---
title: "About evaluation metrics"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{About evaluation metrics}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```


## Root Mean Square Error (RMSE)

RMSE measures the average deviation between predicted values and actual values. It is calculated as follows:

\[ \text{RMSE} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2} \]

## R-squared (R²)

R² measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is calculated as follows:

\[ R^2 = 1 - \frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{\sum_{i=1}^{n}(y_i - \bar{y})^2} \]

## Precision-Recall Area Under Curve (PR-AUC)

PR-AUC measures the area under the precision-recall curve. It is often used in binary classification tasks where the class distribution is imbalanced.

## Performance Ratio

performance ratio is calculated as the ratio of PR-AUC to the PR-AUC of a random classifier (`pr_randm_AUC`). 
It provides a measure of how well the model performs compared to a random baseline.

\[ performanceRatio =  \frac{PR_{AUC}}{PR_{randomAUC}} \]


## Receiver Operating Characteristic Area Under Curve (ROC AUC)

ROC AUC measures the area under the receiver operating characteristic curve. It evaluates the classifier's ability to distinguish between classes.

## Confusion Matrix

|                 | Predicted Negative | Predicted Positive |
|:---------------:|:------------------:|:------------------:|
| Actual Negative | TN                 | FP                 |
| Actual Positive | FN                 | TP                 |

## Accuracy

Accuracy measures the proportion of correct predictions out of the total predictions made by the model. It is calculated as follows:

\[
\text{Accuracy} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}}
\]

## Specificity

Specificity measures the proportion of true negatives out of all actual negatives. It is calculated as follows:

\[
\text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}}
\]

## Recall (Sensitivity)

Recall, also known as sensitivity, measures the proportion of true positives out of all actual positives. It indicates the model's ability to correctly identify positive instances.

\[ \text{Recall} = \text{Sensitivity} = \frac{\text{TP}}{\text{TP} + \text{FN}} \]

## Precision

Precision measures the proportion of true positives out of all predicted positives. It indicates the model's ability to avoid false positives.

\[ \text{Precision} = \frac{\text{TP}}{\text{TP} + \text{FP}} \]