Unverified Commit 2fac1411 authored by Simon Bowly's avatar Simon Bowly
Browse files

fix plots

parent 81028126
......@@ -55,13 +55,12 @@
```
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# split into a training set with 80% of the data, and a testing set as the remainder
X_train, X_test, Y_train, Y_test = train_test_split(nX,Y,test_size=0.8)
X_train, X_test, Y_train, Y_test = train_test_split(nX,Y,test_size=0.8, random_state=1)
linear = LinearRegression() # instantatiate the linear regression model
linear.fit(X_train,Y_train) # fit the data to the model
training_score = linear.score(X_train,Y_train) # calculate rsq for the training set
# use the independent variables for the testing set to predict the target variable
preds_linear = linear.predict(X_test)
......@@ -79,16 +78,18 @@
We can see `AGE`, `SEX`, `BP`, `BMI` and `S6` have very low variance, whereas `S1`-`S5` have high variance due to overfitting. Of the low variance features, `AGE` and `S6` seem to have little effect on the predictions.
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# cross_validate takes the particular model, in this case linear regression which we instantatiated earlier,
# and undertakes a number of runs according the method specified by cv=
# RepeatedKFold splits the data into n sections and repeat the regression modelling 5 times, giving 25 runs
# return_estimator=True returns the fitting data for each run
scores = cross_validate(linear, nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5), return_estimator=True)
scores = cross_validate(
linear, nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5, random_state=23),
return_estimator=True
)
# take the results for each simulation (estimator), extract the coefficients for each run
# and add them to a dataframe with columns being the feature names
coefs = pd.DataFrame([est.coef_ for est in scores['estimator']],columns=feature_names)
# plot the descriptive statics of the coefficients in a box and whisker plot to show variability
ax = coefs.plot(kind='box',figsize=(10,7))
......@@ -97,11 +98,11 @@
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
![](data:image/png;base64,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)
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aZvM2nHs7Q0BCAV/CRtGwMWq1YY2NjjI+PMzAwQHxiCwMDA4yPjzM8PGzQqq0sdea83d+dxaDVijP7pnXHbdOcfe1DxCe27GvPvXv49m3T+72x+aalVnM8eWUzaLXizL459X2sl82nHs7AwMC+ZZOTkwx/vNdr0z4KCx11zbXMkJBqDFqtWKOjowwNDTE+Ps6GDRuYmppiaGiIsbGxVpfWkQxO6dExaLVizY7DDg8PMz09TW9vL2NjY47PSlpWBq1WtMHBQYNVbWMp108Gr6G8Uhi0krRMSlw/GbwQRrvzhBWSJBVk0EqSVJBBK0lSQQatJEkFGbSSJBVk0EqSVJBBK0lSQQatJEkFecIKSVoma3pHOOHKkQLbBfBc1O3KoJWkZbJzepNnhjoEGbSSOprnD1a7M2gldTTPH6x252QoSZIKMmglSSrIrmNJWkYluqTXru5u+jbVPAatJC2TpYwl94xsKTL2rOVn17EkSQUZtJIkFWTQSpJUkGO0kqQVaakTz0qNiRu0kqQVab7gXO6JZnYdS5JUkEe0kjqaV8QRlDnndbPOd23QSupoXhFHAD/sOZ81zd4mAF9peDsGrSSp45X4wNWsD1srKmjbZYaZJC3FfO9d87X73tVZVlTQtssMM0laCt+fVrYVFbSSpENXs8fVm3WxBoNWktTx2vmCDQatpI7npefUzgxaSR2tnY9kJPDMUJIkFVX8iDYiTgHeDXQBf56Zm5qx3RJnAYHmnQlEktRaB77v/+dtn2HH569i5oG7eOz4eta+8HX8xDNftG95R15UICK6gD8BXgbcBVwfEddk5m2NbnvHrhnPBiNJmld9RkxMTDB69Ue4+uor2LBhA1NTUwwNDTE2+FwGBweL1hGZWW7jES8ELsrMl1eP3w6Qmf9nrvWPO+64vPDCCxe17S988wFe8NSfalapxbcrqfX8+z50XX/99Rx//PEcccQR+9oefPBBvvGNb3DSSSc1vP1zzjnnhszsn2tZ6THao4A76x7fVbXtExEbI2JrRGydmVl8V7AkSYv1yCOPsHbt2v3a1q5dyyOPPFJ836WPaF8DnJKZb6oenwk8PzPPm2v9/v7+3Lp166K2XWr2oLMSpZXLv+9DV19fH5s3b2ZgYGBf2+TkJMPDw2zbtq3h7UfEvEe0pSdD3Q0cXfd4fdXWMC+NJUlarNHRUYaGhhgfH99/jHZsrPi+Swft9cDxEXEctYA9A3h9MzbspbEkSYs1O+FpeHiY6elpent7GRsbKz4RCgoHbWbuiYjzgE9Q+3rP5Zl5a8l9SpI0l8HBwWUJ1gMV/x5tZl4LXFt6P5IktaOOPgWj5zeVJLW7orOOl2ops46XwpmG0qFnKR/EfX9Qo1o561iSWsLwVLvwogKSJBW0oo5oF+oqmmuZn3glSaWtqKA1OCVJ7cauY0mSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKmgFXU92k6z0IXqD+S1diWpMxm0LTRXePaMbDFUJWkFsetYkqSCDFpJkgoyaCVJKsiglSSpICdDLYMTL76OHbtmFr3+Ymcjr13dzc0Xnvxoy5IkLQODdhns2DVTZCbxUr4eJElqDbuOJUkqyKCVJKkgu46XwZreEU64cqTAdgE8uYUktTODdhnsnN7kGK0kHaLsOpYkqSCPaJdJiaPPtau7m75NSVJzGbTLYCndxl5UQJJWFruOJUkqyKCVJKkgg1aSpIIco22h+SZIzdXuuK0kdSaDtoUMT0la+ew6liSpIIO2TUxMTNDX10dXVxd9fX1MTEy0uiRJUhPYddwGJiYmGB0dZXx8nA0bNjA1NcXQ0BAAg4ODLa5OktSIyMxW17BPf39/bt26tdVlLLu+vj42b97MwMDAvrbJyUmGh4fZtm1bCyuTJC1GRNyQmf1zLjNoW6+rq4vdu3fT3f1fp1ScmZlh1apV7N27t4WVSZIWY6GgdYy2DfT29jI1NbVf29TUFL29vS2qSJLULAZtGxgdHWVoaIjJyUlmZmaYnJxkaGiI0dHRVpcmSWqQk6HawOyEp+HhYaanp+nt7WVsbMyJUJK0AjhGK0lSgxyjlSSpRQxaSZIKMmglSSrIoJUkqSCDVpKkghoK2oh4R0R8NSJuiYi/i4gj6pa9PSJuj4ivRcTLG65UkqQO1OgR7SeBvsx8NvB14O0AEfFM4AzgWcApwPsioqvBfUmS1HEaCtrMvC4z91QPvwCsr+6fDnw4M3+Qmd8Cbgee18i+JEnqRM0coz0X+Hh1/yjgzrpld1VtPyIiNkbE1ojYet999zWxHEmSWu+gp2CMiE8BT55j0Whm/kO1ziiwB/jQUgvIzMuAy6B2Zqil/rwkSe3soEGbmS9daHlEnA28EnhJ/tf5HO8Gjq5bbX3VJknSIaXRWcenAG8DXpWZj9QtugY4IyIOi4jjgOOBLzWyL0mSOlGjV+95L3AY8MmIAPhCZr45M2+NiKuB26h1Kf96ZnoFc0nSIaehoM3Mpy2wbAwYa2T7kiR1Os8MJUlSQQatJEkFGbSSJBVk0EqSVJBBK0lSQQatJEkFGbSSJBXU6AkrJDWgZ2TLktbfvum0QpVIKsWglVpovuDsGdliqEorhF3HkiQVZNBKklSQQStJUkEGrSRJBRm0kiQVZNBKklSQQStJUkEGrSRJBRm0kiQVZNBKklSQQStJUkEGrSRJBRm0kiQVZNBKklSQQStJUkEGrSRJBXnhd2mZnHjxdezYNbPo9XtGthx0nbWru7n5wpMbKUtSYQattEx27Jph+6bTmrrNxYSxpNay61iSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgL/wuLZM1vSOccOVIk7cJ0NyLyUtqLoNWWiY7pzexfVNzQ7FnZEtTtyep+ew6liSpIINWkqSCDFpJkgoyaCVJKsiglSSpIINWkqSCDFpJkgoyaCVJKsiglSSpIINWkqSCmhK0EXF+RGRErKseR0S8JyJuj4hbIuJnm7EfSZI6TcNBGxFHAycD365rfgVwfHXbCPxpo/uRJKkTNeOI9lLgbUDWtZ0OfDBrvgAcERFHNmFfkiR1lIaCNiJOB+7OzJsPWHQUcGfd47uqNkmSDikHvUxeRHwKePIci0aB36HWbfyoRcRGat3LHHPMMY1sSpKktnPQoM3Ml87VHhEnAMcBN0cEwHrgxoh4HnA3cHTd6uurtrm2fxlwGUB/f3/OtY4kSZ3qUXcdZ+ZXMvOJmdmTmT3Uuod/NjO/C1wDvLGaffwCYEdm3tOckiVJ6hwHPaJ9lK4FTgVuBx4Bzim0H0mS2lrTgrY6qp29n8CvN2vbkiR1Ks8MJUlSQaW6jiXNoWdkS1O3t3Z1d1O3J6n5DFppmWzfdNqi1+0Z2bKk9SW1L7uOJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCjJoJUkqyKCVJKkgg1aSpIIMWkmSCnpMqwuQDmU9I1uWtGz7ptNKliOpAINWaiGDU1r57DqWJKkgg1aSpIIMWkmSCmo4aCNiOCK+GhG3RsQf1bW/PSJuj4ivRcTLG92PJEmdqKHJUBExAJwOnJiZP4iIJ1btzwTOAJ4FPAX4VEQ8PTP3NlqwJEmdpNEj2rcAmzLzBwCZeW/Vfjrw4cz8QWZ+C7gdeF6D+5IkqeM0GrRPB34xIr4YEZ+JiJOq9qOAO+vWu6tq+xERsTEitkbE1vvuu6/BciRJai8H7TqOiE8BT55j0Wj1848HXgCcBFwdEU9dSgGZeRlwGUB/f38u5WclSWp3Bw3azHzpfMsi4i3A32ZmAl+KiB8C64C7gaPrVl1ftUmSdEhptOv474EBgIh4OvBY4H7gGuCMiDgsIo4Djge+1OC+pBVvYmKCvr4+urq66OvrY2JiotUlSWpQo6dgvBy4PCK2Af8POKs6ur01Iq4GbgP2AL/ujGNpYRMTE4yOjjI+Ps6GDRuYmppiaGgIgMHBwRZXJ+nRiloutof+/v7cunVrq8uQWqKvr