Include header describing the space

app.py

@@ -48,20 +48,26 @@ def get_plots(min_alpha, max_alpha):
     plotted_alphas_text = (
         f"**Plotted alphas between 10^({min_alpha}) and 10^({max_alpha})**"
     )
-    return fig, plotted_alphas_text
+    return fig
 
 
 with gr.Blocks() as demo:
-    with gr.Row():
-        with gr.Column(scale=2):
-            gr.Markdown(
-                "Choose the range of alpha values to plot."
-                + " The models you input for alpha are for the exponents of 10,"
-                + " so a value of -6 means 10^6."
-            )
+    gr.Markdown(
+        """
+        # Ridge coefficients as a function of the L2 regularization
+
+        This space shows the effect of different alpha values in the coefficients learned by [Ridge regression](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html).
+
+        The left plot shows how, as alpha tends to zero, the coefficients tend to the true coefficients. For large alpha values—i.e., strong regularization—the coefficients get smaller and eventually converge to zero.
 
-            plotted_alphas = gr.Markdown()
+        The right plot shows the mean squared error between the coefficients found by the model and the true coefficients. Less regularized models retrieve the exact coefficients—i.e., the error equals 0—while stronger regularised models increase the error.
 
+        We generate the dataset using sklearn's [make_regression](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_regression.html) function to ensure we know all the coefficients' true values.
+
+        This space is based on [sklearn’s original demo](https://scikit-learn.org/stable/auto_examples/linear_model/plot_ridge_coeffs.html#sphx-glr-auto-examples-linear-model-plot-ridge-coeffs-py).
+        """
+    )
+    with gr.Row():
         with gr.Column(scale=3):
             with gr.Row():
                 min_alpha = gr.Number(
@@ -80,20 +86,20 @@ with gr.Blocks() as demo:
     min_alpha.change(
         get_plots,
         [min_alpha, max_alpha],
-        [plots, plotted_alphas],
+        plots,
         queue=False,
     )
     max_alpha.change(
         get_plots,
         [min_alpha, max_alpha],
-        [plots, plotted_alphas],
+        plots,
         queue=False,
     )
 
     demo.load(
         get_plots,
         [min_alpha, max_alpha],
-        [plots, plotted_alphas],
+        plots,
         queue=False,
     )