CODE IN PYTHON DONT USE ANY INBUILT LIBRARY IMPLEMENT EVERYTHINF FROM SCRATCH,Note you are not allowed to use libraries which can take data, fit the

model, predict the labels and give final evaluation metrics.

Use MNIST

dataset for this question you can get it from google and select two digits $-0$ and $1.$ Label them as $-1$ and

$1.$ In this exercise you will be implementing AdaBoost.M$1.$ Perform following

tasks.

$$ Divide the train set into train and val set. Keep $1000$ samples from each

class for val. Note val should be used to evaluate the performance of the

classifier. Must not be used in obtaining PCA matrix.

$$ Apply PCA and reduce the dimension to p $=5.$ You can use the train set

of the two classes to obtain PCA matrix. For the remaining parts, use the

reduced dimension dataset.

$$ Now learn a decision tree using the train set. You need to grow a deci$-$

sion stump. For each dimension, find the unique values and sort them

in ascending order. The splits to be evaluated will be midpoint of two

consecutive unique values. Find the best split by minimizing weighted

miss$-$classification error. Denote this as h$1($x$).$ Note as we are dealing

with real numbers, each value may be unique. So just sorting them and

taking midpoint of consecutive values may also result in similar tree.

$$ Compute alpha $1$ and update weights.

$$ Now build another tree h$2($x$)$ using the train set but with updated weights.

Compute alpha $2$ and update weights. Similarly grow $300$ such stumps.

$$ After every iteration find the accuracy on val set and report. You should

show a plot of accuracy on val set vs$.$ number of trees. Use the tree that

gives highest accuracy and evaluate that tree on test set. Report test

accuracy. $[2]$