Create 10.py

Implement the non-parametric Locally Weighted Regression algorithm in order to fit data points. Select appropriate data set for your experiment and draw graphs

Author: fatalcoder524

10.py

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+import numpy as np
+from bokeh.plotting import figure, show, output_notebook
+from bokeh.layouts import gridplot
+from bokeh.io import push_notebook
+
+def local_regression(x0, X, Y, tau):
+ x0 = np.r_[1, x0] # Add one to avoid the loss in information
+ X = np.c_[np.ones(len(X)), X]
+ xw = X.T * radial_kernel(x0, X, tau)
+ beta = np.linalg.pinv(xw @ X) @ xw @ Y 
+ return x0 @ beta 
+ 
+def radial_kernel(x0, X, tau):
+ return np.exp(np.sum((X - x0) ** 2, axis=1) / (-2 * tau * tau))
+
+n = 1000
+X = np.linspace(-3, 3, num=n)
+print("The Data Set ( 10 Samples) X :\n",X[1:10])
+Y = np.log(np.abs(X ** 2 - 1) + .5)
+print("The Fitting Curve Data Set (10 Samples) Y :\n",Y[1:10])
+X += np.random.normal(scale=.1, size=n)
+print("Normalised (10 Samples) X :\n",X[1:10])
+
+domain = np.linspace(-3, 3, num=300)
+print(" Xo Domain Space(10 Samples) :\n",domain[1:10])
+def plot_lwr(tau):
+ prediction = [local_regression(x0, X, Y, tau) for x0 in domain]
+ plot = figure(plot_width=400, plot_height=400)
+ plot.title.text='tau=%g' % tau
+ plot.scatter(X, Y, alpha=.3)
+ plot.line(domain, prediction, line_width=2, color='red')
+ return plot
+
+show(gridplot([
+ [plot_lwr(10.), plot_lwr(1.)],
+ [plot_lwr(0.1), plot_lwr(0.01)]]))