Problem $3$: Scoring a Classification Model

Suppose that $$ is a categorical variable that takes on values selected from a finite collection of classes or labels. A

classification model is a model that attempts to predict the class stored in $$ based on the values of other input variables.

Assume that we know the actual labels for a set of observations. Then we can evaluate the performance of a classification

model by calculating the model's accuracy on the data set. The accuracy score is the proportion of observations in the data

set for which the model generated a correct prediction. In other words:

Accuracy $=$ Number of correct predictions

Total number of observations

Write a function named find$\_$accuracy$()$ that accepts two parameters, true$\_$y and pred$\_$y$.$ The parameter true$\_$y is

expected to be an array of observed classes while pred$\_$y is expected to be an array of predicted classes generated by a

classification model. The function should return the accuracy score for the classification model, as calculated on this set of

observations. Do not call the function from this cell. Your function should use numpy operations and should not involve

any loops.

We will now apply our function to two different classification problems.

Suppose that a classification model is developed for the purposes of detecting the presence of a disease in patients based

on the results of blood work and other medical information. To test the performance of the model, it is applied to $20$

individuals for which the correct diagnosis is already known. We will use $\text{'}$P$\text{'}$ to indicate a positive diagnosis $($presence of

the disease$)$ and $\text{'}$N$\text{'}$ to denote a negative diagnosis $($absence of the disease$).$

The correct diagnoses for these individuals are given as follows:

$\text{'}$P$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},$

$\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'}$

The predicted diagnoses for these individuals are:

$\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$P$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'},\text{'}$N$\text{'},$

$\text{'}$N$\text{'},\text{'}$P$\text{'},\text{'}$N$\text{'}$

Create arrays named true$\_$diag and pred$\_$diag to store the diagnosis information provided above. Use

find$\_$accuracy$()$ to calculate the accuracy of the classification model that generated these these predictions. print the

result in the following format:

Model Accuracy: xxxx

Suppose that an image classification model is created to label images of dogs and cats. The model is applied to a collection

of $24$ images.

The true labels for the images are as follows:

'dog', 'dog', 'cat', 'dog', 'cat', 'cat', 'cat', 'dog', 'cat', 'cat', 'dog', 'cat',

'cat', 'dog', 'dog', 'dog', 'dog', 'cat', 'cat', 'cat', 'dog', 'dog', 'cat', 'cat'

The labels predicted by the image classification model are:

'dog', 'dog', 'cat', 'dog', 'cat', 'dog', 'cat', 'dog', 'cat', 'cat', 'dog', 'cat',

'cat', 'dog', 'cat', 'dog', 'dog', 'cat', 'dog', 'cat', 'dog', 'dog', 'cat', 'cat'

Create arrays named true$\_$labels and pred$\_$labels to store the label information provided above. Use

find$\_$accuracy$()$ to calculate the accuracy of the classification model that generated these these predictions. print the

result in the following format:

Model Accuracy: xxxx