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imalenica committed May 3, 2021
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Expand Up @@ -7,20 +7,32 @@ by _Jeremy Coyle, Nima Hejazi, Ivana Malenica and Rachael Phillips_.

Updated: `r Sys.Date()`

## Learning Objectives
`r if (knitr::is_latex_output()) '\\begin{VT1}\n\\VH{Learning Objectives}'`

`r if (knitr::is_html_output()) '## Learning Objectives{-}'`

By the end of this chapter you will be able to:

1. Differentiate between training, validation and test sets.

2. Understand the concept of a loss function, risk and cross-validation.

3. Select a loss function that is appropriate for the functional parameter to be
estimated.

4. Understand and contrast different cross-validation schemes for i.i.d. data.

5. Understand and contrast different cross-validation schemes for time dependent
data.

6. Setup the proper fold structure, build custom fold-based function, and
cross-validate the proposed function using the `origami` `R` package.

7. Setup the proper cross-validation structure for the use by the Super Learner
using the the `origami` `R` package.

`r if (knitr::is_latex_output()) '\\end{VT1}'`

## Introduction

In this chapter, we start elaborating on the estimation step outlined in the
Expand All @@ -38,14 +50,18 @@ guides the choice of the final learning method, and it gives us a quantitative
assessment of how good the chosen algorithm is doing. In order to assess the
performance of an algorithm, we introduce the concept of a **loss** function,
which helps us define the **risk**, also referred to as the **expected
prediction error**. Our goal, as further specified in the next chapter, will be
prediction error**.

`r if (knitr::is_latex_output()) '\\begin{shortbox}\n\\Boxhead{Constructing a library that is consistent with the data-generating distribution}'`
Our goal, as further specified in the next chapter, will be
to estimate the true risk of the proposed statistical learning method. Our
goal(s) consist of:

1. Estimating the performance of different algorithms in order to choose the
best one.
2. Having chosen a winner, estimate the true risk of the proposed
statistical learning method.
`r if (knitr::is_latex_output()) '\\end{shortbox}'`

In the following, we propose a method to do so using the observed data and
**cross-validation** procedure using the `origami` package [@coyle2018origami].
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