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"book contain a main body of text, a notes section, and asetofproblems. themainbodyofthetextisintendedtobeself-containedandcanbe readwithoutrecoursetotheotherpartsofthechapter. asmuchaspossible,background mathematics is incorporated into the main body of the text. however, for larger topics thatwouldbeadistractiontothemainthreadoftheargument,thebackgroundmaterial isappendicized, andareferenceisprovidedinthemargin. mostnotationinthisbookis appendixa standard. however, some conventions are less widely used, and the reader is encouraged notation to consult appendix a before proceeding. the main body of text includes many novel illustrations and visualizations of deep learning models and results. i’ve worked hard to provide new explanations of existing ideas rather than merely curate the work of others. deep learning is a new field, and sometimes phenomena are poorly understood. i try to make it clear where this is the case and when my explanations should be treated with caution. references are included in the main body of the chapter only where results are de- picted. instead, they can be found in the notes section at the end of the chapter. i do not generally respect historical precedent in the main text; if an ancestor of a current techniqueisnolongeruseful,theniwillnotmentionit. however,thehistoricaldevelop- mentofthefieldisdescribedinthenotessection,andhopefully,creditisfairlyassigned. the notes are organized into paragraphs and provide pointers for further reading. they should help the reader orient themselves within the sub-area and understand how it re- lates to other parts of machinelearning. the notes are less self-contained than the main text. dependingonyourlevelofbackgroundknowledgeandinterest,youmayfindthese sections more or less useful. eachchapterhasanumberofassociatedproblems. theyarereferencedinthemargin of the main text at the point that they should be attempted. as george pólya noted, “mathematics,yousee,isnotaspectatorsport.” hewascorrect,andihighlyrecommend that you attempt the problems as you go. in some cases, they provide insights that will helpyouunderstandthemaintext. problemsforwhichtheanswersareprovidedonthe associated website are indicated with an asterisk. additionally, python notebooks that will help you understand the ideas in this book are also available via the website, and these are also referenced in the margins of the text. indeed, if you are feeling rusty, it notebook1.1 might be worth working through the notebook on background mathematics right now. background mathematics unfortunately, the pace of research in ai makes it inevitable that this book will be a constant work in progress. if there are parts you find hard to understand, notable omis- sions, or sections that seem extraneous, please get in touch via the associated website. together, we can make the next edition better. this work is subject to a creative commons cc-by-nc-nd license. (c) mit press.chapter 2 supervised learning a supervised learning model defines a mapping from one or more inputs to one or more outputs. for example, the input might be the age and mileage of a secondhand toyota prius, and the output might be the estimated value of the car in dollars. the model is just a mathematical equation; when the inputs are passed through this equation,itcomputestheoutput,andthisistermedinference. themodelequationalso contains parameters. different parameter values change the outcome of the computa- tion; the model equation describes a family of possible relationships between inputs and outputs, and the parameters specify the particular relationship. whenwetrainorlearnamodel,wefindparametersthatdescribethetruerelationship between inputs and outputs. a learning algorithm takes a training set of input/output pairs and manipulates the parameters until the inputs predict their corresponding out- putsascloselyaspossible. ifthemodelworkswellforthesetrainingpairs,thenwehope it will make good predictions for new inputs where the true output is unknown. thegoalofthischapteristoexpandontheseideas. first,wedescribethisframework more formally and introduce some notation. then we work through a simple example in which we use a straight line to describe the relationship between input and output. this linear model is both familiar and easy to visualize, but nevertheless illustrates all the main ideas of supervised learning."