Unverified Commit cfbda0e9 authored by Simon Bowly's avatar Simon Bowly
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update regularisation

parent 3e49c1fb
%% Cell type:markdown id: tags:
# Regularization in Linear Regression
# Regularisation in Linear Regression
In this lesson we will investigate the effect of various features on the tendency of patients to develop diabetes, using the `sklearn` methods `LinearRegression` and `Ridge` and `Lasso` regularization. We will look at how coefficients can vary signficantly due to overfitting, and how that can be alleviated using regularization.
In this notebook we will explore the technique of **regularisation** in linear regression models. We have seen how coefficients can vary signficantly due to overfitting; regularisation is a method which can alleviate this problem.
First import the Diabetes dataset. The same dataset can be imported from the `sklearn` example datasets, but is already normalized. We will use the unnormalized dataset initially, to show why data needs to be normalised before modelling.
We will use the Diabetes dataset to explore these methods, as we did in the [multi-linear regression notebook](https://gitlab.erc.monash.edu.au/bads/data-challenges-resources/-/blob/main/Machine-Learning/Supervised-Methods/Regression/Multivariate-Linear-Regression.ipynb). Please review the content there first.
%% Cell type:code id: tags:
``` python
import pandas as pd
......@@ -18,13 +18,13 @@
import seaborn as sns
```
%% Cell type:markdown id: tags:
## Recall
## Recall: Multivariate Linear Regression
Read data, check correlations, construct normalised regression model, as we did in the [multi-linear regression notebook](https://gitlab.erc.monash.edu.au/bads/data-challenges-resources/-/blob/main/Machine-Learning/Supervised-Methods/Regression/Multivariate-Linear-Regression.ipynb).
Following on from previous work on multilinear regression, here we read in the data, check correlations, construct normalised features, and fit a regression model.
%% Cell type:code id: tags:
``` python
df = pd.read_csv('Diabetes_Data.csv') # read the Diabetes dataset in to a pandas dataframe
......@@ -71,34 +71,11 @@
print("Testing score is",rsquared_linear)
```
%% Cell type:markdown id: tags:
Again we can plot the linear regression coefficients, but this time we compare them against our original linear regression coefficients to investigate the variability. It can now be seen that the effect of the blood serum measurements can have considerable variability.
%% Cell type:code id: tags:
``` python
# create a new dataframe with the regression coefficients from the normalised data
ncoefs = pd.DataFrame(linear.coef_.transpose(),columns=['Normalised'],index=feature_names)
# add our original coefficient importance to this dataframe
# ncoefs = pd.concat([ncoefs,coefs],axis=1)
# ncoefs.columns =['Normalised','Original'] # change the column names to show the new and original coefficients
# do a similar horizontal plot as before
ax = ncoefs.plot(kind='bar',figsize=(10,7))
plt.title('Linear Regression')
plt.axhline(y=0, color='.5')
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
%% Cell type:markdown id: tags:
To investigate the variability we can use the `sklearn` methods `cross_validate` and `RepeatedKFold`. The first of these performs a number of runs of a model. The second splits the data in n sections and repeats the calculations m times. This gives n.m runs to investigate the variability of the coefficients. The variability of these can then be plotted using a boxplot.
With this initial model fitted, we investigate coefficient variability using the `sklearn` methods `cross_validate` and `RepeatedKFold`. The first of these performs a number of runs of a model. The second splits the data in n sections and repeats the calculations m times. This gives n.m runs to investigate the variability of the coefficients. The variability of these can then be plotted using a boxplot.
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:
......@@ -121,19 +98,26 @@
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
### Regularization
## Regularization
We now investigate regularization techniques for Linear Regression, to reduce the variance of the model. How does this work?
* Adds a penalty term to the cost function, which penalises large coefficient values for all features (todo add math model).
* Hence, if the model fitting algorithm can reduce the model coefficient sizes while achieving similar error rates, it will. This results in a more stable model.
* It's important to regularise coefficients so that this effect is uniform across all coefficients.
* There are two main types: Ridge and Lasso.
* To achieve a good result, we need to experiment with the model parameter *alpha* which controls the balance between the error measure and the penalty term in the cost function.
We now investigate regularization techniques for Linear Regression, to reduce the variance of the model.
#### Ridge regularization
### Ridge regularization
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:
......@@ -163,11 +147,11 @@
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`.
......@@ -190,15 +174,15 @@
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
#### Lasso regularization
### 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 is alpha approximately 2.
%% Cell type:code id: tags:
......@@ -226,11 +210,11 @@
plt.legend(loc='best');
```
%%%% Output: display_data
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)
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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.
