Multivariate Regression(WIP):
When it comes to multivariate we will resort to sklearns Polyfeatures() along with Pipeline(). This will facilitate for a more readable code.
The steps are very similar to the previous example. The only difference is that we will create function of [x,y] and evaluate it in order to create some dummy data. Then the data is fed through a pipeline that generate the polynomial features and get the score for the k-folds.
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| import numpy as np | |
| from sklearn.linear_model import LinearRegression | |
| import matplotlib.pyplot as plt | |
| from sklearn.model_selection import train_test_split | |
| from sklearn.model_selection import KFold | |
| from sklearn.pipeline import Pipeline | |
| def gaussian_noise(mu,sigma,n): | |
| return np.random.normal(mu,sigma,n) | |
| from sklearn.preprocessing import PolynomialFeatures | |
| degree=8 | |
| mean=0 | |
| sigma=.2 | |
| n=30 | |
| x = np.linspace(–2,2,n) | |
| y = np.linspace(–2,2,n) | |
| X, Y = np.meshgrid(x, y) # create a meshgrid to evaluate z(x,y) | |
| Z=Y**2 – X**2 # evaluate z | |
| # reshape for sklearn and add noise | |
| Z=Z.reshape(1,–1).T+np.array([gaussian_noise(mean,sigma,n**2)]).T | |
| X=X.reshape(1,–1).T | |
| Y=Y.reshape(1,–1).T | |
| # input features shape [2,n**2] n= len(x) or len(y) | |
| data=np.concatenate([X,Y],axis=1) | |
| # split to test train sets | |
| _x,x_test,_y,y_test = train_test_split(data, Z,\ | |
| test_size=0.30, | |
| random_state=1337) | |
| # create expression for pipline | |
| estimators=lambda x:[('PolyFeatures',PolynomialFeatures(degree=x)),\ | |
| ('clf',LinearRegression())] | |
| # create a pipeline for every order of poly. | |
| models=[Pipeline(estimators(m)) for m in range(degree)] | |
| # create a generator for 10 folds | |
| kf=KFold(10) | |
| valid_error=[] # variable to store the valid error | |
| train_error=[] # variable to store the train error | |
| for m in models: | |
| # function: fit and get r2 score of model. | |
| f=lambda t,v:m.fit(_x[t],_y[t]).\ | |
| score(_x[v],_y[v]) | |
| # validation scores for each fold | |
| v_score=[f(train,valid) for valid,train in kf.split(_x)] | |
| # training score for each fold | |
| t_score=[f(train,train) for _,train in kf.split(_x)] | |
| # average valid and test error for all folds | |
| valid_error.append(1–sum(v_score)/len(v_score)) | |
| train_error.append(1–sum(t_score)/len(t_score)) | |
| k=np.argmin(valid_error) | |
| # fit model to training and validation data | |
| models[k].fit(_x[:,0:k+1],_y) | |
| # score model against testing data | |
| k_score=models[k].score(x_test[:,0:k+1],y_test) | |
| print('Optimum polynomial order = {0}\n\ | |
| testing score = {1:.2f}'.format(k,k_score)) | |
| #plotting | |
| fig = plt.figure() | |
| ax = fig.gca(projection='3d') | |
| ax.scatter3D(X, Y, Z,linewidth=0, antialiased=True,marker='.',\ | |
| color='blue',label='original data') | |
| X_p, Y_p = np.meshgrid(x, y) | |
| Z_p=models[k].predict(data).reshape(n,n) | |
| from matplotlib import cm | |
| ax.plot_surface(X_p,Y_p,Z_p,cmap=cm.coolwarm,linewidth=0,\ | |
| antialiased=True,label='Predicted Surface') | |
| fig2,ax2=plt.subplots() | |
| ax2.set_xlabel('Polynomial Order'),ax2.set_ylabel('Error') | |
| ax2.plot(train_error,label='Train Error') | |
| ax2.plot(valid_error,label='Valid Error') | |
| ax2.grid(),ax2.legend() |
As you can see the order of the polynomial is (2) as it was set in the code before adding gaussian noise. this concludes this series about polynomial regression.
Github repository :
https://github.com/b00033811/ml-uae
ML-UAE 