(20th-May-2020)
Learning is defined in terms of improving performance based on some measure. To know whether an agent has learned, we must define a measure of success. The measure is usually not how well the agent performs on the training experiences, but how well the agent performs for new experiences.
In classification, being able to correctly classify all training examples is not the problem. For example, consider the problem of predicting a Boolean feature based on a set of examples. Suppose that there were two agents P and N. Agent P claims that all of the negative examples seen were the only negative examples and that every other instance is positive. Agent N claims that the positive examples in the training set were the only positive examples and that every other instance is negative. Both of these agents correctly classify every example in the training set but disagree on every other example. Success in learning should not be judged on correctly classifying the training set but on being able to correctly classify unseen examples. Thus, the learner must generalize: go beyond the specific given examples to classify unseen examples.
Bias
The tendency to prefer one hypothesis over another is called a bias. Consider the agents N and P defined earlier. Saying that a hypothesis is better than N's or P's hypothesis is not something that is obtained from the data - both N and P accurately predict all of the data given - but is something external to the data. Without a bias, an agent will not be able to make any predictions on unseen examples. The hypotheses adopted by P and N disagree on all further examples, and, if a learning agent cannot choose some hypotheses as better, the agent will not be able to resolve this disagreement. To have any inductive process make predictions on unseen data, an agent requires a bias. What constitutes a good bias is an empirical question about which biases work best in practice; we do not imagine that either P's or N's biases work well in practice.
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