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Fundamentals of prediction

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Prediction is the art and science of leveraging patterns found in natural and social processes to conjecture about uncertain events. We use the word prediction broadly to refer to statements about things we don’t know for sure yet, including but not limited to the outcome of future events. Machine learning is to a large extent the study of algorithmic prediction. Before we can dive into machine learning, we should familiarize ourselves with prediction. Starting from first principles, we will motivate the goals of prediction before building up to a statistical theory of prediction. We can formalize the goal of prediction problems by assuming a population of 𝑁 N instances with a variety of attributes. We associate with each instance two variables, denoted 𝑋 X and 𝑌 Y. The goal of prediction is to conjecture a plausible value for 𝑌 Y after observing 𝑋 X alone. But when is a prediction good? For that, we must quantify some notion of the quality of prediction and aim to optimize t

Home Minimizing errors Modeling knowledge Prediction from statistical models Example: signal versus noise Prediction via optimization Predictors and labels Loss functions and risk Example: needle in a haystack revisited Maximum a posteriori and maximum likelihood Types of errors and successes ROC curves The Neyman-Pearson Lemma Properties of ROC curves Example: the needle one more time Area under the ROC curve Decisions that discriminate Legal background in the United States Formal non-discrimination criteria Merits and limitations of a narrow statistical perspective Chapter notes References P

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