4/NmzczMDCwr21ycpLh4WG2bdvWwsokHUxE3JCZ/XMuM2il9tDV1cXu3bvp7u7e1zYzM8OqVavYu9cOIamdLRS0noJRahO9vb1MTU3t1zY1NUVvb2+LKpLUDAat1CZGR0cZGhpicnKSmZkZJicnGRoaYnR0tNWlSWqA16OV2sTshKfh4WGmp6fp7e1lbGzMiVBSh3OMVpKkBjlGK0lSixi0kiQVZNBKklSQQStJUkEGrSRJBRm0kiQVZNBKklSQQStJUkEGrSRJBRm0kiQVZNBKklSQQStJUkFtdVGBiLgPuKPAptcB9xfYbgnWWkYn1QqdVa+1lmGt5ZSo99jMfMJcC9oqaEuJiK3zXVWh3VhrGZ1UK3RWvdZahrWWs9z12nUsSVJBBq0kSQUdKkF7WasLWAJrLaOTaoXOqtday7DWcpa13kNijFaSpFY5VI5oJUlqCYNWkqSCVkTQRsSrIyIj4hl1bc+LiE9HxDci4saI2BIRJ1TLLoqIuyPiprrbEctU62hE3BoRt1T7fX5V59fqavlIte57IuL3DvjZP1mOOqv97a3qubl6Dn++au+pnu8/rFt3XUTMRMR7q8cXRcRbl6vWJdS9q1p2W0T8WUS0/G9gntfEeRFxe/U8r2t1jbPmqfVD1et3W0RcHhHdra4T5q11vHpd3BIRH4mIx7W6zllz1Vu37D0R8XAr66s3z3N7RUR8q+597DmtrhPmrTUiYiwivh4R0xHxv4oWkZkdfwOuAj4LXFw9fhKwHfj5unU2AK+u7l8EvLUFdb4Q+DxwWPV4HfAU4NNA/xzrHw58E3hqdfsWcMQy1vtw3f2XA5+p7vdUdX25bvlbgJuA97byOV5E3duq+48B/hX4lVbUuIjXxHOrercD61pZ4yJqPRWI6jYBvKWNaz28bp0/BkZaXetC9Vb3+4G/rH9dt2OtwBXAa1pd3yJrPQf4IPBjVfsTS9bxGDpc9Yl0AzAA/CNwIXAecGVm/tvsepk51ZoK93MkcH9m/gAgM+8HiIg5V87MhyJiFHhv1fR7mfngMtQ5l8OB79c9fgSYjoj+zNwKvA64mtqLuJ0cWDcAmbknIv4NeNryl7SfOV8TwHdg/tdGiyxYK0BEfAlY34LaDjRfrQBE7YldDbTLbND53hu6gHcArwd+uXXl7WdJ72MtNl+tbwFen5k/rNrvLVlEy7vNmuB04J8y8+vAAxHxc8CzgBsP8nO/VdfFMVm8yprrgKOr7or3RcSL6pZ9qK6ed8w2ZuYE8JPUPon/5TLVOWt1Vc9XgT8H/uCA5R8GzoiIo4G91L3httjB6iYifhx4CfCV5S7uAAu9JtrNgrVWXcZnAv/Ukur2N2+tEfEXwHeBZwCbW1XgAear9zzgmsy8p4W1HWih18FY1UV7aUQc1qoC68xX608Dr4uIrRHx8Yg4vmQRKyFoB6m94VP9O3jgChHxxaof/t11zZdm5nOq28ByFJqZDwM/B2wE7gOuioizq8VvqKvnt+tqX0/tU9lTWjCetKuq5xnAKcAHY/+Prf8EvAw4g1r3fbtYqO6fjoibgM8BWzLz460qEg76mmgri6j1fcC/ZuZnW1DefhaqNTPPodbzMk2tJ6bl5qn3d4BfpX0+DAALPrdvp/bh5STg8cAFrapx1gK1HgbsztppGD8AXF66kI69UfvPfITahQi2A3cC36Z2BHPxAeu+Briiun8RLRo/nKOmf2SeMdpqnY8CZwGbgHcsc30PH/D4P4Ansv9Y5+XUjg4eD5xNm43Rzld3u95mXxN1j7fTJmO0C9VKbcjm76nGvNrtduDzWrX9N+Bjra5tgXpnqr+t7dXth8Dtra5tkc/ti9vxua17z/0qcFzVFsCOkvvt9CPa1wB/mZnHZmZPZh5NbcLQJ4Gzo5ptWvnxllRYJyJ+5oAuiuewwNWKIuIV1ALig9Q+PPxKRDyzaJHz1/IMoAt44IBF7wQuyMzvLX9VB7dA3W1hqa+JVpqv1oh4E7VJZ4NZjXm12jy1fjsinlYtD+BV1N5wW26eet+fmU+u3tt6gEcys9VzChZ6HRxZLQ/g1cC25a9ufwv8ff09tXk9AC8Cvl6yjk6fDDUIXHJA20er9tcBl0TEUcC91C6J9Pt16/1WRPyPusevzsztBWsFeBywOWpfJdoD3E6tS+Mj1MZod1Xr3Q+8EngXtVl8CfxnRPw2tYlRv1S4zlmrq25WqH3qOysz99b3HmfmrcCty1TPYh207jYy52ui+rrB24AnA7dExLWZ+abWlQnM//r9LrU3r89Xz/HfZubvz7eRZTJXrW8G/i4iDqf2uriZ2mz5djDfc9uO5qv16oh4ArXn9iZqz3erzVfrHmrvub8FPAwU/dvyFIySJBXU6V3HkiS1NYNWkqSCDFpJkgoyaCVJKsiglSSpIINWkqSCDFpJkgr6/3L3SbyuZqCrAAAAAElFTkSuQmCC)
%% Cell type:markdown id: tags:
## Regularisation
......@@ -133,20 +134,19 @@
To use Ridge regularization (which adds a penalty term which is proportional to the sum of the squares of the coefficients), we need to find the optimal value of tuning parameter alpha. Generally this would be done using `RidgeCV`, however here we will graphically compare the training and testing scores. What we want to determine is the value of alpha for which we obtain the maximum value of the testing score. To generate the figure we create an array of alpha values, which in this case are logarithmically distributed, and perform a Ridge regularization for each, and store the testing and training scores ( $R^2$ ). Then we plot these against alpha. From the figure we see the optimal value occurs at alpha approximately 20.
