Update app.py

app.py

@@ -10,7 +10,7 @@ st.markdown(r"""
            Squared Exponential Kernel is formulated as $K(x, x') = \sigma_f^2 \exp \left[\frac{-(x - x')^2}{\ell^2}\right]$ where, $\ell$ is lengthscale and $\sigma_f^2$ is variance.
            $$
            \text{Prior: } \mathbf{f} \sim \mathcal{N}(\boldsymbol{0}, K) \\
-           \text{Likelihood: } \mathbf{y} \sim \mathcal{N}(\mathbf{f}, \sigma_n^2)
+           \text{Likelihood: } \mathbf{y} \sim \mathcal{N}(\mathbf{f}, \sigma_n^2I)
            $$
            where $\sigma_n^2$ is known as noise variance or likelihood noise.
     """)
@@ -69,4 +69,10 @@ hide_streamlit_style = """
             subheader {alignment: center;}
             </style>
             """
-st.markdown(hide_streamlit_style, unsafe_allow_html=True) 
+st.markdown(hide_streamlit_style, unsafe_allow_html=True)
+st.markdown(r"""
+           Here are some observations to note while experimenting with the hyperparameters:
+           * Lengthscale ($\ell$) controls the smoothness of the fit. Smoothness in fit increases with an increase in $\ell$.
+           * Variance controls the uncertainty in smooth (in other words, smoothness in the vertical direction [[Slide 154](http://cbl.eng.cam.ac.uk/pub/Public/Turner/News/imperial-gp-tutorial.pdf)]).
+           * Noise variance is a measure of observation noise or irreducible noise present in the dataset. Increasing noise variance to a certain limit reduces overfitting.
+           """)