Introdução ao Machine Learning

# Introdução ao Machine Learning
## Dataprep e Classificação
### <img src = 'https://d33wubrfki0l68.cloudfront.net/9b0699f18268059bdd2e5c21538a29eade7cbd2b/67e5c/img/logo/cursor1-5.png' width = '40%'>
### May de 2022

---

# Dataprep Parte I

---

# Conteúdo

- Preditores categóricos

- Transformações 1:1

- Transformações 1:n

- Regressão Logística

- Matriz de Confusão

- Métricas de Classificação

- Curva ROC

- Múltiplas Notas de Corte

---

## Preditores Categóricos

### Preditor com apenas 2 categorias

Saldo médio no cartão de crédito é diferente entre homens e mulheres?

$$
y_i = \beta_0 + \beta_1x_i \space\space\space\space\space\space \text{em que}\space\space\space\space\space\space x_i = \Bigg\\{\begin{array}{ll}1&\text{se o i-ésimo carro for }\texttt{manual}\\\\
0&\text{se o i-ésimo carro for } \texttt{automático}\end{array}
$$

.footnote[
Ver [ISL](https://www.ime.unicamp.br/~dias/Intoduction%20to%20Statistical%20Learning.pdf) página 84 (Predictors with Only Two Levels).
]

---

## Preditores Categóricos

### Preditor com 3 ou mais categorias

]

Exemplo: Modelo linear

`$$y_i = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i}$$`

Em que

`$x_{1i} = \Bigg \{ \begin{array}{ll} 1 & \text{se for }\texttt{Multi_Family}\\0&\text{caso contrário}\end{array}$`

`$x_{2i} = \Bigg \{ \begin{array}{ll} 1 & \text{se for }\texttt{Residential}\\0&\text{caso contrário}\end{array}$`

]

---

## Preditores Categóricos

### Preditor com 3 ou mais categorias

"One hot enconding" ou "Dummies" ou "Indicadores".

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> type </th>
   <th style="text-align:right;"> (Intercept) </th>
   <th style="text-align:right;"> typeMulti_Family </th>
   <th style="text-align:right;"> typeResidential </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Residential </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Multi_Family </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Condo </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residential </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Condo </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Multi_Family </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>

steps: `step_dummy()`

---

## Preditores Categóricos

### Preditor com 3 ou mais categorias

As previsões para cada categoria ficaria assim:

`$y_{i} = \left\{ \begin{array}{ll} \beta_0 & \text{se for }\texttt{Condo}\\ \beta_0 + \beta_1&\text{se for } \texttt{Multi_Family}\\ \beta_0 + \beta_2&\text{se for } \texttt{Residential}\end{array}\right.$`

---

## Transformações Não Lineares dos Preditores

### Exemplo: log

---

## Transformações Não Lineares dos Preditores

### Exemplo: log

]

Relação real entre `x` e `y`: `$y = 10 + 0.5log(x)$`

Modelos propostos:

1) `y ~ x` 
  
  2) `y ~ log(x)`
]

Outras transformações comuns: raíz quadrada, Box-Cox.

steps: `step_log()`, `step_BoxCox()`, `step_sqrt()`

---

## Transformações Não Lineares dos Preditores

#### Exemplo: Regressão Polinomial

Modelo proposto: `$y = \beta_0 + \beta_1x + \beta_2x^2 + \beta_3x^3$`

Outras expansões comuns: b-splines, natural splines.

steps: `step_poly()`, `step_bs()`, `step_ns`

---

## Transformações Não Lineares dos Preditores

#### Exemplo: Regressão Polinomial

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> y </th>
   <th style="text-align:right;"> idade </th>
   <th style="text-align:right;"> idade2 </th>
   <th style="text-align:right;"> idade3 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 456.5 </td>
   <td style="text-align:right;"> 5.3 </td>
   <td style="text-align:right;"> 28.2 </td>
   <td style="text-align:right;"> 149.7 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 492.5 </td>
   <td style="text-align:right;"> 7.4 </td>
   <td style="text-align:right;"> 55.4 </td>
   <td style="text-align:right;"> 412.2 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 548.4 </td>
   <td style="text-align:right;"> 11.5 </td>
   <td style="text-align:right;"> 131.3 </td>
   <td style="text-align:right;"> 1503.9 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 758.7 </td>
   <td style="text-align:right;"> 18.2 </td>
   <td style="text-align:right;"> 329.9 </td>
   <td style="text-align:right;"> 5993.0 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 444.7 </td>
   <td style="text-align:right;"> 4.0 </td>
   <td style="text-align:right;"> 16.3 </td>
   <td style="text-align:right;"> 65.6 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 748.3 </td>
   <td style="text-align:right;"> 18.0 </td>
   <td style="text-align:right;"> 322.8 </td>
   <td style="text-align:right;"> 5800.8 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 820.5 </td>
   <td style="text-align:right;"> 18.9 </td>
   <td style="text-align:right;"> 357.0 </td>
   <td style="text-align:right;"> 6744.3 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 517.0 </td>
   <td style="text-align:right;"> 13.2 </td>
   <td style="text-align:right;"> 174.7 </td>
   <td style="text-align:right;"> 2308.3 </td>
  </tr>
</tbody>
</table>

