.

📚 The bias-variance tradeoff is a fundamental concept in random variables.

🔍 The mean square error decomposes into irreducible error and the expected difference between the predicted and actual values.

➗ The expected value of the product of independent random variables is equal to the product of their individual expected values.

📚 The bias of F at X is the expected value of F at X minus f x whole square.

📊 The variance of F at X is the expected value of F at X minus the expected value of F at X minus two expected value of f X minus expected value of F at X.

🤔 The bias is a constant since we subtract f x from the expected value of F at X, and applying expectation to squared bias does not have any effect.

📚 The bias-variance tradeoff is an important concept in machine learning.

⚖️ High bias indicates underfitting, while high variance indicates overfitting.

🧮 The mean square error can be decomposed into bias, variance, and irreducible error.