Final answer:
Line separability in mathematics refers to the ability to separate data points of different classes using a straight line. The trade-off between accuracy and the number of errors on the training data is known as the bias-variance trade-off.
Step-by-step explanation:
In mathematics, when we talk about line separability, we are typically referring to the ability to separate data points of different classes using a straight line. The trade-off between the accuracy and the number of errors on the training data is known as the bias-variance trade-off.
If we have a simple and less flexible model with high bias, it may not be able to capture the intricacies of the training data, resulting in low accuracy. On the other hand, a more complex and flexible model with low bias may fit the training data well but may also pick up noise and outliers, leading to high variance and low precision.
Let's consider a classification problem where we have two classes of data points that are not linearly separable. If we use a linear model such as logistic regression or a perceptron, we may have high bias and low accuracy. This is because a straight line cannot separate the two classes effectively.
However, if we use a non-linear model such as a support vector machine with a radial basis function kernel, we can create a decision boundary that is non-linear and separates the classes accurately. In this case, we may have low bias and high accuracy.