]

Outras expansões comuns: b-splines, natural splines.

steps: `step_poly()`, `step_bs()`, `step_ns`

]

---

## Interações

Interação entre duas variáveis explicativas: `species` e `bill_length_mm`

---

## Interações

Modelo proposto (Matemático): Seja `y = flipper_length_mm` e `x = bill_length_mm`,

`$$\small \begin{array}{l} y = \beta_0 + \beta_1x\end{array}$$`

Modelo proposto (em R): `Sepal.Width ~ Sepal.Length`

---

## Interações

Modelo proposto (Matemático): Seja `y = Sepal.Width` e `x = Sepal.Length`,

`$$\small \begin{array}{l} y = \beta_0 + \beta_1x + \beta_2I_{versicolor} + \beta_3I_{virginica}\end{array}$$`

Modelo proposto (em R): `Sepal.Width ~ Sepal.Length + Species`

---

## Interações

Modelo proposto (Matemático): Seja `y = Sepal.Width` e `x = Sepal.Length`,

`$$\small \begin{array}{l} y = \beta_0 + \beta_1x + \beta_2I_{versicolor} + \beta_3I_{virginica} + \beta_4\color{red}{xI_{versicolor}} + \beta_5\color{red}{xI_{virginica}}\end{array}$$`

Modelo proposto (em R): `step_interact(~flipper_length_mm:starts_with("species_"))`.

---
class: middle, center

## Exemplo 04

---

## Outras referências

- Transformações recomendadas p/ cada modelo: https://www.tmwr.org/pre-proc-table.html

- Lista de transformações do recipes: https://recipes.tidymodels.org/reference/index.html

- Embbed: p/ quando o preditor tem muitas categorias: https://embed.tidymodels.org/

- Textos: quando colunas tem textos https://github.com/tidymodels/textrecipes

- Séries temporais: https://business-science.github.io/timetk/reference/index.html#section-feature-engineering-operations-recipe-steps-

---
exclude: false

---

# Classificação

---

# Regressão Logística

### Para  `$Y \in \{0, 1\}$` (binário)

$$
log\left$\frac{p}{1-p}\right$ = \beta_0 + \beta_1x
$$

Ou...

$$
p = \frac{1}{1 + e^{-(\beta_0 + \beta_1x)}}
$$

```r
### No R:
logistic_reg() %>%
  fit(spam ~ exclamacoes, data = dt_spam)
```

]

.footnote[
Ver [ISL](https://www.ime.unicamp.br/~dias/Intoduction%20to%20Statistical%20Learning.pdf) página 131 (Logistic Regression).
]

]

---

# Regressão Logística

---

# Regressão Logística

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---

# Árvore de Decisão

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---

# Regressão Logística - Custo

A **Métrica** que a regressão logística usa de **Função de Custo** chama-se *log-loss* (ou *Binary Cross-Entropy*):

`$$D = \frac{-1}{N}\sum[y_i \log\hat{y_i} + (1 - y_i )\log(1 - \hat{y_i})]$$`

Para cada linha da base de dados seria assim...

`$$D_i = \begin{cases} \\ -\log(\hat{y}_i) & \text{quando} \space y_i = 1 \\\\\\ -\log(1-\hat{y}_i) & \text{quando} \space y_i = 0 \\ \!\end{cases}$$`

]

]

---

# Regressão Logística - Regularização

A **Métrica** que a regressão logística usa de **Função de Custo** chama-se *log-loss* (ou *Binary Cross-Entropy*):

`$$D = \frac{-1}{N}\sum[y_i \log\hat{y_i} + (1 - y_i )\log(1 - \hat{y_i})]$$`

Regularizar é analogo a Regressão Linear.

`$$D_{regularizado} = D + \color{red}{\lambda}\sum_{j = 1}^{p}|\beta_j|$$`

**PS1:** Se `$\log\left(\frac{\hat{p_i}}{1-\hat{p_i}}\right) = \beta_0 + \beta_1x$` então
`$\hat{p_i} = \frac{1}{1 + e^{-(\beta_0 + \beta_1x)}}$`.

---

# Regressão Logística - Predições

O "produto final" será um vetor de probabilidades estimadas.

