Update app.py

app.py

@@ -0,0 +1,57 @@
+import numpy as np
+import streamlit as st
+import matplotlib.pyplot as plt
+
+st.subheader("Gaussian Process Regression")
+st_col = st.columns(1)[0]
+
+lengthscale = st.slider('Lengthscale', min_value=0.01, max_value=1.0, value=0.25, step=0.01)
+variance = st.slider('Variance', min_value=0.001, max_value=0.1, value=0.025, step=0.001)
+noise_variance = st.slider('Noise Variance', min_value=0.001, max_value=0.01, value=0.0, step=0.001)
+
+def rbf_kernel(x1, x2, lengthscale, variance):
+    x1_ = x1.reshape(-1,1)/lengthscale
+    x2_ = x2.reshape(1,-1)/lengthscale
+    dist_sqr = (x1_ - x2_) ** 2
+    return variance * np.exp(-dist_sqr)
+
+fig, ax = plt.subplots()
+
+x_train = np.array([0.2, 0.5, 0.8]).reshape(-1,1)
+y_train = np.array([0.8, 0.3, 0.6]).reshape(-1,1)
+
+ax.scatter(x_train, y_train, label='train points')
+ax.set_xlim(-0.2,1.2)
+ax.set_ylim(-0.2,1.2)
+
+N = 100
+x_test = np.linspace(-0.2,1.2,N).reshape(-1,1)
+
+k_train_train = rbf_kernel(x_train, x_train, lengthscale, variance)
+k_test_train = rbf_kernel(x_test, x_train, lengthscale, variance)
+k_test_test = rbf_kernel(x_test, x_test, lengthscale, variance)
+
+c = np.linalg.inv(np.linalg.cholesky(k_train_train + noise_variance * np.eye(3)))
+k_inv = np.dot(c.T,c)
+
+pred_mean = k_test_train@k_inv@y_train
+pred_var = k_test_test - k_test_train@k_inv@k_test_train.T
+pred_std2 = 2 * (pred_var.diagonal() ** 0.5)
+
+ax.plot(x_test, pred_mean, label='predictive mean')
+ax.fill_between(x_test.ravel(), pred_mean.ravel()-pred_std2.ravel(), 
+                pred_mean.ravel()+pred_std2.ravel(), alpha=0.5, label='95% confidence')
+ax.set_xlabel('x')
+ax.set_ylabel('y')
+ax.legend()
+
+with st_col:
+    st.pyplot(fig)
+    
+hide_streamlit_style = """
+            <style>
+            #MainMenu {visibility: hidden;}
+            footer {visibility: hidden;}
+            </style>
+            """
+st.markdown(hide_streamlit_style, unsafe_allow_html=True)