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# create an array of 21 alpha values logarithmically distributed between 10**(-2) and 10**2
alfas = np.logspace(-2,2,num=21)
# create two arrays for storage of the same size as alfas, but filled with zeros
ridge_training_score = np.zeros_like(alfas)
ridge_rsquared = np.zeros_like(alfas)
# loop over the values in the alfas array, at each loop the current value is alfa
# and idx is incremented by 1, starting at 0
for idx, alfa in enumerate(alfas):
ridge = Ridge(alpha=alfa) # instantatiate Ridge regularization with the current alfa
ridge = Ridge(alpha=alfa, random_state=1235) # instantatiate Ridge regularization with the current alfa
ridge.fit(X_train,Y_train) # train the model to our data set
# calculate the training score and store in the array ridge_training_score
ridge_training_score[idx] = ridge.score(X_train,Y_train)
preds_linear = ridge.predict(X_test) # calculate the model prediction for the test data
# calculate the correlation between the predicted and actual test data and store in the array ridge_rsquared
......@@ -160,49 +160,50 @@
plt.legend(loc='best');
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
Now can investigate Ridge regularization using the optimal value of alpha approximately 20. Now we see significantly reduced variance in the coefficient and that the most important variables are `BMI`, `BP` and `S5`.
Now can investigate Ridge regularization using the optimal value of alpha approximately 40. Now we see significantly reduced variance in the coefficient and that the most important variables are `BMI`, `BP` and `S5`.
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# cross_validate takes the particular model, in this case ridge regularization
# and undertakes a number of runs according the method specified by cv=
# RepeatedKFold splits the data into n sections and repeat the regression modelling 5 times, giving 25 runs
# return_estimator=True returns the fitting data for each run
scores = cross_validate(Ridge(alpha=20.), nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5), return_estimator=True)
scores = cross_validate(
Ridge(alpha=40.), nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5, random_state=2312),
return_estimator=True
)
# take the results for each simulation (estimator), extract the coefficients for each run
# and add them to a dataframe with columns being the feature names
coefs = pd.DataFrame([est.coef_ for est in scores['estimator']],columns=feature_names)
# plot the descriptive statics of the coefficients in a box and whisker plot to show variability
ax = coefs.plot(kind='box',figsize=(10,7))
plt.title('Ridge regression, alpha = 20.')
plt.title('Ridge regression, alpha = 40.')
plt.axhline(y=0, color='.5')
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
### Lasso regularization
We can repeat the same process for Lasso regularization, which adds a penalty term which is proportional to the sum of the absolute values of the coefficients. Here the optimal value for alpha is approximately 2.