<table>
 <thead>
  <tr>
   <th style="text-align:right;background-color: white !important;text-align: center;"> pts excl </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> classe observada </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> prob </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> classe predita </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 167 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 0.79 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Spam </td>
  </tr>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 129 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 0.45 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Não Spam </td>
  </tr>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 299 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 1.00 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Spam </td>
  </tr>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 270 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 1.00 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Spam </td>
  </tr>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 187 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 0.89 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Spam </td>
  </tr>
  <tr>
   <td style="text-align:right;background-color: white !important;text-align: center;"> 85 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> 0.12 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;color: purple !important;"> Não Spam </td>
  </tr>
</tbody>
</table>

]

]

---

# Matriz de Confusão

.pull-left[
<table class="table table-bordered" style="font-size: 20px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Neg      </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Pos  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Neg </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> TN </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> FN </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Pos </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> FP </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> TP </td>
  </tr>
</tbody>
</table>

<br/>

<table class="table table-bordered" style="font-size: 20px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 50%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 410 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 73 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 52 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 465 </td>
  </tr>
</tbody>
</table>
]

$$
\begin{array}{lcc}
\mbox{accuracy}  & = & \frac{TP + TN}{TP + TN + FP + FN}\\\\
&   & \\\\
\mbox{precision} & = & \frac{TP}{TP + FP}\\\\
&   & \\\\
\mbox{recall/TPR}    & = & \frac{TP}{TP + FN} \\\\
&   & \\\\
\mbox{F1 score}       & =& \frac{2}{1/\mbox{precision} + 1/\mbox{recall}}\\\\
&   & \\\\
\mbox{FPR}    & = & \frac{FP}{FP + TN}
\end{array}
$$

]

---

# Nota de Corte (Threshold)

<table class="table table-bordered" style="font-size: 16px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 10%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 267 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 8 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 195 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 530 </td>
  </tr>
</tbody>
</table>

<table class="table table-bordered" style="font-size: 16px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 25%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 332 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 28 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 130 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 510 </td>
  </tr>
</tbody>
</table>

<table class="table table-bordered" style="font-size: 16px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 50%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 410 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 73 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 52 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 465 </td>
  </tr>
</tbody>
</table>

]

<table class="table table-bordered" style="font-size: 16px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 75%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 443 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 112 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 19 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 426 </td>
  </tr>
</tbody>
</table>

<table class="table table-bordered" style="font-size: 16px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: red !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">p &gt; 90%</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; color: black !important;padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Não Spam </th>
   <th style="text-align:right;background-color: white !important;text-align: center;"> Spam </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Não Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 456 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 171 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> Spam </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 3in; "> 6 </td>
   <td style="text-align:right;background-color: white !important;text-align: center;width: 2in; "> 367 </td>
  </tr>
</tbody>
</table>

]

---

# Curva ROC

.pull-left[
<img src="02-intro-classificacao_files/figure-html/unnamed-chunk-26-1.png" style="display: block; margin: auto;" />

[An introduction to ROC analysis](https://people.inf.elte.hu/kiss/11dwhdm/roc.pdf)

]

<br/>

$$
\begin{array}{lcc}
\mbox{TPR}    & = & \frac{TP}{TP + FN} \\\\
&   & \\\\
\mbox{FPR}    & = & \frac{FP}{FP + TN}
\end{array}
$$

]

---

# Curva ROC - Métrica AUC

[An introduction to ROC analysis](https://people.inf.elte.hu/kiss/11dwhdm/roc.pdf)

]

<br/>

$$
\mbox{AUC} = \mbox{Area Under The ROC Curve}
$$
]

**PS:** AUC varia de 0.5 a 1.0. O que significa se AUC for zero?

---

# Curva ROC - Playground

---

# Múltiplas Notas de Corte

Risco por Segmentação

<table class="table table-bordered" style="font-size: 20px; width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Observado</div></th>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
</tr>
  <tr>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Predito </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Neg      </th>
   <th style="text-align:left;background-color: white !important;text-align: center;"> Pos  </th>
   <th style="text-align:left;background-color: white !important;text-align: center;">  N  </th>
   <th style="text-align:left;background-color: white !important;text-align: center;">  Risco  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> A (até 0,19) </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> 90 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> 11 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 101 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 11% </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> B (até 0,44) </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> 60 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> 40 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 100 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 40% </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> C (até 0,62) </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> 39 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> 60 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 99 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 60% </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; font-weight: bold;"> D (0,62 ou +) </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 3in; "> 20 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;width: 2in; "> 80 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 100 </td>
   <td style="text-align:left;background-color: white !important;text-align: center;"> 80% </td>
  </tr>
</tbody>
</table>

]

Usamos o `score` como preferirmos

```r
dados %>%
  mutate(
    segmento = case_when(
      score <  0.19 ~ "A",
      score <  0.44 ~ "B",
      score <  0.62 ~ "C",
      score >= 0.62 ~ "D"))
```

]

---
class: middle, center

## Exemplo 05

---
class: middle, center

## Exercício 02