code: def example1():
      m, k = 500, 4
      upper = 6
      scale = 10
      xs1a = np.linspace(1, upper, m)[:, np.newaxis]
      xs1 = xs1a * np.ones((1, 4)) + 1 / (
          1.0 + np.exp(np.random.randn(m, k))
      )
      xs1 /= np.std(
          xs1[::k, :], 0
      )  # normalize scale, could use cov to normalize
      y1true = np.sum(np.sin(xs1) + np.sqrt(xs1), 1)[:, np.newaxis]
      y1 = y1true + 0.250 * np.random.randn(m, 1)
  
      stride = 2  # use only some points as trainig points e.g 2 means every 2nd
      gp1 = GaussProcess(
          xs1[::stride, :],
          y1[::stride, :],
          kernel=kernel_euclid,
          ridgecoeff=1e-10,
      )
      yhatr1 = gp1.predict(xs1)
      plt.figure()
      plt.plot(y1true, y1, "bo", y1true, yhatr1, "r.")
      plt.title("euclid kernel: true y versus noisy y and estimated y")
      plt.figure()
      plt.plot(y1, "bo-", y1true, "go-", yhatr1, "r.-")
      plt.title(
          "euclid kernel: true (green), noisy (blue) and estimated (red) "
          + "observations"
      )
  
      gp2 = GaussProcess(
          xs1[::stride, :],
          y1[::stride, :],
          kernel=kernel_rbf,
          scale=scale,
          ridgecoeff=1e-1,
      )
      yhatr2 = gp2.predict(xs1)
      plt.figure()
      plt.plot(y1true, y1, "bo", y1true, yhatr2, "r.")
      plt.title(
          "rbf kernel: true versus noisy (blue) and estimated (red) observations"
      )
      plt.figure()
      plt.plot(y1, "bo-", y1true, "go-", yhatr2, "r.-")
      plt.title(
          "rbf kernel: true (green), noisy (blue) and estimated (red) "
          + "observations"
      )
  
file_path: statsmodels/statsmodels/sandbox/regression/kernridgeregress_class.py
imports: import numpy
  from scipy import spatial
  import matplotlib.pylab
label_desc: Use image node_id 3 for calling a global function with example usage: example1() without return types