k-NN GridSearchCV taking extremely long time to execute - scikit-learn

Question

I am attempting to use sklearn to train a KNN model on the MNIST classification task. When I try to tune my parameters using either sklearn's GridSearchCV or RandomisedSearchCV classes, my code is taking an extremely long time to execute.
As an experiment, I created a KNN model using KNeighborsClassifier() with the default parameters and passed these same parameters to GridSearchCV. Afaik, this should mean GridSearchCV only has single set of parameters and so should effectively not perform a "search". I then called the .fit() methods of both on the training data and timed their execution (see code below). The KNN model's .fit() method took about 11 seconds to run, whereas the GridSearchCV model took over 20 minutes.
I understand that GridSearchCV should take slightly longer as it is performing 5-fold cross validation, but the difference in execution time seems too large for it to be explained by that.
Am I doing something with my GridSearchCV call that it causing it to take such a long time to execute? And is there anything that I can do to accelerate it?
import sklearn
import time
# importing models
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.neighbors import KNeighborsClassifier
# Importing data
from sklearn.datasets import fetch_openml
mnist = fetch_openml(name='mnist_784')
print("data loaded")
# splitting the data into stratified train & test sets
X, y = mnist.data, mnist.target # mnist mj.data.shape is (n_samples, n_features)
sss = StratifiedShuffleSplit(n_splits = 1, test_size = 0.2, random_state = 0)
for train_index, test_index in sss.split(X,y):
X_train, y_train = X[train_index], y[train_index]
X_test, y_test = X[test_index], y[test_index]
print("data split")
# Data has no missing values and is preprocessed, so no cleaing needed.
# using a KNN model, as recommended
knn = KNeighborsClassifier()
print("model created")
print("training model")
start = time.time()
knn.fit(X_train, y_train)
end = time.time()
print(f"Execution time for knn paramSearch was: {end-start}")
# Parameter tuning.
# starting by performing a broad-range search on n_neighbours to work out the
# rough scale the parameter should be on
print("beginning param tuning")
params = {'n_neighbors':[5],
'weights':['uniform'],
'leaf_size':[30]
}
paramSearch = GridSearchCV(
estimator = knn,
param_grid = params,
cv=5,
n_jobs = -1)
start = time.time()
paramSearch.fit(X_train, y_train)
end = time.time()
print(f"Execution time for knn paramSearch was: {end-start}")

Answer 1

With vanilla KNN, the costly procedure is predicting, not fitting: fitting just saves a copy of the data, and then predicting has to do the work of finding nearest neighbors. So since your search involves scoring on each test fold, that's going to take a lot more time than just fitting. A better comparison would have you predict on the training set in the no-search section.
However, sklearn does have different options for the algorithm parameter, which aim to trade away some of the prediction complexity for added training time, by building a search structure so that fewer comparisons are needed at prediction time. With the default algorithm='auto', you're probably building a ball tree, and so the effect of the first paragraph won't be so profound. I suspect this is still the issue though: now the training time will be non-neglibible, but the scoring portion in the search is what takes most of the time.