# AI News, Machine Learning forDiabetes ## Machine Learning forDiabetes

import pandas as pd import numpy as np import matplotlib.pyplot as plt %matplotlib inline diabetes = pd.read_csv('diabetes.csv') print(diabetes.columns) Index([‘Pregnancies’, ‘Glucose’, ‘BloodPressure’, ‘SkinThickness’, ‘Insulin’, ‘BMI’, ‘DiabetesPedigreeFunction’, ‘Age’, ‘Outcome’], dtype=’object’) diabetes.head() Figure 1 The diabetes data set consists of 768 data points, with 9 features each: print('dimension of diabetes data: {}'.format(diabetes.shape)) dimension of diabetes data: (768, 9) “Outcome” is the feature we are going to predict, 0 means No diabetes, 1 means diabetes.

To make a prediction for a new data point, the algorithm finds the closest data points in the training data set — its “nearest neighbors.” First, Let’s investigate whether we can confirm the connection between model complexity and accuracy: from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(diabetes.loc[:, diabetes.columns != 'Outcome'], diabetes['Outcome'], stratify=diabetes['Outcome'], random_state=66) from sklearn.neighbors import KNeighborsClassifier training_accuracy = [] test_accuracy = [] #

test_accuracy.append(knn.score(X_test, y_test)) plt.plot(neighbors_settings, training_accuracy, label='training accuracy') plt.plot(neighbors_settings, test_accuracy, label='test accuracy') plt.ylabel('Accuracy') plt.xlabel('n_neighbors') plt.legend() plt.savefig('knn_compare_model') Figure 5 The above plot shows the training and test set accuracy on the y-axis against the setting of n_neighbors on the x-axis.

from sklearn.linear_model import LogisticRegression logreg = LogisticRegression().fit(X_train, y_train) print('Training set score: {:.3f}'.format(logreg.score(X_train, y_train))) print('Test set score: {:.3f}'.format(logreg.score(X_test, y_test))) Training set accuracy: 0.781 Test set accuracy: 0.771 The default value of C=1 provides with 78% accuracy on the training and 77% accuracy on the test set.

logreg100 = LogisticRegression(C=100).fit(X_train, y_train) print('Training set accuracy: {:.3f}'.format(logreg100.score(X_train, y_train))) print('Test set accuracy: {:.3f}'.format(logreg100.score(X_test, y_test))) Training set accuracy: 0.785 Test set accuracy: 0.766 Using C=100 results in a little bit higher accuracy on the training set and little bit lower accuracy on the test set, confirming that less regularization and a more complex model may not generalize better than default setting.

diabetes_features = [x for i,x in enumerate(diabetes.columns) if i!=8] plt.figure(figsize=(8,6)) plt.plot(logreg.coef_.T, 'o', label='C=1') plt.plot(logreg100.coef_.T, '^', label='C=100') plt.plot(logreg001.coef_.T, 'v', label='C=0.001') plt.xticks(range(diabetes.shape), diabetes_features, rotation=90) plt.hlines(0, 0, diabetes.shape) plt.ylim(-5, 5) plt.xlabel('Feature') plt.ylabel('Coefficient magnitude') plt.legend() plt.savefig('log_coef') Figure 6 Decision Tree from sklearn.tree import DecisionTreeClassifier tree = DecisionTreeClassifier(random_state=0) tree.fit(X_train, y_train) print('Accuracy on training set: {:.3f}'.format(tree.score(X_train, y_train))) print('Accuracy on test set: {:.3f}'.format(tree.score(X_test, y_test))) Accuracy on training set: 1.000 Accuracy on test set: 0.714 The accuracy on the training set is 100%, while the test set accuracy is much worse.

Random Forest Let’s apply a random forest consisting of 100 trees on the diabetes data set: from sklearn.ensemble import RandomForestClassifier rf = RandomForestClassifier(n_estimators=100, random_state=0) rf.fit(X_train, y_train) print('Accuracy on training set: {:.3f}'.format(rf.score(X_train, y_train))) print('Accuracy on test set: {:.3f}'.format(rf.score(X_test, y_test))) Accuracy on training set: 1.000 Accuracy on test set: 0.786 The random forest gives us an accuracy of 78.6%, better than the logistic regression model or a single decision tree, without tuning any parameters.

To reduce overfitting, we could either apply stronger pre-pruning by limiting the maximum depth or lower the learning rate: gb1 = GradientBoostingClassifier(random_state=0, max_depth=1) gb1.fit(X_train, y_train) print('Accuracy on training set: {:.3f}'.format(gb1.score(X_train, y_train))) print('Accuracy on test set: {:.3f}'.format(gb1.score(X_test, y_test))) Accuracy on training set: 0.804 Accuracy on test set: 0.781 gb2 = GradientBoostingClassifier(random_state=0, learning_rate=0.01) gb2.fit(X_train, y_train) print('Accuracy on training set: {:.3f}'.format(gb2.score(X_train, y_train))) print('Accuracy on test set: {:.3f}'.format(gb2.score(X_test, y_test))) Accuracy on training set: 0.802 Accuracy on test set: 0.776 Both methods of decreasing the model complexity reduced the training set accuracy, as expected.

Support Vector Machine from sklearn.svm import SVC svc = SVC() svc.fit(X_train, y_train) print('Accuracy on training set: {:.2f}'.format(svc.score(X_train, y_train))) print('Accuracy on test set: {:.2f}'.format(svc.score(X_test, y_test))) Accuracy on training set: 1.00 Accuracy on test set: 0.65 The model overfits quite substantially, with a perfect score on the training set and only 65% accuracy on the test set.

We will need to re-scale our data that all the features are approximately on the same scale: from sklearn.preprocessing import MinMaxScaler scaler = MinMaxScaler() X_train_scaled = scaler.fit_transform(X_train) X_test_scaled = scaler.fit_transform(X_test) svc = SVC() svc.fit(X_train_scaled, y_train) print('Accuracy on training set: {:.2f}'.format(svc.score(X_train_scaled, y_train))) print('Accuracy on test set: {:.2f}'.format(svc.score(X_test_scaled, y_test))) Accuracy on training set: 0.77 Accuracy on test set: 0.77 Scaling the data made a huge difference!

## accuracy

Accuracy Measures For A Forecast Model Returns range of summary measures of the forecast accuracy.

If x is not provided, the function only produces training set accuracy measures of the forecasts based on f['x']-fitted(f).

S3 method for default accuracy(f, x, test = NULL, d = NULL, D = NULL, ...) Arguments f

It will also work with Arima, ets and lm objects if x is omitted -- in which case training set accuracy measures are returned.

An optional numerical vector containing actual values of the same length as object, or a time series overlapping with the times of f.

By default, the MASE calculation is scaled using MAE of training set naive forecasts for non-seasonal time series, training set seasonal naive forecasts for seasonal time series and training set mean forecasts for non-time series data.

} Documentation reproduced from package forecast, version 8.1, License: GPL (>= 3) Community examples Looks like there are no examples yet.

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