I’m going to keep it short this week, been studying a lot lately (you may see more deep learning and explainable AI posts from me in the future). Anyway, let’s dive:
I realized contour plots in my previous post (here) look extremely bad: - There are no labels annotating the contour lines - No colorbar - No fill between contour lines
So, let’s try to make them better. Before we move on, 2 things: 1. If you are not familiar with what contour plots are, Grant Sanderson (3blue1brown) has a great video on Khan Academy that explains what they are: You can watch it here. It allows you to plot 2-D functions (\(f(x, y)\)) 2. I’m going to skip to the plotting, not showing processes up to that point. If you want to follow along, you can find the previous steps here.
data = df_likeli.unstack()
data.iloc[:5, :5].head()| -1.400000 | -1.393636 | -1.387273 | -1.380909 | -1.374545 | |
|---|---|---|---|---|---|
| -1.200000 | 4.812632e-15 | 5.218338e-15 | 5.654017e-15 | 6.121460e-15 | 6.622520e-15 |
| -1.192857 | 5.117237e-15 | 5.550729e-15 | 6.016454e-15 | 6.516356e-15 | 7.052453e-15 |
| -1.185714 | 5.437699e-15 | 5.900567e-15 | 6.398073e-15 | 6.932326e-15 | 7.505517e-15 |
| -1.178571 | 5.774592e-15 | 6.268495e-15 | 6.799591e-15 | 7.370167e-15 | 7.982601e-15 |
| -1.171429 | 6.128495e-15 | 6.655158e-15 | 7.221728e-15 | 7.830684e-15 | 8.484602e-15 |
This was the joint likelihood from the post that I have mentioned above, and here’s the ugly contour plot:
ut.plot_contour(df_likeli.unstack())
ut.decorate(title = 'Likelihood')
Let’s start by being more explicit. I’ll use matplotlib’s contour for plotting. I provide variables (in this case, column values and indices were corresponding to our model’s parameter spaces), data itself in 2D form, number of lines, and a color map.
plt.contour(data.columns, data.index, data, 10, cmap='viridis')
This looks very similar to our ugly version, lots of information get lost in this one. Let’s play with it, starting by using contourf instead of contour which fills the spaces in between.
plt.contourf(data.columns, data.index, data, 6)
Now, this was a step forward. However, we have no idea what those colors correspond to.
plt.contourf(data.columns, data.index, data, 6)
plt.colorbar()
This looks better but is there more room to improve? I don’t like this discreteness between contours, want more of a smooth transition. imshow allows for such transition, but you need to provide extent since the function does not take x and y as inputs. Also, you need to specify the origin because the default origin is top left.
plt.imshow(data, extent=[data.columns.min(), data.columns.max(), data.index.min(), data.index.max()], origin='lower',
cmap='viridis')
plt.colorbar()
This definitely looks better, but one last touch: Adding contour lines with labels (clabel).
contours = plt.contour(data.columns, data.index, data, 6, colors='black')
plt.clabel(contours, inline=True, fontsize=8)
plt.imshow(data, extent=[data.columns.min(), data.columns.max(), data.index.min(), data.index.max()], origin='lower',
cmap='viridis', alpha=1)
plt.colorbar()
That’s a quick guide to make your contour plots better. Hope you enjoyed it. If you did and want more, you may want to take a look at Python Data Science Handbook by Jake VanderPlas. I learned some tricks from it.
Have a nice weekend!