We can repeat the same process for Lasso regularization, which adds a penalty term which is proportional to the sum of the absolute values of the coefficients. Here the optimal value for alpha is approximately 5.
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# create two arrays for storage of the same size as alfas, but filled with zeros
lasso_training_score = np.zeros_like(alfas)
lasso_rsquared = np.zeros_like(alfas)
# loop over the values in the alfas array, at each loop the current value is alfa
# and idx is incremented by 1, starting at 0
......@@ -223,38 +224,37 @@
plt.legend(loc='best');
```
%%%% Output: display_data
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1DUh1ag6akLyJpaVzrpUwqeZxWdgCALNvF/c0f59jmGcAFqQ2uAdPwjoikpUnN55Yn/DKt7ACTms9NUUSNg5K+iKSlVsU7kiqXxCjpi0h6apuVXLkkRElfRNLTsGnQPLNiWfPMSLnUmJK+iKSn7NFw0Uxo2xWwyO+LZkbKpcZ09o6IpK/s0UryAdOevohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iESEJJ38xGmNkGM9tkZpPjLB9vZh+a2ftm9o6Z9Qo+VBERqa1qk76ZNQUeAc4DegFXxEnqf3D3k909B3gAeDDoQEVEpPYS2dMfBGxy983ufgB4Drg4toK7fx7z9CjAgwtRRESC0iyBOl2ArTHPC4DBlSuZ2Q+AHwIZwNnxGjKzG4AbAI4//vhkYxURkVoK7ECuuz/i7v8K3AFMraLObHfPdffcjh07BvXSIiKSoESS/jaga8zzrGhZVZ4DvleLmEREpI4kkvSXAT3MrLuZZQBjgLzYCmbWI+bpBcDG4EIUEZGgVDum7+6lZnYLsBhoCsxx9zVmdjeQ7+55wC1mdg5QAvwTGFeXQYuISM0kciAXd18ELKpUNi3m8W0BxyUiInVAV+SKiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iESEJz74iINFTL8h6j64oZHOeF7LSObO0/kYEjb0x1WCmjpC8ijdayvMfos3wqmXYADDpRSNvlU1kGoU38Gt4RkUar64oZkYQfI9MO0HXFjBRFlHpK+iLSaB3nhVWU76rnSNKHkr6INFo7Lf69uHdah3qOJH0o6YtIo7W1/0SKPaNCWbFnsLX/xBRFlHpK+iLSaA0ceSOrB9zDDjpyyI0ddGT1gHtCexAXwNw9JS+cm5vr+fn5KXltEZGGysyWu3tuTdfXnr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgklPTNbISZbTCzTWY2Oc7yH5rZWjNbZWavmdk3gw9VRERqq9qkb2ZNgUeA84BewBVm1qtStZVArrtnAy8ADwQdqIiI1F4ie/qDgE3uvtndDwDPARfHVnD3N9x9f/Tp34CsYMMUEZEgJJL0uwBbY54XRMuqch3w53gLzOwGM8s3s/zCwvg3LBYRkboT6IFcM7sKyAVmxFvu7rPdPdfdczt2jH/DYhERqTvNEqizDega8zwrWlaBmZ0D3AkMdfevgglPRESClMie/jKgh5l1N7MMYAyQF1vBzPoBjwEj3X1n8GGKiEgQqk367l4K3AIsBtYB89x9jZndbWYjo9VmAK2B583sfTPLq6I5ERFJoUSGd3D3RcCiSmXTYh6fE3BcIiJSB3RFrohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCjpi4iEiJK+iEiIKOmLiISIkr6ISIgo6YuIhIiSvohIiCSU9M1shJltMLNNZjY5zvLvmNkKMys1s8uCD1NERIJQbdI3s6bAI8B5QC/gCjPrVana34FrgT8EHaCIiASnWQJ1BgGb3H0zgJk9B1wMrC2r4O5bossO1UGMIiISkESGd7oAW2OeF0TLRESkganXA7lmdoOZ5ZtZfmFhYX2+tIiIkFjS3wZ0jXmeFS1LmrvPdvdcd8/t2LFjTZoQEZFaSCTpLwN6mFl3M8sAxgB5dRuWiIjUhWqTvruXArcAi4F1wDx3X2Nmd5vZSAAzG2hmBcAo4DEzW1OXQYuISM0kcvYO7r4IWFSpbFrM42VEhn1ERCSN6YpcEZEQUdIXEQkRJX0RkRBR0hcRCRElfRGREFHSFxEJESV9EZEQUdIXEQmRhC7Oqi8lJSUUFBTw5ZdfpjoUqULLli3JysqiefPmqQ5FRGogrZJ+QUEBbdq0oVu3bphZqsORStyd3bt3U1BQQPfu3VMdjojUQFoN73z55Ze0b99eCT9NmRnt27fXNzGRBiytkj6ghJ/m9PcRadjSLumLiEjdUdKPsXv3bnJycsjJyaFTp0506dKl/PmBAweOuG5+fj4TJkyo9jVOO+20oMIVEUlaWh3ITdaClduYsXgD2/cU07ldJhOH9+R7/Wp++9727dvz/vvvAzB9+nRat27Nj370o/LlpaWlNGsWv8tyc3PJzc2t9jWWLFlS4/jq0pHem4g0Hg12T3/Bym1Mmf8h2/YU48C2PcVMmf8hC1bW6E6OVbr22msZP348gwcPZtKkSSxdupRTTz2Vfv36cdppp7FhwwYA3nzzTS688EIgssH4/ve/z5lnnskJJ5zAzJkzy9tr3bp1ef0zzzyTyy67jJNOOomxY8fi7gAsWrSIk046iQEDBjBhwoTydmOtWbOGQYMGkZOTQ3Z2Nhs3bgTg97//PdnZ2fTt25err74agC1btnD22WeTnZ3NsGHD+Pvf/x73vX300UeMGDGCAQMGcMYZZ7B+/fpA+1JEUq/B7trNWLyB4pKDFcqKSw4yY/GGWu3tx1NQUMCSJUto2rQpn3/+OW+//TbNmjXj1Vdf5cc//jF//OMfD1tn/fr1vPHGG+zdu5eePXty0003HXZu+8qVK1mzZg2dO3fm9NNP569//Su5ubnceOONvPXWW3Tv3p0rrrgibkyzZs3itttuY+zYsRw4cICDBw+yZs0a7rnnHpYsWUKHDh347LPPALj11lsZN24c48aNY86cOUyYMIEFCxYc9t6GDRvGrFmz6NGjB++99x4333wzr7/+eqB9KSKp1WCT/vY9xUmV18aoUaNo2rQpAEVFRYwbN46NGzdiZpSUlMRd54ILLqBFixa0aNGC4447jk8//ZSsrIo3Fxs0aFB5WU5ODlu2bKF169accMIJ5efBX3HFFcyePfuw9k899VTuvfdeCgoKuPTSS+nRowevv/46o0aNokOHDgAce+yxALz77rvMnz8fgKuvvppJkyYd9t727dvHkiVLGDVqVPmyr776qkb9JSLpq8EO73Rul5lUeW0cddRR5Y9/8pOfcNZZZ7F69WoWLlxY5TnrLVq0KH/ctGlTSktLa1SnKldeeSV5eXlkZmZy/vnn13iPvOy9HTp0iHbt2vH++++X/6xbt65GbYpI+mqwSX/i8J5kNm9aoSyzeVMmDu9Zp69bVFREly6R4aMnn3wy8PZ79uzJ5s2b2bJlCwBz586NW2/z5s2ccMIJTJgwgYsvvphVq1Zx9tln8/zzz7N7926A8uGd0047jeeeew6AZ599ljPOOOOw9o4++mi6d+/O888/D0Suvv3ggw+CfnsikmINNul/r18X7rv0ZLq0y8SALu0yue/SkwMfz69s0qRJTJkyhX79+iW1Z56ozMxMHn300fIDqm3atKFt27aH1Zs3bx59+vQhJyeH1atXc80119C7d2/uvPNOhg4dSt++ffnhD38IwK9+9SueeOIJsrOzefrpp3n44Yfjvvazzz7L7373O/r27Uvv3r156aWXAn9/IpJaVnbGSH3Lzc31/Pz8CmXr1q3j29/+dkriSSf79u2jdevWuDs/+MEP6NGjB7fffnuqwyqnv5NI6pjZcnev/vzwKjTYPf3G7Le//S05OTn07t2boqIibrzxxlSHJCKNRIM9e6cxu/3229Nqz15EGg/t6YuIhIiSvohIiCjpi4iEiJK+iEiI6EBujN27dzNs2DAAduzYQdOmTenYsSMAS5cuJSMj44jrv/nmm2RkZJRPnzxr1ixatWrFNddcU7eBi4gkqGEn/VXz4LW7oagA2mbBsGmQPbrGzVU3tXJ13nzzTVq3bl2e9MePH1/jWOqSu+PuNGmiL3oiYdNw/+tXzYOFE6BoK+CR3wsnRMoDtHz5coYOHcqAAQMYPnw4//jHPwCYOXMmvXr1Ijs7mzFjxrBlyxZmzZrFQw89RE5ODm+//TbTp0/nP//zPwE488wzueOOOxg0aBDf+ta3ePvttwHYv38/o0ePplevXlxyySUMHjyYyhetAUyePLn89co2RJ9++imXXHIJffv2pW/fvuVz9T/44IP06dOHPn368Mtf/hKITK/cs2dPrrnmGvr06cPWrVuZMWMGAwcOJDs7m7vuuivQfhOR9NRw9/RfuxtKKs2oWVIcKa/F3n4sd+fWW2/lpZdeomPHjsydO5c777yTOXPmcP/99/Pxxx/TokUL9uzZQ7t27Rg/fnyFbwevvfZahfZKS0tZunQpixYt4qc//