Traceback (most recent call last):
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
    executenb(
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/nbclient/client.py", line 1305, in execute
    return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/jupyter_core/utils/__init__.py", line 166, in wrapped
    return loop.run_until_complete(inner)
  File "/Users/mhjensen/miniforge3/lib/python3.9/asyncio/base_events.py", line 647, in run_until_complete
    return future.result()
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/nbclient/client.py", line 705, in async_execute
    await self.async_execute_cell(
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/nbclient/client.py", line 1058, in async_execute_cell
    await self._check_raise_for_error(cell, cell_index, exec_reply)
  File "/Users/mhjensen/miniforge3/lib/python3.9/site-packages/nbclient/client.py", line 914, in _check_raise_for_error
    raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content)
nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell:
------------------
%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import KFold
from sklearn.linear_model import Ridge
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import PolynomialFeatures

# A seed just to ensure that the random numbers are the same for every run.
# Useful for eventual debugging.
np.random.seed(3155)

# Generate the data.
nsamples = 100
x = np.random.randn(nsamples)
y = 3*x**2 + np.random.randn(nsamples)

## Cross-validation on Ridge regression using KFold only

# Decide degree on polynomial to fit
poly = PolynomialFeatures(degree = 6)

# Decide which values of lambda to use
nlambdas = 500
lambdas = np.logspace(-3, 5, nlambdas)

# Initialize a KFold instance
k = 5
kfold = KFold(n_splits = k)

# Perform the cross-validation to estimate MSE
scores_KFold = np.zeros((nlambdas, k))

i = 0
for lmb in lambdas:
    ridge = Ridge(alpha = lmb)
    j = 0
    for train_inds, test_inds in kfold.split(x):
        xtrain = x[train_inds]
        ytrain = y[train_inds]

        xtest = x[test_inds]
        ytest = y[test_inds]

        Xtrain = poly.fit_transform(xtrain[:, np.newaxis])
        ridge.fit(Xtrain, ytrain[:, np.newaxis])

        Xtest = poly.fit_transform(xtest[:, np.newaxis])
        ypred = ridge.predict(Xtest)

        scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)

        j += 1
    i += 1


estimated_mse_KFold = np.mean(scores_KFold, axis = 1)

## Cross-validation using cross_val_score from sklearn along with KFold

# kfold is an instance initialized above as:
# kfold = KFold(n_splits = k)

estimated_mse_sklearn = np.zeros(nlambdas)
i = 0
for lmb in lambdas:
    ridge = Ridge(alpha = lmb)

    X = poly.fit_transform(x[:, np.newaxis])
    estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)

    # cross_val_score return an array containing the estimated negative mse for every fold.
    # we have to the the mean of every array in order to get an estimate of the mse of the model
    estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)

    i += 1

## Plot and compare the slightly different ways to perform cross-validation

plt.figure()

plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')
plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')

plt.xlabel('log10(lambda)')
plt.ylabel('mse')

plt.legend()

plt.show()
------------------


---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Cell In[1], line 1
----> 1 get_ipython().run_line_magic('matplotlib', 'inline')
      3 import numpy as np
      4 import matplotlib.pyplot as plt

File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
   2430     kwargs['local_ns'] = self.get_local_scope(stack_depth)
   2431 with self.builtin_trap:
-> 2432     result = fn(*args, **kwargs)
   2434 # The code below prevents the output from being displayed
   2435 # when using magics with decorator @output_can_be_silenced
   2436 # when the last Python token in the expression is a ';'.
   2437 if getattr(fn, magic.MAGIC_OUTPUT_CAN_BE_SILENCED, False):

File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99, in PylabMagics.matplotlib(self, line)
     97     print("Available matplotlib backends: %s" % backends_list)
     98 else:
---> 99     gui, backend = self.shell.enable_matplotlib(args.gui.lower() if isinstance(args.gui, str) else args.gui)
    100     self._show_matplotlib_backend(args.gui, backend)

File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606, in InteractiveShell.enable_matplotlib(self, gui)
   3585 def enable_matplotlib(self, gui=None):
   3586     """Enable interactive matplotlib and inline figure support.
   3587 
   3588     This takes the following steps:
   (...)
   3604         display figures inline.
   3605     """
-> 3606     from matplotlib_inline.backend_inline import configure_inline_support
   3608     from IPython.core import pylabtools as pt
   3609     gui, backend = pt.find_gui_and_backend(gui, self.pylab_gui_select)

File ~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1
----> 1 from . import backend_inline, config  # noqa
      2 __version__ = "0.1.6"  # noqa

File ~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6
      1 """A matplotlib backend for publishing figures via display_data"""
      3 # Copyright (c) IPython Development Team.
      4 # Distributed under the terms of the BSD 3-Clause License.
----> 6 import matplotlib
      7 from matplotlib import colors
      8 from matplotlib.backends import backend_agg

ModuleNotFoundError: No module named 'matplotlib'