......@@ -253,11 +237,11 @@
plt.subplots_adjust(left=.3)
```
%%%% Output: display_data
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)
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ghSepHc3VYYV/HkiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGRm0kiRlZNBKkpTRXt0uQOq0wYkNbc2/efVLM1UiSQatdkONgnNwYoOBKqkrbDqWJCkjg1aSpIwMWkmSMjJoJUnKyKCVJCkjg1aSpIw8vUd97eizLmLrtpmW5m31/NplSwa4/Izj51OWJD3AoFVf27ptpuPnx7bb4YUkzcWmY0mSMjJoJUnKyKCVJCkjg1aSpIwMWkmSMjJoJUnKyNN71Nf2GZrgqHUTHV4mgJfUk9QZBq362p211Z5HK6mn2XQsSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkR1WqO91uoOJZUsGOro8SXs2g1Z9rdVeoQYnNnS8BylJaoVNx5IkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGHQnaiFgbETdHxBV14/aPiG9GxK/Kv4/oxLokSeonndqiPRc4Yda4CeBfU0pPAP61vC9J0h6lI0GbUvoucNus0ScC68rb64CTOrEuSZL6Sc59tI9OKd1Y3r4JeHSjmSJiZURsiohNW7ZsyViOJEkLb0EOhkopJSA1mbYmpbQ8pbT8wAMPXIhyJElaMDmD9vcRcRBA+ffmjOuSJKkn7ZVx2V8GTgNWl3+/lHFd0gMGJza0NX7z6pfmLEfSHq4jQRsRU8BxwAERcT1wBkXAnh8R48C1wH/sxLqknTE4JfWSjgRtSmmsyaTnd2L5kiT1K3uGkiQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSM9up2AZIk5TA4saGt+TevfmmWOgxaSdJuqVlwDk5syBaqjdh0LElSRgatJEkZGbSSJGVk0EqSlJFBK0lSRgatJEkZGbSSJGVk0EqSlJFBK0lSRgatJEkZGbSSJGVkX8eSpL539FkXsXXbTMvzt3LBgWVLBrj8jOPnUxZg0EqSdgNbt810/EIB7V79pxmbjiVJysiglSQpI4NWkqSMDFpJkjLyYChJUt/bZ2iCo9ZNdHiZAPM/wMqglST1vTtrqz3qWJKkPZFBK0lSRgatJEkZGbSSJGVk0EqSlJFHHUuSdgudOkp4u2VLBjqyHINWktT32jm1Z3BiQ8dPBZqLTceSJGWUPWgj4oSI+EVEXBMRne22Q5KkHpc1aCNiEfBR4MXAkcBYRByZc52SJPWS3PtonwFck1L6NUBEnAecCFzVaOZbb72Vc889N3NJkqQ92QmLb+Xcc7cs2PpyB+0hwHV1968Hnlk/Q0SsBFYCHHLIIS0v+P3x/g6U19hb01uzLVuq98Nf39rW/M96/CMzVbIjP195+LwurLk+X42m5fp8RUopy4IBIuJk4ISU0uvL+68FnplSelOj+ZcvX542bdqUrR6pXyz0UZGS5iciLk0pLW80LffBUL8DDqu7f2g5TpKkPULupuMfA0+IiMdRBOyrgRWZ1yn1pKPPuoit22Zanr+Vk++XLRng8jOOn09Zu2xqaopqtUqtVmNoaIhKpcLY2FhXapF6WdagTSn9KSLeBHwDWASsTSldmXOdUq/aum2mZ6+X2a6pqSkqlQqTk5OMjIwwPT3N+Pg4gGErzZL9PNqU0ldTSk9MKR2eUqrmXp+k/KrVKitWrGDVqlU89KEPZdWqVaxYsYJq1Y+4NJtdMEpq21VXXcXdd9/N2rVrH9iiPf3007n22mu7XZrUc+yCUVLbFi9ezKpVqxgdHWVgYIDR0VFWrVrF4sWLu12a1HMMWkltu++++zjnnHPYuHEjMzMzbNy4kXPOOYf77ruv26VJPcemY0ltO/LIIznppJNYtWrVA0cdr1ixggsuuKDbpUk9x6CV1LZKpcKb3/xmli5dSkqJu+++mzVr1vDhD3+426VJPcemY0nzEhHdLkHqaQatpLZVq1VWrlzJ0qVLAVi6dCkrV6709B6pAZuOJbXtqquu4p577nlQhxWbN2/udmlSzzFoJbVt8eLFHHvssTscDHXsscdyww03dLs0qefYdCypbffeey/r16/n9NNP58477+T0009n/fr13Hvvvd0uTeo5Bq2ktu29996ccsoprF27ln322Ye1a9dyyimnsPfee3e7NKnn2HQsLZB9hiY4at1Eh5cJsPDXrb3vvvu4+OKLH9QFox1WSA9m0EoL5M7a6t3m6j2NOqw49dRT7bBCasCmY0ltq1QqfPazn+Xss8/mj3/8I2effTaf/exnqVQq3S5N6jlu0Upq2/ZrztZv0VarVa9FKzVg0EraJWNjYwar1AKbjiVJysiglSQpI4NWkqSMDFpJu2Rqaorh4WEWLVrE8PAwU1NT3S5J6kkeDCWpbVNTU1QqlQddVADwAClpFrdoJbWtWq0yOTnJ6OgoAwMDjI6OMjk56WXypAYMWkltq9VqjIyM7DBuZGSEWq3WpYqk3mXTsbSAOt1l4rIlAx1dXquGhoaYnp5mdHT0gXHT09MMDQ11pR6plxm00gJpp5/jwYkNHe8XuZMqlQrj4+MP2kdr07H0YAatpLbZBaPUOoNW0i6xC0apNR4MJUlSRgatJEkZGbSSJGXkPtouaudUj14+AlWS1JxB20WNwrPXT+uQJLXHpmNJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSM7LBC6qK5egdrNM3OTKT+Y9BKXWRwSrs/m44lScrIoJUkKSODVpKkjNxHK2m35GUo1SsMWkm7JS9DqV5h0C6Ao8+6iK3bZlqev9Vf4suWDHD5GcfvalmSpAVg0C6ArdtmsvyKbqdpTJLUHR4MJUlSRgatJEkZGbSSJGVk0EqSlJFBK0lSRgatJEkZGbSSJGVk0EqSlJEdViyAfYYmOGrdRIblAtidnCT1MoN2AdxZW23PUJK0hzJoF0iOUFy2ZKDjy5QkdZZBuwDa2Zr16iKStHvxYChJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysjTeyT1taPPuoit22Zanr/Vc9qXLRng8jOO39WypAcYtJL62tZtM/a8pp5m07EkSRkZtJIkZTSvoI2IV0XElRFxf0QsnzXtXRFxTUT8IiJeNL8yJUnqT/PdR3sF8ArgE/UjI+JI4NXAU4CDgW9FxBNTSn+e5/p2K832ATUab//HktSf5hW0KaUaQETMnnQicF5K6V7gNxFxDfAM4AfzWd/uxvCUpN1frn20hwDX1d2/vhz3IBGxMiI2RcSmLVu2ZCpHkqTu2OkWbUR8C3hMg0mVlNKX5ltASmkNsAZg+fLlab7Lk7Rn2WdogqPWTWRYLoCtTpq/nQZtSukFu7Dc3wGH1d0/tBwnSR11Z22159Gqp+VqOv4y8OqI2DsiHgc8AfhRpnVJktSz5nt6z99ExPXAs4ENEfENgJTSlcD5wFXA14H/4hHHkqQ90XyPOv4i8MUm06pAdT7LlySp39kzlCRJGRm0kiRlZNBKkpSRQStJUkYGrSRJGXnhd0l9L0fnEsuWDHR8mdozGbSS+lo7vUINTmzwYh5acDYdS5KUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGBq0kSRkZtJIkZWTQSpKUkUErSVJGe3W7AEnKYXBiQ8vjN69+ae5ytAczaCXtlgxP9QqbjiVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMDFpJkjIyaCVJysiglSQpI4NWkqSMIqXU7RoeEBFbgGszLPoA4JYMy83BWvPop1qhv+q11jysNZ8c9T42pXRgowk9FbS5RMSmlNLybtfRCmvNo59qhf6q11rzsNZ8Frpem44lScrIoJUkKaM9JWjXdLuANlhrHv1UK/RXvdaah7Xms6D17hH7aCVJ6pY9ZYtWkqSuMGglScpotwjaiDgpIlJEPLlu3DMi4jsR8auI+ElEbIiIo8ppZ0bE7yLisrphvwWqtRIRV0bEz8r1PrOs8xd1tXyunPcjEfEPsx770YWos1zfn8t6Li+fw2PL8YPl8/2eunkPiIiZiDinvH9mRLxtoWpto+5t5bSrIuLjEdH1z0CT98SbIuKa8nk+oNs1btek1s+U798rImJtRAx0u05oWutk+b74WUR8LiIe3u06t2tUb920j0TEXd2sr16T5/bciPhN3ffYMd2uE5rWGhFRjYhfRkQtIv5r1iJSSn0/AOuB7wFnlfcfDWwGjq2bZwQ4qbx9JvC2LtT5bOAHwN7l/QOAg4HvAMsbzL8v8Gvg8eXwG2C/Baz3rrrbLwL+rbw9WNb107rpbwQuA87p5nPcQt1XlLf3Ar4LvKIbNbbwnnhqWe9m4IBu1thCrS8BohymgDf2cK371s3zAWCi27XOVW95eznwqfr3dS/WCpwLnNzt+lqs9W+BTwIPKcc/Kmcde9Hnyl+kI8Ao8BXgDOBNwLqU0ve3z5dSmu5OhTs4CLglpXQvQErpFoCIaDhzSukPEVEBzilH/UNK6Y4FqLORfYHb6+7fA9QiYnlKaRNwCnA+xZu4l8yuG4CU0p8i4vvAEQtf0g4avieAG6D5e6NL5qwVICJ+BBzahdpma1YrAFE8sUuAXjkatNl3wyLgfcAK4G+6V94O2voe67Jmtb4RWJFSur8cf3POIrrebNYBJwJfTyn9Erg1Ip4GPAX4yU4e95a6Jo6N2assXAQcVjZXfCwinls37TN19bxv+8iU0hTwCIpf4p9aoDq3W1LWczXwL8A/zZp+HvDqiDgM+DN1X7hdtrO6iYiHAc8Hfr7Qxc0y13ui18xZa9lk/Frg612pbkdNa42I/wPcBDwZOLtbBc7SrN43AV9OKd3Yxdpmm+t9UC2baD8YEXt3q8A6zWo9HDglIjZFxNci4gk5i9gdgnaM4guf8u/Y7Bki4pKyHf7DdaM/mFI6phxGF6LQlNJdwNOAlcAWYH1EvK6cfGpdPW+vq/1Qil9lB3dhf9K2sp4nAycAn4wdf7Z+HXgh8GqK5vteMVfdh0fEZcDFwIaU0te6VSTs9D3RU1qo9WPAd1NK3+tCeTuYq9aU0t9StLzUKFpiuq5Jve8GXkXv/BgA5nxu30Xx4+XpwP7AO7tV43Zz1Lo38MdUdMP4z8Da3IX07UDxYt5DcSGCzcB1wG8ptmDOmjXvycC55e0z6dL+wwY1fYUm+2jLeT4PnAasBt63wPXdNev+74FHseO+zrUUWwf7A6+jx/bRNqu7V4ft74m6+5vpkX20c9VKscvmAsp9Xr02zH5ey3F/BVzY7drmqHem/GxtLof7gWu6XVuLz+1xvfjc1n3nXg08rhwXwNac6+33LdqTgU+llB6bUhpMKR1GccDQN4HXRXm0aelhXamwTkQ8aVYTxTHMcbWiiHgxRUB8kuLHwysi4sisRTav5cnAIuDWWZPeD7wzpXTbwle1c3PU3RPafU90U7NaI+L1FAedjaVyn1e3Nan1txFxRDk9gL+m+MLtuib1fiKl9Jjyu20QuCel1O1jCuZ6HxxUTg/gJOCKha9uR3N8vi6gOK4H4LnAL3PW0e8HQ40B75017vPl+FOA90bEIcDNFJdE+se6+d4SEa+pu39SSmlzxloBHg6cHcWpRH8CrqFo0vgcxT7abeV8twAvAz5EcRRfAu6OiLdTHBj1vMx1brekbGaF4lffaSmlP9e3HqeUrgSuXKB6WrXTuntIw/dEebrBO4DHAD+LiK+mlF7fvTKB5u/fmyi+vH5QPsdfSCn9Y7OFLJBGtb4B+GJE7Evxvric4mj5XtDsue1FzWo9PyIOpHhuL6N4vrutWa1/ovjOfQtwF5D1s2UXjJIkZdTvTceSJPU0g1aSpIwMWkmSMjJoJUnKyKCVJCkjg1aSpIwMWkmSMvr/vVfviIkvXpYAAAAASUVORK5CYII=)
%% Cell type:markdown id: tags:
### Multicollinearity
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