Smvvvoqjz76KMcccwxr165l9erV5OTkHBbH7t27efHFF1m/fj1mxp49ewCYMGECQ4cO5cUXX+TgwYPs27eP5cuX88QTT/Dee+/h7gwePJihQ4dyzDHHsHHjRp566ilOOeUUXnnlFTZu3MjSpUtxd0aOHMlbb73Fd77znUD6TkTSU0J7+mY2wsw2mNkmM5scZ3kLM5sbXf6emXULPNLKigqSK6+Br776itWrV3PuueeSk5PDPffcQ0FBpP3s7GzGjh3LM888k/Adpy699FIABgwYUD6h2jvvvMOYMWMA6NOnD9nZ2Yet17ZtW1q2bMl1113H/PnzadWqFQCvv/46N910ExCZpbNt27a88847XHLJJRx11FG0bt2aSy+9tPxbxTe/+U1OOeUUAF555RVeeeUV+vXrR//+/Vm/fn35jVhEpPGqNluZWVPgEeBcoABYZmZ57r42ptp1wD/d/UQzGwP8Ari8LgIu1zYrOrQTpzwg7k7v3r159913D1v28ssv89Zbb7Fw4ULuvfdePvzww2rbK5tKOdlplJs1a8bSpUt57bXXeOGFF/j1r39do6mUY6eIdnemTJmiKR5EqrEs7zG6rpjBcV7ITuvI1v4TGTgyuf+bINsY8C9NBiS1YiWJ7OkPAja5+2Z3PwA8B1xcqc7FwFPRxy8Aw8zMahNYtYZNg+aV5s5vnhkpD0iLFi0oLCwsT/olJSWsWbOGQ4cOsXXrVs466yx+8YtfUFRUxL59+2jTpg179+5N6jVOP/105s2LHIdYu3Zt3I3Hvn37KCoq4vzzz+ehhx4qn/J42LBh/OY3vwHg4MGDFBUVccYZZ7BgwQL279/PF198wYsvvhh3KuXhw4czZ84c9u3bB8C2bdvYuXNnUrGLNHbL8h6jz/KpdKKQJgadKKTP8qksy3ssZW3UViJJvwsQu0tdEC2LW8fdS4EioH2tozuS7NFw0Uxo2xWwyO+LZgY2ng/QpEkTXnjhBe644w769u1LTk4OS5Ys4eDBg1x11VWcfPLJ9OvXjwkTJtCuXTsuuugiXnzxxfIDuYm4+eabKSwspFevXkydOpXevXsfNpXy3r17ufDCC8nOzmbIkCE8+OCDADz88MO88cYbnHzyyQwYMIC1a9fSv39/rr32WgYNGsTgwYO5/vrr6dev32Gv+93vfpcrr7ySU089lZNPPpnLLrss6Q2WSGPXdcUMMu1AhbJMO0DXFTNS3kZNVTu1spldBoxw9+ujz68GBrv7LTF1VkfrFESffxSts6tSWzcANwAcf/zxAz755JMKrxXGKXsPHjxISUkJLVu25KOPPuKcc85hw4YN1V4TkEph/DtJOB26qy1N4oxZHHKjyU/3pKSN3Nn7yN9+sMYjKYkcgdwGdI15nhUti1enwMyaAW2B3ZUbcvfZwGyIzKdfk4Abm/3793PWWWdRUlKCu/Poo4+mdcIXCZOd1jHukMpO60CnNGijJhIZ3lkG9DCz7maWAYwB8irVyQPGRR9fBrzuqbo7SwPTpk0b8vPz+eCDD1i1ahXnnXdeqkMSkait/SdS7BV3woo9g639J6a8jZqqdk/f3UvN7BZgMdAUmOPua8zsbiDf3fOA3wFPm9km4DMiG4YacXfq+hiw1Jy25RImA0feyDKInnmzi53Wga0DkjvzJug2YF+yb6OCtLpd4scff0ybNm1o3769En8acnd2797N3r176d69e6rDEQml2t4uMa2uyM3KyqKgoIDCwmDGriR4LVu2JCsruGshRKR+pVXSb968ufYgRUTqUMOdcE1ERJKmpC8iEiJK+iIiIZKys3fMbC+woY5fpi2RKSHqct1E6lVVJ5nyymWVn3cAKlwBXQfSoT+PtDzR/qyuf+ujL6uKI+j1gu7PMH82E6lbH//rPd29TfWhVqHsLkr1/UPkHP+6fo3Zdb1uIvWqqpNMeeWyOM9D0Z9HWp5of1bXv/XRl7Xpz2TWC7o/w/zZrE1/ptP/emMf3llYD+smUq+qOsmUVy6rzXurqXTozyMtT7Q/E+nf+lDT10xmvaD7M8yfzUTqpv3/eiqHd/K9FhcYSEXqz+CoL4Ol/gxWbfszlXv6s1P42o2R+jM46stgqT+DVav+TNmevoiI1L/GPqYvIiIxlPRFREJESV9EJETSMumb2ffM7LdmNtfMvpvqeBo6MzvBzH5nZi+kOpaGyMyOMrOnop/JsamOp6HT5zFYyebLwJO+mc0xs53R++bGlo8wsw1mtsnMJh+pDXdf4O7/DowHLg86xoYkoP7c7O7X1W2kDUuS/Xop8EL0Mzmy3oNtAJLpT30eq5dkfyaVL+tiT/9JYESlQJsCjwDnAb2AK8ysl5mdbGZ/qvRzXMyqU6PrhdmTBNef8rUnSbBfidwXemu02sF6jLEheZLE+1Oq9yTJ92dC+TLw+fTd/S0z61apeBCwyd03A5jZc8DF7n4fcGHlNixy26z7gT+7