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2. Making Decisions

Now that we have developed a few formalisms for discussing data, we can begin examining how to use data to actually make decisions. This section will work through some small, simple examples building up more probabilistic frameworks along the way, preparing you for more advanced mathematical models in later sections.

The goal of machine learning is to make correct decisions using data. This means that given some data from \(p_{\text{data}}\), we want to build a model that has the highest probability of being correct 1. There many ways of classifying what it means to be “correct”. In hypothesis testing this means accepting or rejecting the null hypothesis, in classification problems this means returning the correct label for a given data point, and in regression perhaps this means getting as close as possible to the actual value. As such, we will leave more specific discussions of maximizing “correctness” (or minimizing “incorrectness”) to their respective sections.

This chapter will first discuss how we incorporate data into probabilistic estimates and then lay the ground work for how we make decisions that maximize our probability of being correct.


1

Though this is usually the case, sometimes we want to weigh certain choices more than others, and thus we actually don’t directly optimize the probability of being correct and instead minimize a quantity called risk.