+4qgY2xIguhPOVwy/QoUEEn875OmQ6KplmR/rq3n8BqcZPrTzNaRRL6srw9wF77eU4LIP1GXI9S/FTgHuMzMxtdlYA1UUv1pZu3NbBbQz8ym1HVwDVhV/Tof+Dcz+w2pmWKgoYrbn/o81lhVn8+k8mVa3TmrjLvPBGamOo7Gwt13Exnvkxpw9y+A/5PqOBoLfR6DlWy+rK89/W1A15jnWdEyqRn1Z91QvwZL/RmsQPqzvpL+MqCHmXU3swxgDJBXT6/dGKk/64b6NVjqz2AF0p91ccrmfwHvAj3NrMDMrnP3UuAWYDGwDpjn7muCfu3GSP1ZN9SvwVJ/Bqsu+1MTromIhIhOPxMRCRElfRGREFHSFxEJESV9EZEQUdIXEQkRJX0RkRBR0pdQMrMtZtahtnVEGholfRGREFHSl0bPzBaY2XIzW2NmN1Ra1s3M1pvZs2a2zsxeMLNWMVVuNbMVZvahmZ0UXWeQmb1rZivNbImZ9azXNyRSC0r6Egbfd/cBQC4wwczaV1reE3jU3b8NfA7cHLNsl7v3B34D/Chath44w937AdOAn9dp9CIBUtKXMJhgZh8AfyMyS2GPSsu3uvtfo4+fAYbELJsf/b0c6BZ93BZ4Pnoru4eA3nURtEhdUNKXRs3MziRyg4lT3b0vsBJoWala5QmoYp9/Ff19kK/vP/Ez4A137wNcFKc9kbSlpC+NXVvgn+6+Pzomf0qcOseb2anRx1cC7yTQZtk85tcGEqVIPVHSl8buv4FmMfcR/VucOhuAH0TrHENk/P5IHgDuM7OVpOnd50SqoqmVJdSiN5/+U3SoRqTR056+iEiIaE9fRCREtKcvIhIiSvoiIiGipC8iEiJK+iIiIaKkLyISIkr6IiIh8v8BZfVwkRGyZPwAAAAASUVORK5CYII=)
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)
%% Cell type:markdown id: tags:
Again, it can be seen that the most significant variables are `BMI`, `BP` and `S5`. In this case the coefficients for `AGE`, `S2` and `S4` are zero or close to zero.
%% Cell type:code id: tags:
``` python
rng = np.random.RandomState(1) # make sure the results are repeatable
# cross_validate takes the particular model, in this case lasso regularization
# and undertakes a number of runs according the method specified by cv=
# RepeatedKFold splits the data into n sections and repeat the regression modelling 5 times, giving 25 runs
# return_estimator=True returns the fitting data for each run
scores = cross_validate(Lasso(alpha=2.), nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5), return_estimator=True)
scores = cross_validate(Lasso(alpha=5), nX, Y, cv=RepeatedKFold(n_splits=5, n_repeats=5), return_estimator=True)
# take the results for each simulation (estimator), extract the coefficients for each run
# and add them to a dataframe with columns being the feature names
coefs = pd.DataFrame([est.coef_ for est in scores['estimator']],columns=feature_names)
# plot the descriptive statics of the coefficients in a box and whisker plot to show variability
ax = coefs.plot(kind='box',figsize=(10,7))
plt.title('Lasso regression, alpha = 2.')
plt.title('Lasso regression, alpha = 5.')
plt.axhline(y=0, color='.5')
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
### Multicollinearity
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